Power source

Abstract

A power source (100) comprises an ignition region (108) comprising a target material arranged to receive a flux of protons and generate neutrons in response thereto. A reactor core containing a sub- critical quantity of actinide material (104) is arranged as a structure having at least one layer around the ignition region (108). The actinide material comprises at least Thorium or Uranium and generates insufficient neutrons by spontaneous fission in the absence of the flux of protons to the ignition region to maintain a critical or super-critical reaction. The power source further comprises an accelerator (112) arranged to supply a flux of protons having an energy of between 4MeV and 200MeV to the target material in the ignition region (108) and a control arrangement to control the power of the proton flux to modulate reactor core power.

Description

[0001] POWER SOURCE The present invention relates to a power source. Increasing moves towards green energy and volatility in energy markets have intensified a need for power sources that do not rely on fossil fuels or intermittent environmental factors such as sunshine and wind. Thermal nuclear reactors are well positioned to meet these needs but traditionally require enormous investment, large amounts of land and long construction timetables. In addition, control of conventional reactors is complicated and has, on a few occasions, failed resulting in serious accidents. Another issue is the build-up of nuclear waste, often toxic isotopes with long half-lives that require secure storage over the very long term. In addition, thermal nuclear reactors require enriched fuel, for example uranium with a higher proportion of the isotope U-235 than is found in naturally occurring uranium. Not only is enrichment of naturally-occurring uranium a complex process, it results in a surplus of U-238 which is essentially low-level nuclear waste. Enriched fuel represents a security risk (as it can be used in nuclear weapons) and plutonium is expensive and highly toxic. Reactor technologies that are capable of more rapid deployment and smaller form factors have been researched for a long time but have failed, at least to date, to come to fruition. The vast majority of nuclear research has focussed on thermal fission, that is using neutrons with relatively low energies to trigger fission. The principal reasons for this are multiple. Firstly, the fission cross section is much higher at such energies making it easier to generate a self-sustaining reaction. The fission cross-section is typically a U shaped curve (see accompanying Figures A13 & A14), with high values at very low energies a minimum around a couple of MeV and rising with higher energy. A second reason is that convenient materials, notably water, can be used as both a coolant and a moderator for thermal neutrons. Thirdly thermal fission with enriched fuel happens to align with weapons programs which has often helped unlock significant state funding. Fast fission has mostly only been considered practically viable in combination with thermal fission with an enriched fuel. One avenue of research is in Accelerator Driven Sub-critical Reactors (ADSR). This has the promise of not requiring dangerous or expensive fuel. Nearly 30 years ago, in 1993, Nobel Prize-winning nuclear physicist and former director of CERN, Carlo Rubia filed EP-A-725967 directed to an energy amplifier which comprised a reactor arranged to be sub-critical in the absence of incoming particles from a particle accelerator. The paper “Accelerator-driven Sub-critical reactor system (ADS) for nuclear energy generation” published in the journal of physics Pramana at vol.59, No.6, December 2002, gives an overview of the process. Dr. Charles Bowman of Los Alamos National Laboratory has published widely in this field, including “Accelerator-Driven Systems for Nuclear Waste Transmutation” Annu. Rev. Nucl. Part. Sci., 48 (1) (1998), pp505-556. Following this work, there have been a number of IAEA sponsored meetings on the subject. One key problem is that high energy neutrons are required to initiate the nuclear reactions and, because they have no electrical charge, it is impossible to accelerate neutrons using a particle accelerator. To generate such neutrons, a technique known as spallation has been used. US-A-8983017, assigned to Texas A&M University System, utilises spallation. Spallation relies on high energy particles, such as protons, disintegrating a nucleus to generate, inter alia, high energy neutrons. Spallation, however, requires an incident particle to have an energy in excess of 500million electron- volts. Particle accelerators capable of providing particles at such high energies are very large and very expensive. A linear accelerator having an energy level of 800MeV or more is required, and this may be around 1km or more in length. Another difficulty with US8983017 is that the reactor contains a molten salt which is extremely corrosive. This is a problem that it shares with the reactor disclosed in United States patent US9368244. An IAEA paper from 2015 “Status of Accelerator Driven Systems Research and Technology Development” available at https: / / www.iaea.org / publications / 10870 / status-of-accelerator-driven- systems-research-and-technology-development is still focussed on spallation. of Energy, a high beam power of 10 to 20 Megawatts is required (https: / / www.youtube.com / watch?v=fgQzkCEteAI). It took a team in China, 10 years to develop a particle accelerator capable of producing a 10mA proton current at sufficiently high energy to provoke spallation https: / / cerncourier.com / a / high-power-linac- shows-promise-for-accelerator-driven-reactors / accelerator driven sub-critical system” by Bin Liu et. al. in Nuclear Engineering and Design, Volume 386, January 2022, 111567, available at https: / / www.sciencedirect.com / science / article / pii / S0029549321005197#b0015 a neutron from a nucleus. Despite very high power inputs, in part to try and operate in a region where cross-sections rise again, results have not been promising. Such proposals with huge accelerators and vast power demands have generally been dismissed as interesting research but not promising technically or commercially for energy production. Recent energy and global warming concerns have prompted a resurgent interest in nuclear power. However, the recent focus in the art points clearly towards the prevailing wisdom of thermal fission with variously enriched fuels, albeit often in smaller reactors, despite the serious safety concerns of runaway and weapons proliferation. Further patent activity in the field is represented by US-A-2008232533, WO-A-2014204536, US-B- 10839971, WO-A-2011120555, US-A-2013028364, CN102708936, CN-A-107767966, US2006 / 0215799, CN 202662298U and WO215 / 077554. Despite decades of extensive and expensive research by leading scientists and technology groups, providing an arrangement permitting a technically and commercially viable accelerator-driven sub- critical reactor has proved elusive. It is a general object of the present invention to provide a viable accelerator driven reactor or components or techniques useful for the production of one. Aspects of the invention address various problems in the prior art. According to a first aspect of the present invention, there is provided a power source as set out in accompanying claim 1. Preferred features of the present invention are set out in accompanying claims 2 to 28. According to another aspect of the present invention, there is provided a power source comprising: an ignition region comprising a target material arranged to receive a flux of protons and generate neutrons in response thereto; a reactor core containing a sub-critical quantity of fissionable material arranged as a structure having a plurality of layers around the ignition region; a coolant containing at least one metal; wherein the reactor core includes at least one metal incorporated with the fissionable material to modify the structural and / or thermal properties of the fissionable material such that the structure is substantially self-supporting and such that the structure has a melting point above the melting point of the coolant and below the boiling point of the coolant, an accelerator arranged to supply a flux of protons with an energy at least 5MeV and with a beam current of at least 5µA to the target material in the ignition region, a window in the reactor core to permit the passage of said flux of protons unimpeded by coolant or fissionable material; a control arrangement to control the power of the proton flux to modulate reactor core power; a heat exchanger arranged to absorb heat from the molten metal coolant for transfer to a power consumer; wherein the control arrangement is arranged to model future neutron flux based on a measure of reactor state and to modulate the proton flux power based on said model. According to another aspect of the present invention, there is provided an electricity generation system comprising a reactor core, a source of protons, a heat exchanger for extracting heat from the reactor and transferring extracted heat to a generating arrangement, the reactor comprising: a reactor vessel containing a mass of fissionable fuel arranged in at least one layer spaced from an ignition region, the ignition region containing actinide material, the at least one layer of fuel comprising a plurality of elements arranged to permit the flow of coolant around the fuel, a path through a wall of the reactor vessel permitting the passage of protons to the ignition region, and a coolant of metal or metal alloy, the coolant in thermal contact with the fissionable fuel elements, the coolant further having a melting point lower than that of the fuel and a boiling point greater than the melting point of the fissionable fuel, wherein the fuel generates insufficient neutrons by spontaneous fission in the absence of a flux of protons to the ignition region to maintain a critical or super-critical reaction. According to another aspect of the present invention, there is provided a An electricity generation system comprising a reactor, a source of protons, a heat exchanger for extracting heat from the reactor and transferring extracted heat to a generator, the reactor comprising: a reactor vessel containing fuel arranged in at least one layer spaced from an ignition region containing actinide material and material for a proton-neutron reaction in which a parent atom and an inbound proton generates a reaction that emits one or more neutrons and a daughter element reverts to the parent element via beta decay or electron capture, whereby the material for the proton-neutron reaction is arranged to be irradiated by protons and to supply neutrons to the actinide element at the ignition region, the at least one layer of fuel comprising a plurality of elements arranged to permit the flow of coolant around the fuel, a path through a wall of the reactor vessel permitting the passage of particles to the ignition region from the source of protons, and a coolant selected from metal or metal alloy, the coolant thermally in contact with the fuel, and the coolant further having a melting point lower than that of the fuel and a boiling point greater than the melting point of the fuel. According to another aspect of the present invention, there is provided an energy multiplier comprising a reactor and a particle accelerator, the energy multiplier comprising: a reactor vessel, at least one ignition region within the reactor vessel, containing material responsive to incident protons to provide neutrons for irradiating an actinide material, the actinide material responsive to incident neutrons to provide further neutrons, a particle accelerator which, in use, consumes a quantity of electrical energy, the particle accelerator being arranged to feed a path to convey particles to the at least one ignition region, actinide fuel comprising a plurality of elements supported by a structure within the reactor vessel and around the ignition region in at least one layer, a coolant comprising metal or metal alloy in thermal contact with the plurality of fast-fission fuel elements, the coolant having a melting point below a melting point of the fast-fission fuel and a boiling point above the melting point of the fast-fission fuel, and a heat exchanger for extracting heat from the coolant, and an electrical generator for generating electrical energy from the extracted heat such that, in use, a larger quantity of electrical energy is generated than the quantity of electrical energy consumed by the particle accelerator. According to another aspect of the present invention, there is provided an actinide fuel for use in a nuclear reactor, the fuel comprising: at least one actinide element and 2.5 to 35 atomic weight percent of material comprising at least one of tungsten, rhenium, tantalum, molybdenum, niobium, and zirconium. According to another aspect of the present invention, there is provided an actinide fuel structure for a reactor comprising at least one source of neutrons, the fuel structure comprising: at least one layer comprising a plurality of elements of actinide fuel arranged on a support, the plurality of elements in a particular layer arranged to be substantially equidistant from the at least one source of neutrons in the reactor. According to another aspect of the present invention, there is provided a power source comprising: a reactor vessel comprising shielding material, at least one ignition bulb, arranged within the reactor vessel, containing material responsive to incident protons to provide neutrons for irradiating an actinide material, the actinide material responsive to incident neutrons to provide further neutrons, a path to convey protons from outside the reactor vessel to the at least one ignition bulb, fast-fission fuel comprising a plurality of elements arranged within the reactor vessel and around the ignition bulb in at least one shell, at least one structure supporting the fuel in use while permitting substantially free flow of coolant around the fuel, a coolant comprising metal or metal alloy in thermal contact with the plurality of fast-fission fuel elements, the coolant having a melting point below a melting point of the fast-fission fuel and a boiling point above the melting point of the fast-fission fuel, and a heat exchanger to extract heat from the coolant. According to another aspect of the present invention, there is provided a power source comprising: a reactor vessel containing, at least one neutron source, arranged within the reactor vessel, containing material capable of a proton neutron reaction, and an actinide material, the actinide material arranged to receive incident neutrons from the material capable of a proton / neutron reaction, a path to convey protons from outside the reactor vessel to the at least one neutron source, nuclear fuel comprising uranium and between 2.5 and 35 percent by atomic weight of at least one of tungsten, rhenium, tantalum, molybdenum, niobium, and zirconium, the fuel arranged as a plurality of elements in at least one layer, the fuel elements supported by a frame around the neutron source, a metal or metal alloy coolant directly surrounding the plurality of fuel elements, the coolant having a melting point below a melting point of the fast-fission fuel and a boiling point above the melting point of the fast-fission fuel, and a heat exchanger to extract heat from the coolant. According to another aspect of the present invention, there is provided a power source comprising: at least one ignition region, arranged within a reactor vessel, the ignition region containing actinide material responsive to incident protons to generate neutrons, a path to convey protons from outside the reactor vessel to the at least one ignition region, fissionable fuel comprising a plurality of fuel elements arranged around the ignition region in at least one shell,at least one structure supporting the fuel in use while permitting substantially free flow of coolant around the fuel, a coolant comprising metal or metal alloy in contact with the plurality of fast-fission fuel elements, the coolant having a melting point below a melting point of the fast-fission fuel and a boiling point above the melting point of the fast-fission fuel. According to another aspect of the present invention, there is provided a power source comprising: a reactor vessel containing shielding material, at least one ignition means, arranged within the reactor vessel, containing material responsive to incident particles to provide neutrons for irradiating fast- fission fuel, a path to convey particles from outside the reactor vessel to the at least one ignition means, fast-fission fuel comprising a plurality of sub-critical elements arranged around the ignition means, at least one means for supporting the fuel in use while permitting substantially free flow of coolant around the fuel, a coolant comprising metal or metal alloy in contact with the plurality of fast- fission fuel elements, the coolant being a solid at ambient temperature and a liquid at the reactor operating temperature. According to another aspect of the present invention, there is provided a nuclear reactor comprising a reactor vessel, the reactor further comprising: fissionable fuel arranged in at least one layer spaced from an ignition region, the ignition region containing actinide material, the at least one layer of fuel comprising a plurality of elements arranged to permit the flow of coolant around the fuel, a window through a wall of the reactor vessel permitting the passage of energetic particles to the ignition region, and a coolant of metal or metal alloy, the coolant in contact with the fuel elements, the coolant further having a melting point lower than that of the fuel and a boiling point greater than the melting point of the fuel, wherein the reactor is arranged such that insufficient neutrons are generated from spontaneous fission of the fissionable fuel to propagate a critical reaction in the absence of excitation by said energetic particles. According to another aspect of the invention, there is provided nuclear reactor comprising a reactor vessel, the reactor further comprising: fuel arranged in at least one layer spaced from an ignition region containing actinide material, and material for a proton-neutron reaction in which a parent atom and an inbound proton generates a reaction that emits one or more neutrons and a daughter element reverts to the parent element via beta decay or electron capture, whereby the material for the proton- neutron reaction is arranged to be irradiated by protons and to supply neutrons to the actinide element at the ignition region, the at least one layer of fuel comprising a plurality of elements arranged to permit the flow of coolant around the fuel, a window through a wall of the reactor vessel permitting the passage of particles to the ignition point, and a coolant selected from metal or metal alloy, the coolant directly in contact with the fuel, and the coolant further having a melting point lower than that of the fuel and a boiling point greater than the melting point of the fuel. According to another aspect of the present invention, there is provided a method of rendering a fast fission nuclear reactor safe in response to an uncontrolled heat transfer rate, the nuclear reactor comprising a reactor vessel containing at least one actinide fuel element supported by a support structure and arranged in thermal contact with a coolant, the coolant being a metal or metal alloy having a melting point lower than the melting point of the fuel and a boiling point greater than the melting point of the fuel, the method comprising: the at least one fuel element being subject to a nuclear reaction that heats the fuel element, a portion of the at least one fuel element melting, detaching at least a portion of the at least one fuel element from the support structure, the detached portion of the at least one fuel element reducing its participation in a critical or super-critical nuclear reaction, the coolant and fuel reducing in temperature, and the coolant and fuel solidifying in response to the reduction in temperature. According to another aspect of the present invention, there is provided a power source comprising: an ignition region comprising a target material arranged to receive a flux of protons and generate neutrons in response thereto; a reactor core containing a sub-critical quantity of actinide material arranged as a structure having a at least one layer around the ignition region, wherein the actinide material comprises at least Thorium or Uranium and generates insufficient neutrons by spontaneous fission in the absence of the flux of protons to the ignition region to maintain a critical or super-critical reaction; a coolant containing at least one metal; an accelerator arranged to supply a flux of protons having an energy of between 4MeV and 200MeV to the target material in the ignition region, a window in the reactor core to permit the passage of said flux of protons unimpeded by coolant or actinide material; a control arrangement to control the power of the proton flux to modulate reactor core power. According to another aspect of the present invention, there is provided a nuclear reactor comprising: a container containing a coolant, a central support arranged within the container, a source of a flux of protons, the central support carrying a plurality of substantially identical fuel elements extending radially outward from the support, wherein the elements generate insufficient neutrons by spontaneous fission in the absence of the flux of protons to the ignition region to maintain a critical or super-critical reaction, an ignition region arranged in proximity to the fuel elements, the ignition region being responsive to the flux of protons to generate neutrons, wherein the fuel elements are supported so as to be in thermal contact with the coolant and sustained application of protons having energies greater than 4MeV to the ignition region generates an increasing amount of neutrons in the fuel elements over time. According to another aspect of the present invention, there is provided a nuclear reactor comprising: a reactor vessel for containing a coolant, the reactor vessel containing at least one element of actinide material including at least one of thorium and uranium or a mixture of both which is fissionable in response to a flux of neutrons, an ignition region arranged to produce neutrons in response to a flux of protons, wherein the actinide material generates insufficient neutrons by spontaneous fission in the absence of a flux of protons to an ignition region to maintain a critical or super-critical reaction, wherein the reactor further comprising means for forced distribution of coolant within the vessel. According to another aspect of the present invention, there is provided a nuclear reactor comprising: a container containing a coolant, a support arranged within the container, the support carrying a plurality of substantially identical fuel elements, the support structure arranged to rotate within the container about an axis, an ignition region arranged in proximity to the fuel elements, the ignition region being responsive to a flux of protons to generate neutrons, a path for conveying protons from outside of the container to the ignition region, wherein the fuel elements are supported so as to be in thermal contact with the coolant, and wherein the fissionable material generates insufficient neutrons by spontaneous fission in the absence of a flux of protons to the ignition region to maintain a critical or super-critical reaction. According to another aspect of the present invention, there is provided a nuclear reactor comprising: a reactor vessel comprising shielding material, at least one ignition bulb, arranged within the reactor vessel, containing material responsive to incident protons to provide neutrons for fissionable material, a path to convey protons from a particle accelerator outside the reactor vessel to the at least one ignition bulb, fissionable fuel comprising a plurality of elements arranged within the reactor vessel and around the ignition bulb in at least one shell, at least one structure supporting the fuel in use while permitting substantially free flow of coolant around the fuel, a coolant comprising metal or metal alloy having a density at room temperature of greater than 5g / cm3in thermal contact with the plurality of fuel elements, and a pump external to the vessel, the container comprising at least a flow line for carrying coolant to the external pump and a return line for carrying the coolant from the external pump to the container. According to another aspect of the present invention, there is provided a power source comprising: an ignition region comprising a target material arranged to receive a flux of protons and generate neutrons in response thereto; a reactor core containing a sub-critical quantity of fissionable material arranged as a plurality of fuel elements of substantially the same size; a coolant containing at least one metal; an accelerator arranged to supply a flux of protons with an energy of between 4MeV and 200MeV and having a beam current of at least 100µA to the target material in the ignition region, a window in the reactor core to permit the passage of said flux of protons unimpeded by coolant or fissionable material; a control arrangement to control the power of the proton flux to modulate reactor core power; a heat exchanger arranged to absorb heat from the molten metal coolant for transfer to a power consumer; wherein the control arrangement is arranged to model future neutron flux based on a measure of reactor state and to modulate the proton flux power based on said model. According to another aspect of the present invention, there is provided a nuclear fuel element comprising; a support structure, and an actinide portion comprising at least 80% by weight of Thorium, and at least 1% of another metal selected from Iron, Nickel, magnesium and Uranium to reduce the melting point of the actinide portion, wherein the fuel element is attached to the support structure such that the actinide portion deforms under its own weight at temperatures exceeding 1700˚C. According to another aspect of the present invention, there is provided a nuclear reactor comprising: a particle accelerator, a reactor vessel comprising shielding material, at least one ignition bulb, arranged within the reactor vessel, containing material responsive to incident protons to provide neutrons for fissionable material, a path to convey protons from the particle accelerator outside the reactor vessel to the at least one ignition bulb, fissionable fuel comprising a plurality of elements arranged within the reactor vessel and around the ignition bulb in at least one shell, at least one structure supporting the fuel in use while permitting substantially free flow of coolant around the fuel, a coolant comprising metal or metal alloy in thermal contact with the plurality of fuel elements, and a heat exchanger to extract heat from the coolant, the reactor further comprising a controller arranged to control the output of the particle accelerator to provide at least two distinct output levels from the nuclear reactor. According to another aspect of the present invention, there is provided an energy multiplier comprising a nuclear reactor and a particle accelerator, the reactor comprising: a reactor vessel for containing a coolant, at least one fissionable fuel element arranged within the reactor vessel, an ignition region arranged in the reactor vessel, the ignition region comprising a first portion containing an element responsive to an incoming proton to generate a neutron and a second portion containing an element responsive to neutrons generated in the first portion to provide further neutrons, the particle accelerator coupled to supply protons to the first portion of the ignition region, whereby the particle accelerator comprises a linear particle accelerator arranged to generate protons having energies in excess of 4MeV. According to another aspect of the present invention, there is provided a method of operating an electricity generation system, the system comprising: a subcritical fast fission nuclear reactor, the nuclear reactor comprising a reactor vessel containing at least one actinide fuel element supported by a support structure and arranged in thermal contact with a coolant and a source of particles to drive the reactor into the critical or super-critical region, the method being responsive to an uncontrolled heat transfer rate and comprising: the at least one fuel element being subject to a nuclear reaction that heats the fuel element, a portion of the at least one fuel element melting and changing its geometry, the melted portion of the at least one fuel element reducing its participation in a critical or super-critical nuclear reaction, the coolant and fuel reducing in temperature, and the coolant and fuel solidifying in response to the reduction in temperature. According to another aspect of the present invention, there is provided a system for treating material at high temperatures, the system comprising: an ignition region comprising a target material arranged to receive a flux of protons and generate neutrons in response thereto; a reactor core containing a sub-critical quantity of fissionable material arranged as a structure having at least one layer around the ignition region; a coolant containing at least one metal; an accelerator arranged to supply a flux of protons with an energy of between 4MeV and 200MeV, and having a beam current of at least 100µA to the target material in the ignition region, a window in the reactor core to permit the passage of said flux of protons unimpeded by coolant or fissionable material; a control arrangement to control the power of the proton flux to modulate reactor core power; a heat exchanger arranged to absorb heat from the molten metal coolant for transfer to a working fluid; wherein the control arrangement is arranged to model future neutron flux based on a easure of reactor state and to modulate the proton flux power based on said model, and a kiln enclosure for containing material to be heated, and at least one conduit arranged to conduct heat from the working fluid to the kiln enclosure. According to another aspect of the present invention, there is provided a system for treating material at high temperatures, the system comprising a reactor vessel comprising shielding material, at least one ignition bulb, arranged within the reactor vessel, containing material responsive to incident protons to provide neutrons for irradiating an actinide material, the actinide material responsive to incident neutrons to provide further neutrons, a path to convey protons from outside the reactor vessel to the at least one ignition bulb, actinide fuel comprising a plurality of elements arranged within the reactor vessel and round the ignition bulb in at least one shell, at least one structure supporting the fuel in use while permitting substantially free flow of coolant around the fuel, a coolant comprising metal or metal alloy in thermal contact with the plurality of fuel elements, and a heat exchanger to transfer heat from the coolant to a working fluid, a kiln enclosure for containing material to be heated, and at least one conduit arranged to conduct heat from the working fluid to the kiln enclosure. According to another aspect of the present invention, there is provided a system for treating material at high temperatures, the system comprising: at least one ignition region, arranged within a reactor vessel, the ignition region containing actinide material responsive to incident protons to generate neutrons, a path to convey protons from outside the reactor vessel to the at least one ignition region, fissionable fuel comprising a plurality of fuel elements arranged around the ignition region in at least one shell, at least one structure supporting the fuel in use while permitting substantially free flow of coolant around the fuel, a coolant comprising metal or metal alloy in contact with the plurality of fuel elements, a heat exchanger to transfer heat from the coolant to a working fluid and a kiln enclosure for containing material to be heated, at least one conduit arranged to conduct heat from the working fluid to the kiln enclosure. According to another aspect of the present invention, there is provided a propulsion system for driving a vehicle via a shaft, the propulsion system comprising: an ignition region comprising a target material arranged to receive a flux of protons and generate neutrons in response thereto; a reactor core containing a sub-critical quantity of fissionable material arranged as a structure having at least one layer around the ignition region; a coolant containing at least one metal; an accelerator arranged to supply a flux of protons with an energy of between 4MeV and 200MeV to the target material in the ignition region, a window in the reactor core to permit the passage of said flux of protons unimpeded by coolant or fissionable material; a control arrangement to control the power of the proton flux to modulate reactor core power; a heat exchanger arranged to absorb heat from the molten metal coolant for transfer to a working fluid; and a turbine arranged to rotate a shaft in response to the working fluid. According to another aspect of the present invention, there is provided a propulsion system for driving a vehicle via a shaft, the propulsion system comprising: a reactor vessel comprising shielding material, at least one ignition bulb, arranged within the reactor vessel, containing material responsive to incident protons to provide neutrons for irradiating an actinide material, the actinide material responsive to incident neutrons to provide further neutrons, a path to convey protons from outside the reactor vessel to the at least one ignition bulb, fissionable fuel comprising a plurality of elements arranged within the reactor vessel and around the ignition bulb in at least one shell, at least one structure supporting the fuel in use while permitting substantially free flow of coolant around the fuel, a coolant arranged in thermal contact with the plurality of fuel elements, and a heat exchanger to transfer heat from the coolant to a working fluid, and a turbine arranged to rotate a shaft in response to the working fluid. According to another aspect of the present invention, there is provided a propulsion system for driving a vehicle via a shaft, the propulsion system comprising: at least one ignition region, arranged within a reactor vessel, the ignition region containing actinide material responsive to incident protons to generate neutrons, a path to convey protons from outside the reactor vessel to the at least one ignition region, fissionable fuel comprising a plurality of fuel elements arranged around the ignition region in at least one shell, at least one structure supporting the fuel in use while permitting substantially free flow of coolant around the fuel, a coolant comprising metal or metal alloy in contact with the plurality of fuel elements, the coolant having a melting point below a melting point of the fuel and a boiling point above the melting point of the fuel, a heat exchanger to transfer heat from the coolant to a working fluid, and a turbine arranged to rotate a shaft in response to the working fluid. According to another aspect of the present invention, there is provided a system for generating heat for an industrial process, the system comprising: an ignition region comprising a target material arranged to receive a flux of protons and generate neutrons in response thereto; a reactor core containing a sub-critical quantity of fissionable material arranged as a structure having at least one layer around the ignition region; a coolant containing at least one metal; an accelerator arranged to supply a flux of protons with an energy of between 4MeV and 200MeV, and having a beam current of at least 100µA to the target material in the ignition region, a window in the reactor core to permit the passage of said flux of protons unimpeded by coolant or fissionable material; a control arrangement to control the power of the proton flux to modulate reactor core power; a heat exchanger arranged to absorb heat from the molten metal coolant for transfer to a working fluid; and at least one conduit arranged to conduct heat from the working fluid to the industrial process. According to another aspect of the present invention, there is provided a system for generating heat for an industrial process, the system comprising a reactor vessel comprising shielding material, at least one ignition bulb, arranged within the reactor vessel, containing material responsive to incident protons to provide neutrons for irradiating an actinide material, the actinide material responsive to incident neutrons to provide further neutrons, a path to convey protons from outside the reactor vessel to the at least one ignition bulb, actinide fuel comprising a plurality of elements arranged within the reactor vessel and around the ignition bulb in at least one shell, at least one structure supporting the fuel in use while permitting substantially free flow of coolant around the fuel, a coolant comprising metal or metal alloy in thermal contact with the plurality of fuel elements, and a heat exchanger to transfer heat from the coolant to a working fluid, and at least one conduit arranged to conduct heat from the working fluid to the industrial process. According to another aspect of the present invention, there is provided a system for generating heat for an industrial process, the system comprising: at least one ignition region, arranged within a reactor vessel, the ignition region containing actinide material responsive to incident protons to generate neutrons, a path to convey protons from outside the reactor vessel to the at least one ignition region, fissionable fuel comprising a plurality of fuel elements arranged around the ignition region in at least one shell, at least one structure supporting the fuel in use while permitting substantially free flow of coolant around the fuel, a coolant comprising metal or metal alloy in contact with the plurality of fuel elements, a heat exchanger to transfer heat from the coolant to a working fluid, and at least one conduit arranged to conduct heat from the working fluid to the industrial process. According to another aspect of the present invention, there is provided a system for generating heat for residential, district or commercial consumers, the system comprising: at least one ignition region, arranged within a reactor vessel, the ignition region containing actinide material responsive to incident protons to generate neutrons, a path to convey protons from outside the reactor vessel to the at least one ignition region, fissionable fuel comprising a plurality of fuel elements arranged around the ignition region, a coolant comprising metal or metal alloy in thermal contact with the plurality of fuel elements, a heat exchanger to transfer heat from the coolant to a working fluid, and at least one conduit arranged to conduct heat from the working fluid to at least one heating consumer. According to another aspect of the present invention, there is provided a nuclear reactor comprising a nuclear fuel source and a control arrangement for adjusting the power level of the reactor, wherein the thermal output of the reactor coolant is arranged to supply a first thermal consumer arranged to provide electricity and a second thermal consumer arranged to supply heat to a heating circuit and a control system arranged arranged to vary the balance of heat supplied to each of the first and second circuits and to adjust the power level of the reactor wherein the control system includes a module for estimating a prediction of demand from at least one of the first and second thermal consumers and is arranged to determine a control strategy including adjusting the balance and adjusting total reactor power wherein total reactor power level is expected to vary less rapidly than individual power demand from the first and second thermal consumers. Embodiments contrast with conventional approaches to nuclear power generation which mostly deliberately slow neutrons to a region of high cross section or try to use very high energies, the higher the better, to try to operate in a higher cross section region. Instead, embodiments typically use a novel core structure with patience such that a non-critical mass of material undergoes a gradual buildup of activity under the action of a sustained but relatively low energy accelerator, with manageable power requirements. The following preferred features may be applied to any aspect of the invention. The ignition source or region may operate on two similar, but different principles: a two-stage process and a single stage process. Firstly, the target material may comprise a first material responsive to proton bombardment at energies below 20MeV to generate neutrons within a first energy range and a second material responsive to the neutrons in the first energy range to generate neutrons in a second energy range. This has a significant advantage in that the neutrons can be generated by a relative low cost cyclotron. The first material may comprise material for a proton-neutron reaction in which a parent element emits a neutron and a daughter element of the parent reverts to the parent element via beta decay or electron capture. When the material exhibits a circular reaction, no material is consumed, promoting a long lifetime of the ignition source. The first material is preferably selected from lithium-7, oxygen-18, nitrogen-14, nickel-64, zinc-68 and cadmium-112 which materials all exhibit a suitable circular reaction. Lithium-7 is particularly preferred. The material for a proton-neutron reaction is preferably arranged to be withdrawn from the reactor without disturbing the fuel and / or the coolant. Despite the circular reaction, some degradation of the material is unavoidable, so it is beneficial to be able to replace the material with minimal disruption to the reactor. The fuel bulb / region operates at 1000ºC and above meaning that the material for a proton-neutron reaction is preferably contained in a tungsten or molybdenum container to withstand the high temperatures. Secondly, in embodiments of the invention, the ignition region may contain actinide material responsive to incident protons to generate neutrons. This “one-step” process allows for a more straightforward design of ignition bulb but requires a more powerful and expensive particle accelerator. In certain embodiments of the invention, at least one further ignition bulb is provided which is arranged to receive protons from the at least one particle accelerator. This will require fuel comprising a further plurality of fast fission fuel elements arranged around the at least one further ignition bulb. Preferably, the further ignition bulb and the further plurality of fast fission fuel elements are controlled independently. An ignition arrangement comprises a first chamber and a second chamber, the first chamber containing a first material responsive to incident protons to provide a number of first neutrons, the second chamber containing an actinide material responsive to first neutrons to provide a number of second neutrons, greater than the number of first neutrons, the first chamber being arranged, in use, to receive protons from a particle accelerator and the second chamber is arranged, in use, to receive at least a proportion of the first neutrons from the material in the first chamber, wherein the second chamber is located, in use, relative to the fissionable fuel such that at least a proportion of the second neutrons impinge on the fuel. The first material preferably comprises material for a proton-neutron reaction in which a parent atom and the inbound proton generates a reaction that emits one or more neutrons. The first material preferably comprises at least one of lithium-7, oxygen-18, nitrogen-14, nickel-64, zinc-68 and cadmium-112, more preferably Lithium-7. The second material is preferably uranium-238. The second chamber is preferably at least partially defined by the wall of a reactor vessel. The first chamber is preferably separable from the second chamber. The at least one actinide element comprising the fuel is preferably selected from Thorium, Uranium, Neptunium, Plutonium and Americium. Preferably, the actinide element comprises uranium or thorium due to a combination of abundance and cost. More preferably the actinide element is uranium due to improved reactivity when compared with thorium. More preferably still the uranium comprises uranium-238, which may comprise depleted uranium or spent uranium, available at low cost. The fuel containing the actinide element may also comprise an alloy with a proportion of another metal to raise the melting point of the actinide element. This allows a reactor to be operated at a higher temperature which is more efficient. The another metal preferably has a higher melting point than the actinide material and may comprise at least one of tungsten, rhenium, tantalum, molybdenum, niobium, and zirconium in a proportion from 2.5% to 35%, more preferably in a proportion between 2.5% and 10%, and still more preferably substantially 3%. At least in the case of uranium, tungsten is preferred as the another metal since a lower proportion of tungsten is required to elevate the melting point of the actinide element. A lower proportion of the another metal is preferred since it has less of an impact on the reactivity of the actinide material. A fuel element comprising another metal thus contains 65 to 97.5 percent by weight of the actinide fuel material, more preferably 90 to 97.5 percent by weight of the actinide fuel material and more preferably still, substantially 3 percent by weight of the actinide fuel material. The actinide element in the fuel material preferably comprises at least 90% uranium-238, more preferably at least 98% uranium-238. One of the benefits of a fast-fission core is that it does not need enriched fuel which provides an enormous cost saving over thermal nuclear fuel. According to certain embodiments of the invention, a doped actinide fuel may be used, containing a portion of another actinide with a greater cross section to improve reaction rates. Plutonium is the most effective such doping material. The fuel structure preferably comprises fuel elements are provided as self-supporting structural elements within the coolant. This simplifies the mounting of the fuel and allows faster manufacture. More preferably, the structure supporting the fuel elements comprises a cantilevered structure. This further simplifies the mounting of the fuel. A fuel element according to embodiments of the invention are preferably shaped to form a cantilevered self-supporting component of a reactor core extending from a root to be attached to a base element. By using a cantilevered structure, there are fewer support elements to interrupt the flow of neutrons and coolant within the reactor. The fuel elements are preferably attached to the support structure by at least one pin. For even further simplification of the structure, the fuel elements are preferably integrally formed with a base element. This reduces the amount of assembly required for the reactor. Still further simplification is attained when the fuel element is integrally formed with another fuel element. Structural elements of the fuel preferably comprise tungsten or molybdenum to withstand the high core temperatures. The fuel elements in a particular layer of fuel are preferably arranged substantially equidistant from the ignition region or bulb. This helps to ensure a predictable and consistent reaction rate within the core. The fuel elements in the first layer are preferably arranged to be substantially 200mm from the source of neutrons. The exact geometry of the fuel relative to ignition source is determined from considerations of cooling and neutron flux but this distance is a good compromise in certain embodiments of the present invention. The at least one fuel layer is arranged, in use, to be surrounded by coolant and at a distance from the source of neutrons selected to permit coolant flow around the layer and source sufficient to remove heat generated in use. The or each layer of fuel is preferably substantially cylindrical or spherical, more preferably substantially spherical to best exploit the neutrons from the ignition bulb or region. The fuel elements in a particular layer are preferably arranged to substantially surround the ignition region. This better utilises space within the reactor and neutrons from the ignition source. Each layer preferably comprises a plurality of groups of three elements arranged to substantially surround the source of neutrons. This provides a good compromise between ease of assembly and number of parts required. It is preferred to allow a small gap between each of the three elements so that they are arranged to extend substantially 110 degrees around the source of neutrons. Each layer may equally comprise groups of four (or even more) elements. The plurality of elements in the at least one layer of fuel are preferably arranged to promote thermal convection of the coolant. This improves cooling of the fuel to prevent undue thermal stresses on the fuel which might cause deformation and / or cracking. To promote coolant circulation and neutron propagation, the fuel elements preferably comprise elongate structures, more preferably ribs. The ribs are preferably attached substantially centrally to the support to reduce stresses in the fuel element. While a reactor according to embodiments of the invention may comprise a single layer of fuel, to generate more heat, there is preferably provided at least one further layer of fuel comprising a plurality of elements. The at least one further layer is preferably arranged to be between 50 and 200mm, preferably substantially 100mm, from adjacent layers. Each fuel element is preferably spaced from adjacent fuel elements by between substantially 15mm and 20mm. Each fuel element is preferably arranged, in use, to be surrounded by coolant and at a distance from adjacent fuel elements selected to accommodate the heat transfer ability of the coolant. When at least one further layer is provided, the at least one layer arranged to be closer to the source of neutrons preferably has fewer elements than at least one layer arranged to be further away from the source of neutrons. An actinide fuel structure for use with embodiments of the invention preferably comprise at least 3 layers. This provides a good power output when uranium is used as the fuel. An actinide fuel structure for use with embodiments of the invention may additionally comprise at least 5 layers. This provides a good power output when thorium is used as the fuel. Further layers of fuel, for example at least 7 layers, provide higher power outputs but may have a drawback in terms of coolant. Solder may cease to be appropriate at this number of layers due to absorption of neutrons (moderation) from the ignition source. LBE still provides an excellent coolant for this size of reactor. A fuel structure according to at least some embodiments of the present invention comprises at least some fuel elements which are arranged, in use, to cause the reactor to react in a critical or super- critical manner in response to bombardment by a predetermined quantity of neutrons. The plurality of fuel elements preferably comprise fast-fission fuel. The coolant comprises a metal or metal alloy which is a solid at room temperature and a liquid at reactor operating temperature. This makes the reactor easy to transport when shut-down and also reduces problems of pressure within the reactor vessel. Suitable coolants include at least one of tin, lead, lead-bismuth-eutectic, lead / tin solder and Babbitt type two. The coolant preferably comprises at least a proportion of lead. Lead, being a heavy atom, has a minimal moderating effect on the neutrons within the reactor. This is particularly important in a fast fission reactor. One preferred coolant is lead bismuth eutectic or LBE which is known to have excellent performance. This comprises lead and bismuth in proportions of 44.5% and 55.5% respectively. LBE des have one drawback, however, and that is density. A lighter coolant that still has excellent cooling properties is solder. The solder preferably comprises at least 37% lead. Solder does exhibit a greater degree of moderation than LBE so is not preferred for larger reactors, for example, exceeding 5 layers of fuel. For 6 layers of fuel and above, LBE is preferred. An important consideration for the coolant is that it has a boiling point higher than the melting point of the fuel. This ensures that the fuel will melt and diminish its participation in fission before the coolant boils, ensuring that no overpressurisation of the reactor vessel occurs. To provide a degree of headroom, the boiling point of the coolant is preferably greater than the melting point of the fuel by at least, 10 degrees Celsius, more preferably 50 degrees Celsius. The heat exchanger may be located internally or externally of the reactor vessel. An internal heat exchanger can be arranged to extract heat from the coolant across a large volume within the reactor vessel. The heat exchanger is preferably arranged above the fuel since the upper part of the vessel will generally contain hotter coolant. On the other hand, an external heat exchanger that is supplied with coolant from the reactor vessel allows that vessel to be smaller and easier to manufacture. Embodiments of the present invention preferably further comprise a turbine for extracting power from the reactor vessel. Selection of a particle accelerator is dictated in large part by the arrangement of the ignition bulb. If the ignition bulb, or region, contains only actinide material, then more energetic protons are required to generate neutrons, necessitating a larger and more expensive particle accelerator arranged to irradiate the actinide material located at the ignition region with protons having an energy at least 20MeV on target. The particle accelerator preferably generates protons with an energy of at least 20MeV. For a uranium-238 target in the ignition bulb, the particle accelerator is preferably arranged to irradiate the material responsive to incident protons with protons with an energy of substantially 27MeV on target If, however, the ignition region is arranged to operate on a two-stage basis, a smaller and cheaper particle accelerator will suffice. In this case, the at least one particle accelerator is arranged to irradiate the proton-neutron reaction material located at the ignition region with protons having an energy of at least 1.88MeV on target. This energy level is the minimum required to generate protons from a lithium 7 source. Preferably, however, the particle accelerator is arranged to irradiate the proton-neutron reaction material with protons having an energy of substantially 7MeV on target. This provides something close to maximum neutron output per proton. In the two-step process, the particle accelerator generates energetic protons with an energy below 20MeV and more preferably between 5 and 20 MeV with a beam current of at least 50µA. A preferred output level for the particle accelerator is substantially 15MeV. For reasons of space and cost, the particle accelerator is preferably a cyclotron. A control arrangement is preferably provided and arranged to model future neutron flux based on a measure of reactor state and to modulate proton flux power based on said model. The measure of reactor state may be based at least in part on a measure of current neutron flux. The neutron flux is preferably measured by at least one sensor in, on or adjacent the reactor shielding The measure of reactor state may be based at least in part on a measure of reactor core temperature. The measure of reactor state may be derived based on a current measure of one or more reactor physical properties and a past measure of reactor state. The control arrangement may be arranged to model reactor response to power consumed and current neutron flux and to modulate proton flux power based on said model. The control arrangement may be arranged to model thermal energy demand from the reactor and to modulate proton flux based on current temperature, for example reactor core temperature, and current reactor state. The control arrangement is preferably arranged to deactivate the particle accelerator in response to a signal from at least one sensor, more preferably a plurality of sensors, being above a threshold. That sensor may comprise at least one of a neutron sensor, a temperature sensor and a pressure sensor. Embodiments of the present invention are preferably arranged so that, on heating of the reactor above a threshold cut-off temperature, the fuel elements deform before the coolant boils such that in a deformed configuration, including complete melting of the fuel, the power output is degraded. Alternatively, detached portion of the fuel elements will sink within the reactor vessel and reduce its participation in the fission reaction. These both provide a key passive safety feature that avoids vessel overpressurisation. Deactivation of the or each particle accelerator is preferably arranged to follow from a detected fault condition and a breach of the reactor vessel is preferably sealed as the coolant solidifies as it cools. A fire suppression system is preferably provided in certain embodiments and is arranged to be deployed in response to a detected fault condition. The fire suppression system is preferably provided to protect at least the particle accelerator. Certain embodiments of the present invention preferably further comprise a shipping container housing the majority of the components. The beam current of the flux of protons is at least 100µA preferably at least 250µA and more preferably at least 500µA The accelerator is preferably arranged to provide a flux of protons having an energy between 4MeV and 15MeV. In alternative embodiments the accelerator is arranged to provide a flux of protons having an energy of between 15MeV and 100MeV, preferably between 15MeV and 50MeV. The actinide material preferably comprises at least 80% by weight of Thorium, and at least 1% of another metal selected from Iron, Nickel, Magnesium and Uranium. The proportion of the another metal is preferably selected to cause the melting point of the actinide material to be below a predetermined value. The actinide material preferably comprises at least 90% by weight Thorium and more preferably 95% by weight Thorium. The reactor vessel preferably further contains means for forced distribution of coolant within the vessel, for example an impeller. Forced convection of coolant may alternatively comprise at least one element of actinide material rotatable about an axis. The actinide elements are preferably arranged evenly around the axis. The actinide elements are preferably identical. The material preferably rotates at between 1 and 25 rpm, more preferably at between 4 and 8 rpm. The axis is preferably rotated by a motor and further preferably horizontal. The fuel elements are preferably shaped to promote the movement of coolant within the container. The flow of coolant is preferably turbulent. In other embodiments the forced distribution of coolant comprises a pump external to the reactor vessel. The means for forced distribution preferably comprise an electromagnetic pump. A flow line to the motor is preferably above a return line from the motor. The reactor preferably comprises a plurality of distinct output levels, wherein one the distinct output levels comprises an idle level from which the reactor can be arranged to generate full power in a shorter time than the time required from a zero output level. The idle level preferably generates less than 20% of the maximum thermal output of the reactor and more preferably generates less than 10% of the maximum thermal output of the reactor. The controller is preferably arranged to control the particle accelerator to provide at least three distinct output levels from the nuclear reactor. The linear particle accelerator is preferably arranged to generate protons having energies in excess of 4MeV and more preferably is arranged to generate protons having energies of less than 15Mev. The actinide fuel is preferably arranged to deform at excessive temperatures, whereby the the melted portion of the fuel element detaches from the remainder of the fuel element. A propulsion system preferably further comprises a gearbox having an input coupled to the shaft and an output shaft. Where the propulsion system is for a water-borne vessel, the propulsion system further comprising: at least one propellor coupled to the shaft or the output shaft of the gearbox. Alternatively, the propulsion system is for a train. The industrial process preferably comprises one or more of a chemical process, a drying process, refining hydrocarbons, an extrusion process and construction of composite materials. The heating system preferably comprises a control system arranged to control the output of the source of protons in response to an output from at least one environmental sensor. The environmental sensor may comprise a temperature sensor. Alternatively or in addition, the control system is arranged to control the output of the system in response to weather predictions. It has been appreciated by the present inventor that metallic, fast-fission capable fuel such as U-238 or Th-232 is capable of solving several surface-level issues such as heat transfer to a coolant at a high operating temperature and increased fuel density when compared with prior art oxide fuels. The embodiments of the present invention are derived from a complete change of mindset when compared with previous approaches. In particular, the general consensus has been that criticality was a core-wide concept. In the present case, however, the geometry of neighbouring cells within actinide fuel is evaluated for a “local” criticality. More details are provided in the Appendix below. Additionally, the inventor has concluded that the industry has an over-reliance on Monte Carlo mathematical methods. The present invention will now be described by way of example, with reference to the accompanying drawings, in which: Figure 1 is a schematic diagram of an electricity generating system in accordance with an embodiment of the present invention, Figure 2 is a more detailed cross section of a reactor core is accordance with an embodiment of the present invention, Figure 3 is a sectional view of fuel elements according to an embodiment of the present invention, Figures 4 to 10 show various isometric and perspective views of fuel elements in accordance with embodiments of the present invention, Figure 11 shows isometric views of a stem support beam for supporting the fuel elements illustrated in Figures 4 to 7, Figure 12 shows a bottom view and a side view of a source bulb assembly for use with a reactor according to embodiments of the present invention, Figures 13 to 15 show various views of a heat exchanger suitable for use with embodiments of the present invention, Figure 16 shows a block diagram of a control system suitable for use with embodiments of the present invention, Figure 17 shows a flow chart of the operation of a controller of Figure 16, Figure 18 shows a perspective view of an electricity generation system according to an embodiment of the present invention that may be mounted within a shipping container, Figure 19 shows orthographic views of the system of Figure 18, Figure 20 shows a graph of first law mirror function over time for various actinides, Figure 21 shows a graph of first law mirror function over time for various actinide, excluding plutonium Figure 22 shows the thermal output for a seven-layer reactor core at switch-on, Figure 23 shows a graph of the thermal output from a seven-layer reactor core at switch-off, Figure 24 shows a block diagram of an industrial application to high-temperature kilns, Figure 25 shows a block diagram of an application to propulsion systems, Figure 26 shows a block diagram of an application to domestic, district or commercial heating, Figure 27 shows a block diagram or a reactor with forced coolant convection, and Figure 28 shows a block diagram of a reactor using forced circulation of coolant. Figure A1 shows a graph of Nusselt number vs. P / D ratio, Figures A2 and A18 show properties of uranium tungsten alloy, Figure A3 shows properties of a uranium molybdenum alloy, Figure A4 shows properties of a uranium zirconium alloy, Figure A5 shows properties of a uranium niobium alloy, Figure A6 shows properties of a uranium rhenium alloy, Figure A7 shows properties of a uranium thorium alloy, Figure A8 shows properties of a tungsten molybdenum alloy, Figure A9 shows properties of a Tungsten-Rhenium alloy, Figure A10 shows a graph of neutron energy according to proton initial energy, Figure A11 shows particle production cross section, Figure A12 shows prompt neutron multiplicities, Figure A13 shows fast fission cross section for Th-232, Figures A14 and A23 show fast fission cross section for U-238, Figure A15 shows two nodal elements, Figure A16 shows a linear set of elements, Figure A17 shows a spherical source tunnelling effect, Figure A19 shows cubic elements all 1-unit length away, Figure A20 shows 12 elements at root 2 distance from the source, Figure A21 shows 8 elements at root 3 distance from the source, Figure A22 shows a neutron field mesh grid, Figure A24 shows a neutron field mesh grid for node two, Figure A25 shows a third neutron field, Figure A26 shows fourth law superposition as a component of total multiplication of the source, Figure A27 shows a fourth law superimposed source multiplier, Figure A28 shows a neutron ADS source, Figure A29 shows a graph of source multiplier for Th-232 over time, Figure A30 shows another graph of source multiplier for Th-232 over time, Figure A31 shows a second source multiplier for Th-232, Figure A32 shows a graph of U-238 multiplier over time, Figure A33 shows a second plane source multiplier for U-238, Figure A34 shows a mesh grid, Figure A35 shows immediate adjacent elements summed for Th-232, Figure A36 shows immediate adjacent elements summed for U-238, Figure A37 shows a rose core of fuel elements, Figure A38 shows a portion of fuel elements, Figure A39 shows the INES scale, Figure A40 shows code for flux equation, Figure A41 shows code for fission rate, Figure A42 shows performance of a three-layer core with Li-7 ignition, Figure A43 shows a 7-layer stage core, Figure A44 shows one tritosphere of a three-layer core, Figure A45 shows a block diagram of an electricity-generating system, Figure A46 shows a block diagram of another electricity-generating system, Figures A47, A38 and A49 identify the degree of shielding provided by various levels of ferro-boron content in concrete, Figure A50 shows average secondary neutron energy, Figure A51 shows neutron multiplicities in prompt fission of Thorium 232, Figure A52 shows the fission and capture cross section of Uranium 238, Figure A53 shows neutron multiplicities in prompt fission of Uranium 238, Figure A54 shows prompt fission neutron multiplicities in Plutonium 239, Figure A55 shows a side and top view of a three fuel-element design, Figure A56 shows a side and top view of a five fuel-element design, Figures A57 and A58 show a heat map from above and from the side with Thorium fuel, Figure A59 shows the rise time, Figures A60 andA61 show heat maps with Uranium fuel, Figure A62 shows the rise time, Figures A63 and A64 show heat maps for a Trinity core with Thorium fuel, Figure A65 shows the rise time, Figures A66 and A67 shows heat maps for a Trinity core with Uranium as the fuel, Figure A68 shows the rise time, Figures A69 and A70 shows heat maps for a Willow Run core with Thorium fuel, Figure A71 shows the rise time, Figures A72 and A73 show geat maps for a Willow Run core with Uranium fuel, Figure A74 shows the rise time, Figure A75 shows a Trinity Three Pipe Model, Figure A76 shows a Trinity five Pipe Model, Figure A77 shows the fluid velocity equation vector, Figure A78 shows the density of melted LBE versus temperature, Figure A79 shows the dynamic viscosity of melted LBE versus temperature, Figure A80 shows the Molecular Prandtl number as a function of temperature, Figure A81 shows Thermal Conductivity Of Molten Lead, Bismuth And lbe Versus temperature, Figure A82 shows a graph of heat transfer capability versus r.p.m. for the Trinity and Willow Run cores, Figure A83 shows a thermal cycle having twin Rankine with reheat and re-gen, Figure A84 shows a test core having a non-rotating natural convection impeller with Thorium fuel, Figures A85 and A86 show heatmaps for the test core, Figure A87 shows the output power of the test core, Figures A88 and A89 show the heatmaps for the test core with Uranium fuel. Figure 90 shows the output power, Figure A91 shows a rotating fuel micro reactor assembly, Figure A92 shows various views of the fuel elements for the micro reactor, Figures A93 and A94 show heat maps for Thorium fuel Figure A95 shows the power output, Figures A96 and A97 show the corresponding heat maps for Uranium fuel, Figure A98 shows the power output, Figure A99 shows a control system graph for a core, Figure A100 shows reactor ramp up for a Thorium 5-layer core, Figure A101 shows reactor ramp up for thorium trinity rose core, Figure A102 shows various views of an alternative fuel arrangement, Figure 103 shows locations for neutron sensors, Figure A104 shows a diagram of a steam cycle, and Figure A105 shows a block diagram of a control system. While some of the accompanying drawings include dimensions, these are to be interpreted only as suitable examples and are in no way limiting of the scope of the present invention. Figure 1 shows a block diagram of electricity generating system 100 including a reactor vessel 102, a cyclotron 112 and a compressor / generating system 116, 118. The reactor vessel contains a fuel arrangement comprising ribs of actinide fuel in a leaf arrangement 104. At a central point within the leaf arrangement is an ignition bulb 108 comprising ignition material that converts protons to high energy neutrons. Although the reactor is shown in section, the leaf arrangement 104 substantially surrounds the ignition ball. The cyclotron 112 has a beam line 114 connected to the ignition bulb 108. The beam line is a vacuum contained within a tungsten sheath. The reactor vessel is substantially filled with a coolant 106 that is solid at room temperature and a liquid at operating temperature. Towards the top of the reactor vessel is a heat exchanger 110 that is coupled to a further heat exchanger 116 for generating steam. The steam drives a turbine that in turn drives a generator 118. One suitable model of the turbine, at least for some embodiments of the present invention is a Siemens SST200. The reactor vessel 102 includes a container wall and core neutron shielding comprising Hastelloy® a nickel-chromium-molybdenum material with a very high melting point. Traditional reactor core vessel made of steel alloys are not suitable due to the high operating temperature of the present reactor, likely to exceed 1000ºC. Inconel 601 may also be used. Beyond this is shielding comprising a carbide layer followed by concrete mixed with boron and about 1m in length. One attractive feature of a reactor according to embodiments of the present invention is that a lead- based alloy coolant provides more than sufficient shielding for gamma rays. Assuming that 15cm of coolant between the fuel in the core and the reactor vessel, then the 1m concrete wall may be replaced with just 35cm of concrete at a ferro-boron content of 50%. Further material details are provided in the Appendix. The Actinide fuel may comprise Thorium or Uranium 238 which has been alloyed with another metal to increase its melting point, as well as other actinide elements such as Neptunium, Plutonium Americium, Protactinium, Curium and Californium. The fuel arrangement as a whole is designed and dimensioned to form a sub-critical core in the absence of additional neutrons emitted by the ignition bulb. This provides important controllability for the reactor and comprises a key safety feature. While three layers of fuel are illustrated any number of layers from 1 to 7 or more may be used, dependent upon the desired power output. The fuel is supported on a metal structure such as a tungsten structure described further below. Because the fuel arrangement comprises a sub-critical core, in order for the reactor to operate, a source of neutrons is provided at the centre of the fuel arrangement. In one embodiment this comprises Uranium-238 located within the ignition bulb 108. When bombarded with protons from the cyclotron, the Uranium emits neutrons which maintain the reactor core in the critical or super-critical operating region. In another embodiment, the ignition bulb contains uranium-238 and another material such as lithium- 7. This provides a “two-stage” ignition process in which the lithium is irradiated by the protons from the cyclotron to generate neutrons which then impinge on the uranium. This generates further neutrons at a suitable energy to maintain the nuclear reaction. The benefit of this arrangement is that the reactor will operate satisfactorily with lower-energy protons, meaning that a simpler and cheaper cyclotron or other particle accelerator may be used. For example, a linear particle accelerator may be used which is significantly cheaper than a cyclotron. A higher output will be required since the output of a linear particle accelerator is pulsed. Other materials besides Uranium and Lithium can be used as will be discussed further below. While a substantially hemispheric shape is shown, the ignition bulb may be replaced by other suitable shapes as dictated by the shape of the fuel arrangement such as a rod or cylinder. The core is filled with a coolant 106 which, in one embodiment, comprises lead-bismuth eutectic (LBE). The coolant is selected be a solid at room temperature, a liquid at the operating temperature of the reactor and also to remain a liquid at the melting point of the fuel. In other words, the boiling point of the coolant is preferably higher than the melting point of the fuel. This provides a key safety feature of the reactor because, should the fuel overheat and melt, there is no risk that the coolant will boil and endanger the containment of the core. As an additional safety feature, should the fuel melt, the reaction will become sub-critical and the core will cool. The boiling point of the coolant is preferably at least 50 ºC greater than the melting point of the fuel to provide a safety margin. The coolant is preferably in direct contact with the fuel but a heat-conducting barrier may also be placed between the fuel and the coolant. Other coolants are also suitable, including solder which has the benefit of being substantially lighter than LBE. Further alternative coolants are lead, tin and Babbitt type two. While a heat exchanger is shown that is within the reactor vessel, it may be preferred instead to provide a pair of ports on the reactor vessel comprising send and return paths for the coolant. The coolant may then be directed to flow through a heat exchanger external to the reactor vessel. This provides a simpler structure for the reactor vessel. The coolant flowing through the heat exchanger is used to heat steam for driving a turbine and generating electricity in known manner. In operation, the cyclotron is switched on and provides (via the ignition bulb) high energy neutrons to the fuel arrangement. A fast fission reaction then occurs in the fuel and the fuel starts to increase in temperature. Since the fuel is in thermal contact with the coolant, the temperature of the coolant starts to increase as well. Once the reactor reaches operating temperature (which may take several days), the coolant will travel around the fuel due to convection. The shape and arrangement of the fuel is preferably designed to promote this. Coolant at a higher temperature will rise towards the top of the reactor vessel where it will encounter the heat exchanger. This has the effect of reducing the temperature of the coolant which will then descend within the vessel. Convection currents then provide lower temperature coolant to the fuel elements and the cycle continues. Once the reactor has reached a critical or super-critical condition then the cyclotron will be switched on and off to maintain the reaction without permitting an uncontrolled heat transfer rate. The nature of the cyclotron and control thereof will be discussed further below. Many types of particle accelerators are suitable for use with embodiments of the present invention including: 1. Cyclotron (7 – 20 MeV for Li-7 target, 30 MeV – 200 MeV for direct to fissionable material targets) 2. Synchrotron (above 200 MeV – this is traditionally used for spallation, whose drawbacks are addressed by embodiments of the present invention but it would still be viable) 3. Linear accelerator (7 – 20 MeV for Li-7 target, 30 MeV and above for direct to fissionable material targets) Figure 2 shows a more detailed cross-sectional view 200 of a reactor vessel 200 according to an embodiment of the present invention. Wall shielding 202 is capped by a top cap 204 and contains the ignition ball 206 surrounded by fuel 208 supported by tungsten supports 210. The ignition ball is fed by a beam line sheath 212 containing a vacuum. A cyclotron input 224 is connected to the beam line 212 via a 90º magnet 214. Beneath the magnet is extra shielding 216 because gamma rays from the ignition ball / source bulb would otherwise have a direct view along the accelerator beamline. The shielding 216 comprises a boron-cement plate which is large enough to capture gamma rays in a “cone” of radiation from the source bulb. In operation, the coolant will rise by convention from a cool zone 218 to a hot zone 220 where it is cooled by a heat exchanger 222 and will then drop back down towards the base of the vessel. A coolant run-over zone is provided at 226. The beam line sheath 212 may be removed while the reactor is in its solid (dormant) state together with the ignition ball 206 to permit replacement of the ignition ball. This may be required after around 5 years of operation. The reasons for this requirement are explained below. Figure 3 shows a more detailed sectional view 300 of the reactor fuel and ignition ball together with coolant flows. The ignition ball 302 is coupled to a beam line 304 for receiving protons from the cyclotron (not shown). The fuel is arranged in substantially spherical layers around the ignition ball of which two are shown 306, 308. The fuel is supported by a tungsten support 310. Once the reactor is operational, coolant flows as shown by arrows 312 to cool the fuel layers and heat the heat exchanger (not shown). Two fuel layers or shells are shown for clarity but three are preferred in a uranium-fuelled reactor while 5 would usually be required for a Thorium-fuelled reactor. A heterogenous core may be provided whereby the inner elements of the fuel (closer to the ignition region) comprise Thorium or a Thorium-heavy alloy and the outer elements comprise uranium or a uranium-heavy alloy. Figures 4 to 10 show isometric views of fuel elements in accordance with embodiments of the invention. Figure 4 shows various views 400 of a part of a first layer of fuel, called a ring one leaf sub-assembly. Three of these would comprise the first layer of fuel. Each sub-assembly is 110º so three would occupy 330º, i.e. almost fully surrounding the ignition bulb (with a 10º gap between each of the sub- assemblies. The sub assembly comprises a number of elements, in this case 14. The individual elements are elongate members called ribs and, in one embodiment, have a height of 2cm and a thickness of 5cm. Further arrangements will be clear to the skilled person on consulting the Appendix below. By using a plurality of fuel members the fuel can adjust / warp in use to account for thermal stresses that may cause larger pieces of fuel to crack. The perspective view of the sub-assembly shows a mounting point 402 for connection to a stem support described below with reference to Figure 11. A support member 404 holds each of the ribs in place. The support member must have a melting point higher than the actinide fuel, preferably significantly higher than the fuel melting point to provide a safety margin. One preferred material is tungsten. The remaining sub-assemblies described with reference to Figure 5 to 10 have a similar support member. In some embodiments of the present invention, a single layer of fuel elements is used. Figure 5 shows various views of a part of a second layer of fuel, called a ring two leaf sub-assembly. Three of these would comprise the second layer of fuel with a 10º gap as for the first layer. The sub assembly comprises 15 ribs, reflecting its slightly greater size than the first layer sub-assembly. The perspective view of the sub-assembly shows a mounting point 502 for connection to a stem support described below with reference to Figure 11. Figure 6 shows various views 600 of a part of a third layer of fuel, called a ring three leaf sub-assembly. Three of these would comprise the third layer of fuel with a 10º gap as for the first and second layers. The sub assembly comprises 17 ribs, reflecting its slightly greater size than the second layer sub- assembly. The perspective view of the sub-assembly shows a mounting point 602 for connection to a stem support described below with reference to Figure 11. Figure 7 shows various views 700 of a three-ring tritosphere which comprises the sub-assemblies shown in Figures 4, 5 and 6. Mounting points 702 attach to the stem support of Figure 11 by means of pins (not shown). Three layers of fuel comprise a preferred embodiment of the present invention when the fuel is uranium-238 as this provides sufficient reaction rate and heat production for this fuel. Figure 8 shows various views 800 of a part of a fourth layer of fuel, called a ring four leaf sub-assembly. Three of these would comprise the fourth layer of fuel with a 10º gap as for the lower layers. The sub assembly comprises 17 ribs as for the third layer sub-assembly. The perspective view of the sub-assembly shows a mounting point 802 for connection to a stem support of the type described below with reference to Figure 11. Figure 9 shows various views 900 of a part of a fifth layer of fuel, called a ring five leaf sub-assembly. Three of these would comprise the fifth layer of fuel with a 10º gap as for the lower layers. The sub assembly comprises 25 ribs, reflecting its greater size than the lower layer sub-assemblies. The perspective view of the sub-assembly shows a mounting point 902 for connection to a stem support of the type described below with reference to Figure 11. Figure 10 shows various views 1000 of a five-ring tritosphere which comprises the sub-assemblies shown in Figures 4, 5, 6, 8 and 9. Mounting points 1002 attach to the stem support of the type shown in Figure 11. Five layers of fuel comprise a preferred embodiment of the present invention when the fuel is Thorium as this provides sufficient reaction rate and heat production for this fuel. While three fuel elements have been shown in each layer to substantially surround the ignition bulb, it will be understood that other arrangements such as 1, 2, 4, 5 or more are possible. Three elements provide a good compromise between complexity of support structure and ease of manufacture. While a substantially spherical arrangement of fuel has been described (bearing some resemblance to a beehive) other arrangements are possible, for example a substantially cylindrical arrangement. Figure 11 shows orthographic views of a stem support beam 1100 for holding the three ring tritosphere of Figure 7. Three such stem supports would be required to hold the three sub-assemblies of the tritosphere. The stem supports are attached to each of the fuel layers using a tungsten pin (not shown). A similar stem support beam would hold the sub-assemblies of five fuel layers as shown in Figure 10. The appendix includes a comparison of five actinide elements that may be used as fuel. Of these, Uranium-238 is preferred with Thorium as a runner up. One issue with Uranium is its melting point is quite low at 1132ºC and while it is preferred to operate the reactor at a higher temperature than this, it is perfectly possible to use pure U-238. In embodiments of the present invention, uranium is alloyed with Tungsten to increase its melting point. Note the constraint is that the melting point of the fuel preferably does not exceed the boiling point of the coolant. A uranium / tungsten alloy with 3% tungsten has a boiling point of 1650ºC, comfortably below the boiling point of LBE at 1660ºC. A uranium / tungsten alloy will generally require a binding agent between the two metals. Molybdenum and niobium are suitable, although alternatives will be apparent to the skilled person. To expand a little on the preference for tungsten, it is important to operate with a safe temperature "head room". Tungsten provides a drastic change to the melting point of Uranium with an insignificant change in atomic density of the fuel unit. Newtons cooling law states Q = h*A*(T2 -T1) Consequently, there will be a greater heat transfer with a larger temperature headroom. In addition, it provides an additional safety mechanism as well as boosting the overall heat transfer per unit area. Tungsten alloy would allow a run over event before damage and some elements within the core may operate at varying temperatures (bulb may operate above 1200ºC while edges of the core may operate at 800 ºC). Despite this, other materials besides tungsten to alloy with uranium to increase its melting point will be apparent to the skilled person. Alloys of the other 4 actinide elements with tungsten may also be used. This alloying permits the reactor to run on depleted uranium (i.e. nearly pure U-238 extracted from natural uranium as part of the conventional fuel-enrichment process). Since U-238 is minimally radioactive, the reactor requires very few shielding precautions in its dormant state. Even the decay products of U-238, Th-234 and Pa-234, only emit beta particles. This also addresses a problem of stockpiling of low-level nuclear waste. Alternatives to tungsten include Rhenium, Tantalum, Molybdenum, Niobium and Zirconium. However, these are less desirable as the uranium alloy must contain a greater proportion of these materials to achieve the same melting point (rhenium at 25%, zirconium and niobium at 35%). This is less desirable since the fuel will then contain a lower proportion of uranium with negative consequences for reaction rate. Each of the fuel elements is self-sustaining in terms of the nuclear reaction and this, as well as determining the arrangement of the fuel and ensuring the criticality thereof, will be discussed in more detail in the Appendix. Another approach to actinide fuel is to provide a doped fuel mixture. Figure 20 shows a graph of first law mirror function for the most common actinides. The excluded elements are not available in any significant quantity due to their half-lives, or, in the case of actinium due to having an unknown fission cross section. It will be seen that while all of the common actinides exhibit an exponential growth in the function over time, plutonium far exceeds that of any of the other isotopes. While thorium has a fast fission cross section of 0.2 barns and uranium 0.6 barns, plutonium has a fast fission cross section of a few barns. Figure 21 shows a graph of the first law mirror function with plutonium excluded and an expanded vertical axis to better illustrate the relative performance of the other actinides. These graphs illustrate that doping of actinides such as Th-232, Pa-231, U-238, Np-237, Am-241, Cm-246 and Cf-250 with some plutonium (or other actinide with a higher cross section) will improve performance, particularly at reactor start-up. Against this, of course, are the known issues with plutonium. Figure 12 shows a view from below and a sectional view on the line A-A of a source bulb assembly 1200 for use with a reactor according to embodiments of the present invention. The bulb has an external cylindrical wall 1202 that is closed off by a hemispherical portion 1204. An internal wall 1206 isolates a cavity 1208 within the hemispherical portion. This cavity contains the uranium 238 source of neutrons that sustain the fast fission reaction in the core of the reactor. The wall 1206 comprises a smaller hemispherical portion 1210 that protrudes into the cavity 1208 at the centre of the cylindrical wall. Fitting snugly within this portion 1210 is another hemispherical member 1212 defining another cavity 1214. This cavity contains the first ignition material such as Lithium 7. A beam line 1216 defined by a smaller cylindrical wall 1218 is provided within the cylindrical wall. Protons from the cyclotron 112 (Figure 1) travel along this beam line and irradiate the Lithium 7. In response the Li-7 emits neutrons in a reaction described fully in the Appendix. These neutrons pass into the cavity 1208 containing uranium which in turn provides further neutrons at a high enough energy to sustain the fast fission reaction in the core. The ignition bulb also includes a window 1220 through which the protons from the particle accelerator have to pass to reach the Li-7 material. Ideally, this window reduces the energy of the protons by the smallest possible amount. The window is preferably titanium which imposes a minor energy reduction on the protons (e.g. a proton from a 15MeV cyclotron may still possess an energy of 13Mev on target. However, in some embodiments, the conduction of heat from the reactor core to the ignition bulb will cause the temperature of the titanium to rise too high. In those cases, the window may comprise tungsten which will impose a greater reduction in proton energy – for example from 15MeV to around 9MeV. Li-7 has a peak reaction at 7MeV (see Appendix) so a tungsten window may be used with a 15 MeV accelerator. The larger atoms discussed below have peak reactions in the 11 – 13MeV range so a tungsten window is likely to slow the reaction rate slightly. The Lithium-7 proton bombardment is a reaction that would create a circular decay function (Li7 + p = Be7 + n, Be7 decays back into Li7 by electron capture). Effectively it’s a target that replenishes itself with a 53-day half-life and would drastically extend the replenishment timeframe for the source bulb. Lithium’s low atomic weight also means that a small particle accelerator may be used because the coulomb barrier for a proton interaction with the target is lower. This provides a very good life for the Li-7 material and contributes to excellent reactor up-times. The full reaction is explained in the Appendix. There are, however, other possible reactions that can occur and these act to degrade the quality of the Li-7 material over time. Consequently, it is anticipated that this material will need to be replaced in a period of approximately 5 years to ensure continued good performance. Since this is much less than the expected lifetime of the reactor (up to 100 years but more typically around 20), a means of replacing the Li-7 material is provided. The hemispherical member 1212 containing the Li-7 can be removed from the reactor without disturbing the coolant, fuel or neutron- providing material in the cavity 1208. To do this the reactor is shut down and allowed to return to ambient temperature, the proton feed from the cyclotron is disconnected and the hemispherical member 1212 can be withdrawn. While the cavity 1214 has been disclosed as containing Li-7, other suitable materials will be apparent, with the general constraint that they provide a p-n reaction whereby the daughter element decays back into the parent element through beta decay or electron capture. While there are too many such reactions to list, some are more suitable than others. These include: 1. The reaction that creates Florine-18 is Oxygen-18 irradiated by protons with the creation of a neutron as a by-product. Florine-18 decays into Oxygen-18 – creating the same circular decay function as Lithium-7 – but with a more expensive target. Oxygen-18 has a natural abundance of 0.2% but, due to its extensive use in the medical industry, the bulk cost has reduced drastically in recent years to around 200 USD / gram. 2. Nitrogen-14 bombardment with deuterium particles produces a neutron and Oxygen-15, Oxygen 15 rapidly decays into Nitrogen-15 which is stable. Hitting a newly formed Nitrogen-15 with the same reaction would likely create Oxygen-16 and another neutron. This reaction scheme requires a deuterium accelerator – increased cost – and deuterium particles – an isotope of hydrogen found in “heavy water”. A similar reaction exists with a Nitrogen-15 target and proton bombardment to create a neutron and Oxygen-15 which is within the reach of a 15 MeV particle accelerator, but the drawback is Nitrogen-15 has a natural abundance of 0.33% - marginally increasing the cost, but there’s viability for it. The Oxygen-15 decay into Nitrogen-15 is another circular decay function. 3. Nickel-64 proton bombardment creates Copper-64 and a neutron with Copper-64 decaying back to Nickel-64 via a dual-branch decay where one branch leads back to Nickel-64 and another leads to Zinc- 68. The branch decay back to Nickel-64 only happens 61% of the time, with the remainder going back to Zn-64. Although the Nickle-64 reaction has a peak production at 18 MeV, a 15 MeV cyclotron is still viable for this reaction. There’s room for viability in this, but once again, Nickel-64 has a low natural abundance and doesn’t share the same industrial backbone as Oxygen-18. High purity Nickel-64 can be purchased at around 48200 USD / g and about 9grams would be required for at least some embodiments. 4. Zinc-68 proton bombardment creates Gallium-68 and a neutron, much the same as the Nickel-64 reaction, at a similar cost but without the branch decay (100% decay of Gallium-68 back into Zinc-68 in another circular decay function). The cost of Zinc-68 is a 10thof that of the Nickel-64 target at 4850 USD / g making it a better choice than that of the Nickel-64 target. This reaction is also viable under a 15 MeV cyclotron. 5. Cadmium-112 under proton bombardment creates Indium-111 with a p-2n reaction. Indium-111 decays back to Cadmium-111 – so this isn’t a perfect circular reaction – but Cadmium-111 is also a viable target for a singular p-n reaction within the same energy spectrum creating a circular decay function with Indium-111. This reaction is viable at a 15 MeV cyclotron but is beginning to become ineffective at this atomic weight. Natural Cadmium may be used and a wide variety of p-xn reactions will occur to create various Isotopes of Indium that all decay back into Cadmium. As will be seen from the Appendix, only a small proportion of impinging protons actually participate in a reaction with the Li-7 (or other material) but the “unused” protons cause no difficulties as follows. There are three possible outcomes for a proton that does not generate a neutron as described: complete escape and into the core via no collision due to the semipermeable nature of matter at that velocity; entrapment within the Lithium-7 body due to a scattering reaction and “bounce back” into the beam line. In the first and second case, the proton is floating within the Uranium / Lithium and is of no consequence to the system - there simply isn’t enough of these protons to ever create a genuine problem. There will be of the order of 2.5E15 protons entering the source bulb every second so it would take 241 million seconds (2800 years) before 1 gram of hydrogen has entered the system under constant use. The third case, where hydrogen fills the beam line, is slightly more consequential as it may reduce the efficiency of the beam line over time, but this will also provide a trivial effect. While a two-stage neutron generation process has been described, the ignition bulb shown in Figure 12 may readily be adapted to provide the one-step neutron generation using, for example, uranium 238 and a higher power cyclotron, having an energy on target of at least 26.8 MeV. In practice, to address efficiency issues as discussed, this requires a cyclotron having an output in the region of 35MeV. Described embodiments of the invention use LBE as the coolant and, as discussed further in the appendix, this is an excellent material for the purpose. LBE is a eutectic alloy of lead and bismuth in the atomic proportion 44.5% and 55.5% respectively. It has a boiling point of 1660ºC which suits the current application very well. However, it does have a drawback and that is its density at around 13g / cm3. This may cause problems in a reactor that is designed to be mobile. As an alternative, tin / lead solder (in, for example, proportion 63% / 37%) also functions well as a coolant and has a much lower density than LBE at 8.6 / cm3. It is also cheaper than LBE. This may thus be a preferred coolant in a smaller, portable reactor. Some of the possible coolants have the following advantages / disadvantages. Solder contains tin, which has a very low cross-section of interaction with neutrons but a smaller atomic mass than bismuth – the effect is that tin has a lower chance of having a neutron collide into it, but a larger effect on the neutron when it does collide. The scattering reaction slows neutrons down in a moderation process. This may take the neutrons out of the fast spectrum, which in a fast reactor is something to avoid. Solder’s thermal properties, when we take into account the density change, is comparable to LBE. Solder’s downside of slight moderation comes more into effect at a large scale facility as neutrons travelling to the 7thring would now have to pass through so much coolant that there would be a larger effect. Although LBE is the standard for fast fission, Solder was posed as a coolant in the 1970s but was overlooked for that size reason. It works well in a smaller core such as certain embodiments of the present invention. Babbitt is another possibility that works, but it’s less attractive than LBE or solder due to the low lead content. There are very few consequences of tin being bombarded by neutrons. Tin is unique in that its stable isotope range is very wide; 112, 114, 115, 116, 117, 118, 119, 120, 122. If it absorbs a neutron, it will simply move up the chain of stable isotopes. The cross section for absorption is also very low in the fast spectrum. The unstable isotopes, 113 and 121, are on opposite ends of the spectrum which also helps. For 113 to exist, 112 needed to absorb a neutron and it only has a natural abundance of 0.97%. For 121 to exist, it would require 120 (natural abundance of 32%) to absorb a neutron or a multi-stage absorption of the lower isotopes.121 decays into Antimony-121 which is stable and part of Babbitt type 2. You can follow a multi-stage absorption on that line and you'll land on a chain of stable tellurium until 127. Figures 13 to 15 show an embodiment of a heat exchanger for use with a reactor according to embodiments of the present invention. Figure 13 shows a side view and a view from below of a fuel arrangement and a heat exchanger according to an embodiment of the present invention. A fuel arrangement 1302 is shown mounted beneath a heat exchanger 1304 comprising 10 layers of piping in which adjacent layers have pipes arranged orthogonally. The side view illustrates a suitable spacing for the fuel core and the heat exchanger. The view from below gives a good sense of the relative size of the core and the heat exchanger – the heat exchanger has a larger diameter than the core to ensure efficient capture of the heat from the circulating coolant (not shown). Figure 14 shows an orthographic and an isometric view of the heat exchanger 1400. The orthographic view shows that there are 13 heat conducting pipes in each orthogonal direction. The isometric view shows more clearly the ends of the pipes which are linked together by short U-shaped pipes to provide a serpentine path through the heat exchanger. The heat exchanger is preferably constructed from Hastelloy® a nickel-chromium-molybdenum material with a very high melting point although Inconel 601 may also be used. Figure 15 shows a single layer of the heat exchanger showing the paths of the parallel cooling pipes 1502. This figure also illustrates the modular nature of the heat exchanger, in that each of the layers may be identical to facilitate manufacture. It also facilitates variation of the capacity of the heat exchanger by selection of the number of layers used. As an alternative to a heat exchanger located within the reactor vessel, a heat exchanger may be located outside and be coupled to receive and return coolant from within the reactor. This may usefully reduce the size and weight of the reactor vessel, important considerations for a mobile reactor. Figures 22 and 23 show the power generated by a 7 layer core at switch-on and switch-off respectively. The graphs show the power developed by each ring separately and also by the ignition bulb. As can be seen from Figure 22, the core takes several hours to heat up but, as shown in Figure 23, the corresponding cool down (once the particle accelerator is switched off) is very rapid. This provides an excellent level of safety for embodiments of the invention. In a preferred embodiment of the present invention, the entire electricity generating apparatus is mounted in a standard 40ft shipping container. Figure 16 shows an isometric view of such an arrangement 1600 mounted on the floor 1602 of a shipping container. A cyclotron 1604 is mounted between two reactor cores 1606 and 1608. This exploits the fact that cyclotrons generally have two outputs so makes more efficient use of this expensive component. Having two reactor cores also provides redundancy and allows the use of smaller cores for an equivalent energy output. Between the cores is an Electronic Control Unit (ECU) / transformer 1610. Reactor core two 1608 is coupled to a Siemens SST-200 turbine 1610 which in turn is coupled to transmission 1612. The transmission is coupled in turn to an AC generator 1614 and an intercooler 1616. Beneath the turbine 1610 are a pair of compressors 1618, 1620. This provides a 20MWe system. While the ECU is shown as located between the two cores, this may necessitate an undue amount of insulation and cooling (since the cores run at around 1000ºC). An alternative arrangement may place these sensitive electronic components in a module that can be removed from the container after shipping. The module is connected to the arrangement by an umbilical cable but located, in use, in a less hostile environment. Figure 17 shows an orthographic view 1700 of the arrangement of Figure 16 showing the cyclotron 1704 is mounted between the two reactor cores 1706 and 1708. Between the fuel cells is the Electronic Control Unit (ECU) / transformer 1710. Reactor core 1708 is coupled to the Siemens SST-200 turbine 1710 which in turn is coupled to the transmission 1712. The transmission is coupled in turn to the AC generator 1714 and the intercooler 1716. Beneath the turbine 1710 are the pair of compressors 1718, 1720. An embodiment of the invention thus provides an electricity generating system that meets the size and weight restrictions of a standard shipping container. Given the extensive Worldwide network of facilities for shipping and handling containers, this gives the generating system an unparalleled flexibility in terms of deployment. Figure 18 shows a block diagram of a control arrangement 1800 for use with the embodiments of the present invention. A reactor core 1802 comprises a number of sensors, such as neutron flux sensors 1804, 1806 embedded in the reactor shielding. Temperature sensors 1808, 1810 are also provided. These sensors are coupled to a controller 1812 which is also connected to control a cyclotron 1814. Figure 19 shows a flow chart 1900 illustrating the operation of the controller 1812 (Figure 18). The operation starts at 1902 and at 1904 sensor outputs from the neutron flux sensors and the temperature sensors is collected. At 1906 the neutron flux sensor outputs and the temperature sensor outputs are compared with predetermined safe values and, if the values are within acceptable limits, processing proceeds to 1908 in which the controller activates the cyclotron (or allows it to remain activated, if it is already on). If the values are not within acceptable limits, the control returns to step 1904 via step 1910 in which the cyclotron is deactivated (or remain deactivated if it is already off). After step 1908, control reverts to step 1904 at which the sensor outputs are collected again and the process repeats. A more sophisticated control strategy may be applied, for example one that uses hysteresis to prevent unduly frequent switching of the cyclotron. That is to say that the flux and / or temperature levels at which the cyclotron is activated are lower than those at which the cyclotron is deactivated. While only temperature and neutron flux sensors have been described, other types, quantities and locations of sensors may be deployed, in particular gamma ray sensors. A control strategy may be deployed that uses an algorithm to combine various sensor inputs to make on / off decisions. Such a strategy may be arranged to take account of sensor failure (neutron flux sensors occupy a rather hostile environment) by analysing outputs from a plurality of sensors and, taking account of their location and typical relations in their readings, determine whether a sensor output is trustworthy. In addition to the control strategy described, the reactor may be provided with a “shut-down” mode in which sensor levels that do not reduce when the cyclotron is deactivated result in no further activation of the cyclotron until troubleshooting has taken place. Figure 24 shows a block schematic diagram 2400 of an application of the reactors comprising embodiments of the present invention. Certain industrial processes require materials and components to be treated at very high temperatures. For example, carbon fibre brake discs for performance cars require treatment for several hours at a temperature of approximately 700 degrees Celsius as part of their manufacture. Heating an appropriate kiln for this task using electricity or gas is an extremely expensive undertaking. Using a reactor as previously described to directly heat (i.e. without going via an intermediate electrical step) is an attractive, cost-effective alternative. The figure shows a reactor 2402 driven by a particle accelerator 2404. The reactor is coupled to a steam heat exchanger 2406 that transfers heat from the reactor coolant to superheated steam (also referred to as working fluid) at a temperature of around 1000 degrees Celsius. The steam is piped to a kiln 2408 and is arranged to heat the kiln via pipework 2410 within the kiln. The pipework effectively comprises a steam-to-air heat exchanger. This provides enough thermal energy to the kiln to maintain the temperature of 700 degrees Celsius. The skilled reader will appreciate that other arrangements for transfer of the heat will also be suitable. The kiln includes at least one temperature sensor 2412 whose output is coupled to a controller 2414 arranged to control the operation of the accelerator 2404. This feedback loop maintains the temperature of the kiln at the desired level. The reactor 2402 may comprise any and all of the features disclosed herein, for example with regard to the number of fuel elements, fuel materials, single or two-stage ignition, coolant material and so on. Figure 24 also shows an optional turbine / generator 2416 which may be as described previously and an optional further kiln 2418. This arrangement coverts the superheated steam from the heat exchanger 2406 to electrically heat kiln 2418. Some industrial processes require higher temperatures than the direct heating of kiln 2408 can achieve. For example, the carbon fibre brake discs discussed above also need to be treated at around 1600 degrees Celsius for a short time later in their manufacture. However, the reactor 2402 cannot generate such high temperatures due to operating temperature limits of the fuel and the coolant. By providing a turbine / generator arrangement 2416, a reactor according to embodiments of the present invention may also be arranged to power the higher-temperature kiln. The turbine / generator also provides the electrical power to the accelerator 2404. It may be desirable, even in the absence of the further kiln, to provide the turbine / generator arrangement to provide electrical power to the accelerator 2404. Subject to generating sufficient electrical energy to drive the accelerator 2404, the output of the reactor 2402 may be adjusted and the balance of heat output between the first kiln and the turbine / generator adjusted to operate the reactor to meet the energy demands of both kilns. The arrangement shown in the figure may be modified to provide a source of heat to other industrial processes such as chemical processes, drying processes, extrusion processes and refining or cracking of hydrocarbons. Broadly speaking, this arrangement is applicable to any industrial process that requires heat but particularly those that require temperatures above 400 degrees Centigrade. Figure 25 shows a block schematic diagram 2500 of another application of reactors according to embodiments of the present invention, namely a propulsion system for a vehicle. A reactor 2502 driven by an accelerator 2504 is coupled to a steam heat exchanger 2506, in turn connected to a turbine 2508 to convert the thermal energy in the superheated steam to mechanical energy in a rotating shaft 2510. The shaft is coupled to an optional gearbox 2512 and to a propeller or screw 2514. A speed sensor 2516 provides feedback to a controller 2518 which in turn controls the particle accelerator 2504. Also shown in the figure is an optional arrangement of a generator 2520, motor 2522 and propellor 2524. The output of the generator is connected to supply electrical energy to the accelerator 2504. The further motor and propellor may be replaced by a hybrid drive arrangement that uses the electricity generated by the turbine / generator 2520 to drive the propellor 2514. While an arrangement with a propellor or screw is shown in the figure, the propulsion system may equally be applied to land-based vehicles such as trains. Also, while a single propellor is shown in the figure, multiple propellers may be employed. The presently-disclosed reactors have a particular benefit when applied to water- and land-based propulsion systems which is that the reactor may be quickly placed in a standby or idle mode by reducing the output of the accelerator 2504. Appendix figures A98, A99 and A100 together with their descriptions illustrate graphs of output power against time for such arrangements. The reactor may thus be operating normally at a desired power output but when the drive to the particle accelerator is reduced the output power of the reactor reduces very quickly to around 1MWt. While this may appear to still be a significant amount of heat, it may very easily be dissipated to water surrounding a vessel or even to air around a land-based vehicle. The controller is arranged to maintain the reactor at this output level until more power is required and the accelerator output is increased. The reactor can attain full power output quite quickly from an idle state. Although the resumption of power output is slower than the reduction, this is seldom an issue in practice. For example, a ship leaving port will be forced to travel more slowly until it is in open water and the speed of trains is often constrained while they are in urban areas (i.e. near the station). An alternative to placing the reactor in an idle mode comprises selling electricity to the grid. When a diesel-powered ship or boat is in port, it is usually connected to a land-based source of electricity usually called shore-power so that no engine is required to run on the ship or boat. In the present case, such a connection may be used in reverse, to supply electricity to the local grid. This may provide a useful source of income to cover or offset berthing fees for boat owners. Likewise trains sitting idle overnight could also provide electricity to the grid. Although nighttime has traditionally been a time of low electricity demand in most countries, the increase in the number of electric cars being charged at this time should provide a ready demand. Figure 26 shows an arrangement 2600 in accordance with embodiments of the invention for heating of domestic premises, district heating systems and commercial property heating systems. A reactor 2602 is coupled to a first heat exchanger 2604 and a second heat exchanger 2606. The first heat exchanger is connected to a turbine 2608 and a generator 2610 to generate an electrical output. This output may be coupled to a particle accelerator (not shown) to drive the reactor as previously discussed. It may also be arranged to provide electricity to other consumers such as an electricity grid. The second heat exchanger 2606 is coupled to a working fluid path 2612 comprising send 2614 and return 2616 paths. The working fluid path may pass through a building, a number of buildings or an entire neighbourhood. Multiple fluid paths may be provided to serve different locations and / or different classes of consumers. Heating consumers such as a house 2618, an apartment block 2620 or commercial premises 2522 are arranged to derive heat from the working fluid path 2612. This will typically be via a further heat exchanger as is known from district heating systems. The reactor 2602 is controlled by a controller 2624 in response to a temperature sensor 2626 arranged to detect the temperature of the working fluid in the working fluid path. Alternatively, or additionally, other sensors may be provided as inputs to the controller such as temperature sensors in the heated buildings. Figure 27 shows a diagram 2700 of a forced-convection reactor which uses the fuel as an impeller. A reactor vessel 2702 contains actinide fuel 2704 of any of the disclosed varieties mounted to a hollow shaft 2706 which is driven by a motor 2708 under control of a controller 2710. The controller is responsive to at least one temperature sensor 2712 or other suitable sensors for detecting the state of the reactor. At the top of the vessel 2702 is a heat exchanger 2714 and the vessel is filled with a coolant 2716. External connections to the heat exchanger, particle accelerator and further control connection are omitted for clarity. The ignition region (not shown) is housed within the hollow shaft 2706 and receives particles from a particle accelerator via a path 2718 as previously discussed. In operation, the motor 2708 rotates the actinide fuel 2704 to force convection within the coolant 2716. The shape of the fuel elements is preferably selected to enhance the convection flow. Further details of suitable fuel elements are given in the Appendix. By forcing convection within the reactor vessel, the reactor performance and control are enhanced. Figure 28 shows a diagram 2800 of a forced-convection reactor using an external pump. A reactor vessel 2802 contains elements of actinide fuel 2804 surrounding an ignition region 2806. Further details of the fuel elements are provided in the Appendix. The ignition region is supplied, as before, by a particle accelerator and proton path (not shown). The vessel also contains a heat exchanger 2812 towards the top of the vessel. A pump 2814 is provided externally of the vessel and connected between the send pipe 2816 and a return pipe 2818. The send line is connected towards the top of the reactor vessel and the return pipe is connected towards the bottom of the reactor vessel. The pump is controlled by a controller 2820 responsive to one or more sensors such as a temperature sensor 2822. In one embodiment the pump is an electromagnetc pump as described in“Optimization of an extra vessel electromagnetic pump for Lead-Bismuth eutectic coolant circulation on a non-refueling full-life small reactor” by Tae Uk Kang et. al. published in the journal of Nuclear Engineering and Technology 20223919-3927 (Elsevier). Electromagnetic pumps do not operate with high efficiency. However, in this application this is not a major concern as waste heat generated by the pump will mostly be returned to the reactor and / or coolant and will thus be used by the reactor’s thermal cycle. In operation, the pump operates to move coolant from the top of the reactor vessel (where the coolant will generally be hotter) to the bottom of the reactor vessel (where the coolant will generally be cooler). As for the embodiment shown in Figure 27, the reactor performance and controllability are enhanced by the addition of forced coolant circulation. An optional heat exchanger 2824 may be placed in the send or return pipes to permit the extraction of heat from the reactor either to extract energy or to improve cooling (or both). APPENDIX Embodiments of the present invention are based upon an understanding that, instead of spallation, it is possible to instead target the reactor fuel directly. The following analysis illustrates the viability of this principle. The European Spallation source uses a linear accelerator, well over a kilometre in length, to induce spallation – the shattering of an atom into many smaller pieces – within the GW range of the lead coolant of a fast fission core. While the European spallation source represents a large step forward for accelerator-driven design, it is by no means a perfect system. The enormous complexity and size of a linear accelerator designed to allow a proton to reach a fractional percentage of the speed of light are immense. Unattainable or economically non-competitive may be a more apt description for the prospects of wide adoption of such a system, regardless of its technological leap. However, a lower energy particle accelerator is capable of generating an ejection of neutrons from an actinide element, generating proton-induced fission as a direct event post this ejection. The minimum for such a reaction is 26.5 MeV – a stark reduction from the multi-GW requirement of spallation. This new minimum allows for the adoption of more widely available cyclotrons, widely adopted within the medical industry, as a suitable alternative generator. In addition, embodiments of the present invention exploit the use of a two-stage ignition of a light atom target – Lithium-7 – to generate fast neutrons for adjacent fuel pieces to further reduce the size of the particle accelerator needed to power the reactor system. Atom targets formed of other elements are also suitable. Regarding the fuel, Uranium-238 metallic alloy is a preferred fuel to solve several surface-level issues; increased heat transfer capacity to the coolant with a higher operating temperature and increased fuel density for a centre point source coming from the accelerator beam. One key element of the following analysis is that fuel elements individually are to be evaluated for a “local” criticality, rather than previous approaches which regarded criticality as a state for the entire core. As background to the following analysis, we discuss some key data regarding actinide elements, coolants, fuels and Lithium 7 as an ignition element. Proton-induced fission on actinide nucleii In 2008 the Institut de Physique Nucléaire, Université catholique de Louvain, Louvain-la-Neuve, Belgium and the Institute of Nuclear Physics, NCSR “Demokritos”, Athens, Greece conducted a research study into the proton induced fission reactions of a number of actinide elements, namely, 232Th, 238U, 237Np, 239Pu, and 241Am. Key focus points of the research study included: A. The proton fission cross-section according to proton energy values, B. Number of fission neutrons of the collision-induced fission at proton energies of 26.5MeV and 62.9Mev, C. Neutron dispersion patterns post fission. The results are captured in Table 1. For further clarity, the above data point for “total neutrons per interaction” is an average summation of all neutrons which include immediate neutrons of the proton, x-neutron reaction as well as fission reaction neutrons. The fission reaction is induced due to the increased energy imparted onto the target atom as well as the loss of the neutrons caused by the proton bombardment reaction. The amount of neutrons pre-fission and post are heavily dependent on the target atom. While the research paper and simulation done under the study had a rough conclusion on the total number of neutrons per interaction, the distribution of these neutrons was far less conclusive on the lines of pre- and post-scission neutrons. This discernment is of great importance as the pre-scission neutrons induced by bombardment have far greater energy values than that of the post-scission neutrons. While both are within the fast spectrum, the pre-scission neutrons carry additional kinetic energy depending on the proton MeV value at collision, and in doing so would place these neutrons in the upper echelon of neutron energy spectrum within a reactor. Lead Bismuth Eutectic Coolant Regarding suitable coolants, Lead-bismuth eutectic is a eutectic alloy comprising 45% Lead (Pb) and 55% Bismuth (Bi). The alloy itself is often abbreviated to LBE. Some highlighted characteristics of LBE from a 2015 analysis by the Nuclear Energy Agency are captured in the following table: A. LBE Properties LBE is an excellent coolant for high-temperature applications as – unlike water – does not require additional pressurisation to adequately be used as a working fluid at high temperatures. LBE also serves as a coolant that does not moderate due to its exceptionally low scattering and absorption cross-section and heavy elemental nature. For context, if a neutron were to be absorbed by Bi-209 it would decay into Po-210 which is a highly radioactive alpha emitter (with Pb-206 as a daughter) with high specific heat output. If Pb-207 would absorb a neutron it would take a multi-neutron absorption to become Pb-209 which decays rapidly to Bi-209 and the above interaction with Bismuth would simply reoccur in an infinite cycle. The thermal cross-section is also just as comparably low as the fast neutron spectrum leading to nearly no effect on the behaviour of neutrons within the system – an excellent primary core coolant for fast fission systems. The report from IAE on LBE is a complete summation of all of the known properties of LBE and the available heat transfer technical data. The handbook concludes an immense difficulty and lack of knowledge on pool thermo-hydraulics. LBE behaves similar to a liquid metal with a low Prandtl number of between 0.041 at its melting point and 0.007 at 900 degrees Celsius. Effectively, the heating dynamics of a pool of LBE should instead be viewed as a highly conductive unit. Establishing heat transfer dynamics for a fully three-dimensional solution using computational fluid dynamics methods based on the Navier-Stokes equation is the preferred method of evaluation. The report is highly detailed for heat transfer dynamics with the use of cylindrical pipes – the most likely case for heat transfer units – and suggests similar performance in the use of LBE in a shell and tube type heat exchanger in a turbulent flow dynamic. Figure A1 shows the Nusselt numbers in fully developed flow in rod bundles arranged in a triangular array as a function of the Peclet number Pe and P / D for constant wall heat flux. Uranium Alloys for High Temperature Applications Regarding fuel, a key component in reactors according to embodiments of the invention is the density of uranium. It is of great importance that as much fissionable material as possible is located as close to the source plate as feasibly possible. The obvious choice then is to use Uranium metal, however, due to the metal’s lower melting point, this would create a structural issue as the core would begin to melt down. Natural Uranium metal has a melting point of 1135°C or roughly 1400K which would greatly limit the operating domain of the LBE coolant. It is, of course, possible to operate the reactor with pure, or nearly pure, uranium 238 but the lower operating temperature would impact efficiency. A novel solution to this is deployed in some of the embodiments of the present invention, namely the use of a Uranium-Tungsten alloy. Even a small percentage of tungsten incorporated into the Uranium metal greatly increases the operating range of the reactor. Figure A2 is a phase diagram created by Dr Wang of the Department of Materials Science and Engineering, College of Materials, and Research Centre of Materials Design and Applications, Xiamen University, Xiamen, PR China. Even a moderately low atomic percentage of Tungsten drastically increases the melting point of Uranium. A 3% atomic abundance of Tungsten within the Uranium metallic alloy would increase the melting point to roughly 1650°C – which would match that of the LBE boiling point. Newton’s law of cooling, as explained below, means that a margin of just 10º is adequate as the fuel will melt before the coolant is at risk of boiling. Even with no margin, a small amount of localised boiling of the coolant is permissible as discussed further below. However, one issue with the uranium tungsten alloy is a failure to bond and, thus, having the uranium separating from the tungsten. A simple solution lies within the method used to alloy the metal; powder bed fusion, with its high-temperature laser, has a tendency to create different bonding structures within two different metals. Other materials that may be used as alternatives or in addition to Tungsten are Molybdenum, Zirconium, Niobium, Rhenium and Thorium. These are now discussed. Figure A3 is a phase diagram for a Uranium-Molybdenum alloy. Uranium has a better bonding effect with the molybdenum than tungsten but requires a higher percentage of the added alloy – in this case, Molybdenum –to reach a melting point of 1650˚C (around 40% molybdenum) which would severely impact reaction rates within the alloy. Meaningful improvements to the alloy melting temperature only begin at 33%. Figure A4 is a phase diagram for a uranium zirconium alloy. Zicronium’s melting point is low and, thus, requires an unsatisfactory ratio; roughly 60% zirconium is required to achieve a melting point of 1650˚C. Figure 5A is a phase diagram for a uranium niobium alloy. Niobium underperforms in comparison to the other alloys within this section. At least 70% of the alloy would need to be Niobium to create an alloy having a melting point of 1650˚C. Figure A6 is a phase diagram for a uranium rhenium alloy. Rhenium performs well with only Tungsten able to outperform in terms of effect-per-mass-unit added. 25% Rhenium is significant enough to produce an alloy having a melting point of 1650˚C. Figure A7 shows properties of a uranium thorium alloy. This approach binds Uranium with the lower reacting Actinide to form a pure fast-fission alloy. The alloy would benefit from Thorium’s higher melting temperature (1755˚C) while having the potential to not heavily impact reaction rates due to the secondary element added to the matrix – thorium – also being able to fission under the bombardment of fast protons. Alloys of Uranium – Thorium has been well studied under the 1960s breeder reactor program (thermal neutron breeder) to enhance the efficiency of the use of Uranium. Further approaches comprise three-metal systems. One such system is a Uranium, Tungsten and Molybdenum triple system exist. Since Molybdenum can bind to Uranium fairly well, this system effectively uses the molybdenum as a ‘bridge” between the other two metals. The suggestion is to construct a system in which Uranium comprises 92% of the alloy with the remaining 8% evenly distributed between Tungsten and Molybdenum. Figure A8 shows phase diagram of tungsten-molybdenum alloy. Another three-metal system is to use a Rhenium binder. However, Tungsten-Rhenium produces an unstable alloy with more even distributions (Ekman, et al., 2000, Figure A9). While in a bcc configuration (less than 30% Rhenium) and above a critical point (Rhenium percentage greater than 70%) the alloy is stable. The phase diagram for the alloy also shows a negatively impacting relationship between the two metals which suggests the elements do not favour bonding together. In this, Rhenium may fail to produce a binder to Uranium-Tungsten if the Uranium cannot balance the system. An alternative is to use a zirconium binder. Zirconium additions exert a pronounced effect on the alloy structures, a wide variety of structures being obtained as the uranium and zirconium content and the heat treatment are varied. In alloys quenched from elevated temperatures, the uranium is present as a gamma solid solution. On slow cooling, the gamma transforms to the intermediate uranium- zirconium delta phase. Niobium additions to the zirconium-containing alloys stabilize the gamma phase. The study looked at small quantities of doping of Zirconium (under 10%) with various Thorium dominant alloys (75% and above Thorium). More analyses would be needed on a heavy Uranium- based alloy. Summary table for estimates of the constitution of a suitable binary alloy Binary Alloys Alloy name Constitution Variability Notes Uranium – U-97, W-3 2.5 – 10% · Higher than 4.5% Tungsten produces an Tungsten W alloy that would fail to melt at the boiling point of lead, thus, removing the passive safety element of controlled meltdown. · Requires a binder in the form of an additional element or in the method of fabrication. Powder bed fusion by laser (lpbf) has a tendency to form bonds that produce different metallurgical effects (similar to how quenching produces thermos-chemical effects). Uranium – U-60, Mo - 33%-45% · Higher concentrations of molybdenum void Molybdenum 40 Mo the controlled meltdown passive safety feature. · No binder was required until 1283 C. Significant Improvements were seen at 33% Molybdenum with the formation of a close- packed hexagonal phase at this point. Quenching and other heat treatments may allow for the system to join rather than dissimilate above this temperature. Uranium – U-40, Zr-60 40% -75% · Higher than 75% Zirconium voids the passive Zirconium Zr safety feature · Zirconium forms a strong bond, and, in some studies, it was noted that the bonding of zirconium stabilises alloys of Uranium and Thorium. Unfortunately, as a stand-alone metal, the alloy performance is poor due to zirconium’s melting point. Uranium – U-30, Nb-70 30-80% Nb · Higher than 80% Niobium voids the safety Niobium factor. · Like Zirconium, the reaction is strong but produces an alloy that would be unsuccessful as a stand-alone addition due to the high concentrations needed. Uranium – U-75, Re-25 20-30% Re · Higher than 30% Rhenium voids passive Rhenium safety. · May require a binder – it’s unclear from the phase diagram if that region is a sublimation zone for Uranium. Binary Alloys Uranium - U-78, Th-22 * · This alloy does not have a variability Thorium requirement because the entire spectrum is viable. Thorium’s melting point is below that of Lead’s boiling point and, thus, is always safe in addition to Thorium being a fissionable fuel. · This alloy needs a binder to stabilise the different states so as to not have a dual liquid mixture state. · More Uranium is preferred, thus, the upper limit of a Uranium based alloy is chosen. · The study briefly mentioned a melting temperature of 1224C Summary table for estimates of the constitution of a suitable ternary alloy Ternary Alloys Alloy name Constitution Variability Notes Uranium – U-92, W-4, 10% WMo · Heavy assumptions were made Tungsten – Mo-4 distributed 2.5- here. This alloy has never been Molybdenum 7.5% on a scale studied. of either · The idea is to have Molybdenum element act as a binder since there is a positive bond between tungsten- based alloys of molybdenum as well as Uranium based. This is a massive assumption based on intuition. Uranium – U-94.8, W-4, 2.5% W (0,75 · Heavy assumptions were made Tungsten – Re-1.2 Re) – 4.5% W here. This alloy has never been Rhenium (1.35 Re) studied. · The instability of the Rhenium – Tungsten alloy implies that Rhenium must be less than 30% of the atomic percentage of Tungsten or greater than 70%. Since Tungsten is the preferred Alloy, values for the lower limit have been given. Uranium – U-10, Zr-5, * · This Alloy is one of the few Ternary Thorium – Nb-2, Th-83 alloys that have been studied, but Zirconium / not in the way we want. The thermal Niobium doping melting point was not a massive consideration for the study, only the Ternary Alloys crystalline structure for thermal breeding impacts. · Briefly mentioned was the use of zirconium doping, when quenched, created a heart-treated Uranium- gamma-zirconium state that was stable beyond the melting temperature of Uranium. Lithium-7 Neutron ADS source In preferred embodiments of the present invention, a two-stage ignition process is employed at the ignition source (bulb / ball). Firstly, incoming protons impinge on an atom such as LI-7 to generate neutrons. The following illustrates the process. This study was conducted as a joint study between Ohio State University and the University of Texas with the focus on neutrons generated from laser-driven protons striking a 4.5mm thick natural lithium target. The reaction in focus is the Li7 (p, n) Be7 reaction, written out: Equation 1: Li7 (p,n) Be7 reaction ^^ ^^7 + ^^ → ^^ ^^7 + ^^ ^^Threshold= 1.88 ^^ ^^ ^^ Thus a comparatively low energy proton can initiate the reaction, meaning that a small and cost- effective particle accelerator can be used. Additionally, Beryllium-7 will decay by electron capture to become Lithium-7 once more: Equation 2: Electron capture decay of Beryllium-7 − 53.2 ^^ ^^ ^^ ^^ ^^ ^^7 + ^^ → ^^ ^^7 This is an important feature of Li-7 as the first material in the two-stage neutron generation process, meaning that the material performing the p-n reaction is not consumed over the longer term. The study suggested a number of key findings: i. A resonance peak interaction probability of 580 mbarns at 2.25 MeV. ii. A wider peak interaction spectrum around 5 MeV of 400 mbarns. iii. A 200 mbarns sustained interaction beyond 5 MeV until a decline to 50 mbarns at 10 MeV. Starting at a higher energy proton interaction and allowing the proton to scatter down into the lower energy ranges within the material showed a favourable result as it increases the probability of reaction significantly. This effect does taper off at 13 MeV as the second type of reaction becomes dominant past this energy point. Figure A10 illustrates these findings as empirical value of neutrons generated per proton according to the proton’s initial energy value. The maximum yield point is 2.5E-3 neutrons per proton at a value of 13 MeV. For a 400 ^A source this would conclude a source value of 6.241E12 neutron per second. Although only 2.5 neutrons are generated per 1000 protons, the surplus protons do not cause any particular difficulties due to the fairly low accumulation of protons over time. Equation 3: Storm et, al result adjusted for a 400 ^A current ^^^^ ^^ ^^ ^^ ^^, ^^ ^^ ^^ ^^.= 2.5 ^^ − 3 Neutrons⁄ proton ∙ 400 ^^ − 6 Amps ∙ 6.241 ^^18 protons⁄ Amps ^^^^ ^^ ^^ ^^ ^^, ^^ ^^ ^^ ^^.= 6.241 ^^12 neutrons⁄ second The results suggested a slight bias for a forward conical production of neutrons (Storm et. al.,2013). The Los Alamos National Laboratory conducted an investigation into particle emission from the proton-induced reaction of a Lithium target in the energy range of between 2 MeV and 150 MeV. Several key reactions exist within the spectrum: Equation 4: Proton absorption to double alpha emission ^^ ^^7 + ^^ → ^^ ^^8 + ^^ 8.19 ^^ ^^ ^^ ^^8 → 2 ^^ ( ^^ = 91.84 ^^ ^^ ^^) Equation 5: Li7 (p,n) Be7 reaction ^^ ^^7 + ^^ → ^^ ^^7 + ^^ Equation 6: Tritium emission ^^ ^^7 + ^^ → ^^ ^^5 + ^^3 ( ^^ = 1.97 ^^ ^^ ^^) 4.43 ^^ ^^ ^^) Equation 7: Deuterium ^^ ^^7 + ^^ → ^^ ^^6 + ^^2 The summation of the interaction within the spectrum may be seen in Figure A11. Equation 4, the double alpha emission from Beryllium-8 is the dominant reaction at lower energies with the single neutron emission reaction becoming dominant after 2 MeV. Within the spectrum of interest (below 15 MeV) the peak interaction point is 340 mbarns at 5 MeV. This does conflict with the reports of the follow-up study from Storm et al. suggesting a 580 mbarn peak at 2.25 MeV but is consistent with the value of 400 mbarns at 5 MeV. The alpha reaction peak at 13 MeV is the dominant reaction that eventually decreases the neutron production between 13 MeV and 25 MeV – this is also consistent with Storm et al. Fast-Fission Cross-Sections for Uranium and Thorium Reaction rates for the two main fuels of interest, Uranium-238 and Thorium-232 depend upon the cross section of the nuclei. Fast fission – upon which most embodiments of the present invention rely – is a type of atomic fission employing the use of fast neutrons. While the fast neutron mechanism has a more effective use of source neutrons – in that neutrons aren’t lost to diffusion in great quantities – the chance of interactions in the fast spectrum is far lower than in the thermal spectrum. This is directly counteracted by both the neutron multiplicities and the easily available fuel. Neutron multiplicities in the fast region vary proportionally to the incident neutron. Figure A12 is a collection of cross-sectional data and prompt neutron multiplicities for Uranium-238 (the standard stable isotope of uranium with 99.3% natural abundance) and Thorium-232 (an element three times more common than Uranium). Both Uranium-238 and Thorium-232 have been considered fuels for fast fission. Both natural Uranium and Thorium have near-complete abundance in these isotopes and the energy output of fast fission is nearly identical. Where Thorium falls short is its lower fission cross-section compared with U-238. Compare Figure A13: Th-232 Fast Fission cross-section and Figure A14: U-238 Fast Fission cross- section. Fast fission has a number of fuel-related advantages. Both of the listed fuel isotopes have significantly lower fuel costs than their enriched counterparts. Most thermal reactors use 3.6% enriched Uranium material at a cost of 1400 USD / kg, while processed Uranium has a cost of about 70 USD / kg and similarly 30 USD / kg for Thorium. According to the invention, we counteract the low cross-section by an innovative reactor design. Since the embodiments of the present invention use an ADS the “source rod” would emit neutrons in an area within the reactor. Pursuant to aspects of the invention with a concentration of fuel in this area, with the addition of coolant that does not moderate / slow neutrons, it is possible to make effective use of the source flux. Power requirements for particle accelerator Based on cycle of a 1mA, 15MeV cyclotron which is roughly 0.4769 , the energy requirement for the 0.5mA, 15 MeV cyclotron can be estimated. This is an overestimation and serves only to show that the energy requirement for the cyclotron is very low in comparison to the larger reactor. Where: ^^ = ^^ ^^ ^^ ^^ ^^  ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ = 500 × 10−6^^ ^^ = 15 × 106^^ ^^ ^^ ^^ ^^ ^^  ^^ ^^ ^^ ^^ ^^ = 0.4769 Therefore: ^^ = 15.726 ^^ ^^ Principles of Accelerator Driven Fission according to embodiments Without wishing to be bound by any theory, the basic explanation of the method is to break up high- density fuel into a finite element mesh grid and analyse each element from its centre point node, from here one node is selected to be a source node (the impacted node from the accelerator) and all other nodes are considered inert fuel pieces. The source is multiplied by the second law mirror equation – which is based on the geometry of the surrounding fuel – and this second law function carries on to create a neutron impact field neighbouring fuel. Neighbouring elements, impacted by the source node, are then treated as source nodes, individually, with an initial fission rate stemming from the source element and, thus, with a corresponding neutron source rate. The process begins again by assigning a second state to this field. All states are then superimposed onto one another to get a governing equation for each nodal source element commanded by the same time step as the source function. During the superposition step, the original neutron field is extended beyond its boundaries as the neighbouring fuel elements help create the source functions for these out-of-bound elements. This process continues until every element, system-wide, has an individual local criticality function. The advantage of this method shows chain fission impacts as kinetic impacts on neighbouring fuel pieces with a high degree of accuracy. Basic Concepts While studying the concept of metallic fast fission cores – reactor cores based on the fast fission mode of heavy actinide elements, whereby, the structure of the core comprises fuel material in its metallic form – an interesting effect appeared within the calculations. Consider Figure A15 which represents two nodal elements, each perfectly cubical with dimensional length “L”, and both consisting of a uniform, homogenous, fissionable material that is incapable of absorbing neutrons in any other reaction type other than fission. Let’s assume nodal element one undergoes fission at a set rate, “S”, which is caused by an external factor and is unaffected by changes within the system. Source flux “S” should be considered to be spherical in nature and, therefore, take the form of; Equation 8: Spherical source flux ^^ ^^ Where “r” is the radial distance away from source It's important to note that the above equation does not apply for values where the denominator function is less than one, that is to say: 4 ^^ ^^2≮ 1 1 ^^ ≮√4 ^^ ^^ ≮ 0.282 Taking a mid-point analysis, that is to say, that the distance from mid-point to mid-point equates to the radial “r” distance, the effect of the fission node 1 on node 2 equates to; Equation 9: Fission function ^^2,1= ^^2∙ ^^^^,2∙ ^^2∙ ^^2,1 Where: ^^ = barns value (cm2) Note: Since the volume of the node is 1cm cubic, the value “V” will be omitted henceforth for convenience’s sake. During this fission process, it is obvious that node 2’s fission neutrons then impact node 1’s material such that: Equation 10: Reciprocating source function ^^ ∙ ^^ ^^ ^^ ^^2,1 Where; ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ∙ ^^ ∙ ^^ ∙ ^^02 ^^,2 2∙ ^^ = ^ 4 ^^ ^^21 ^0+ ^^ ∙ ^^1∙ ^^^^1∙ 4 ^^ ^^2since this is material is homogenous; ^^1= ^^2= ^^ Equation becomes: ^^22 ∙ ^^ ∙ ^^2^^∙ ^^ Equation 11: Source multiplication ^^2∙ ^^2∙ ^^^2 ^ We can continue with this every step ^^2∙ ^^2∙ ^^^2 ^ 2^^ ∙ ^^^2 3 ^^ ∙2^ ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ It is only appropriate for the time step function “n” to also have the same time unit as the source function. The standard convention is per second; hence a second time step is required. For simplification’s sake “n” will now become “t” with units “second”: Equation 1: time-dependent source multiplication equation 222 ^^ ^^ ∙ ^^ ∙ ^^^^ The concept of source multiplication but has not hitherto been utilised to advantageous effect as in embodiments here. This source growth, in a typical generation three core, is fairly low and often goes unannounced because of the low fuel density and the need for moderation. Neighbouring Uranium-Oxide fuel pellets have relatively low atomic densities compared to solid- metallic fuel: For Uranium-fuel pellets at 10g / cm3and 10% enrichment: ^^^^, ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^= 0.0223 ^^24 ^^ ^^ ^^ ^^ ^^⁄ ^^ ^^^3 Of these, only 10% are U235 so susceptible to fission from thermal neutrons so the effective density becomes a factor of 10 lower. Meanwhile, for metallic uranium (19g / cm3): ^^^^, ^^ ^^ ^^ ^^ ^^ ^^ ^^ ( ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^)= 0.0481 ^^24 ^^ ^^ ^^ ^^ ^^⁄^^ ^^^3 The metallic fuel density is more than twenty times that of the uranium oxide pellets, because (1) the fuel is all Uranium (without oxygen lowering the proportion of uranium atoms), (2) all of it is useful fuel rather than the 10% U235 and the density is higher. Note the Np factor is squared and because of the compound nature of equation 5, this represents a multiplication factor that is far higher in the metallic fuel. The overall effect we have appreciated pursuant to the invention is that, when computing fast fission rates, the geometry of the neighbouring fuel cells becomes a far more important factor than conventionally assumed. To complicate matters, in a metallic fast-fission core, the lack of moderation increases the “area-of- effect” of this multiplication effect. The example given is small, but apply it to a large mass of fuel, and even small source functions eventually build to produce large-scale energy outputs. The current gold-standard computation method for nuclear reactions is the Monte-Carlo method. However, despite being the accepted model it doesn’t take into account geometry with such a high degree of accuracy. The method computes a number of particles in a system and computes them for the lifetime of the particle. A small number of the same particles are simulated and then a normal statical distribution is then extrapolated from the sample. This method loses resolution when upscaled as some reactions are so rare that it doesn’t pick up enough of that type of reaction to establish the true reaction value. The error is typically around 10% for Monte-Carlo codes (when computing for thermal-fission cores) if we compute the multiplication factor within equation 12 for uranium oxide fuels under fast fission with our example of a single neighbouring node: ^^2∙ ^^2∙ ^^^2 ^ The effect would likely get lost within the 10% error and the lack of geometric resolution. Such an effect has accordingly not been considered significant in prior art research. However, pursuant to our innovative design, the multiplication factor for metallic uranium cores is: ^^2∙ ^^2∙ ^^^2 ^ This gap in traditional presents an un-appreciated; a reaction mode of secondary fissions adding to an original, external source that is impactful enough, over time, to drastically impact energy values while, on a first computational basis, would seldom be picked up by Monte-Carlo code and conventional modelling methods. In our arrangement this becomes as important as the reaction equation itself. This is not meant to discourage or disprove the Monte-Carlo method but rather to compensate for the shortfall in the particular situation which is exploited in embodiments of the invention. However in a core such as in embodiments, the additional flux becomes important over time. Having appreciated the importance of this factor with the explanations herein, those skilled in the art will be able to construct improved models and arrive at designs taking advantage of this information. The invention is not intended to be limited to a particular design of reactor or modelling method but to encompass alternative arrangements which take advantage of the positive multiplication of neutrons due to geometry and composition in a sub critical core excited by an accelerator. However, to assist, and without wishing to be bound by any theory or limited to any particular modelling method we further develop modelling for this phenomenon. This is intended to assist those wishing to develop computational simulations. First Law of Semi-transparency Neutrons – and other atomic reactions – interact in a semi-transparent nature with a volume of material, however, when a particle is absorbed by the material in a reaction it must be considered to have been removed from the source flux as a matter of conservation of energy. This is to say: Equation 13: First law of semi-transparency from energy conservation [∑^^fission^^, ^^, ^^ +∑^^absorption^^, ^^, ^^ ] Where: ^^, ^^)= All of the fission events between the source point and the target point = All of the point and the target point ^^0= Flux if unimpeded by any material ^^^^= Area of the node under review in respect to the source And finally, ^^( ^^, ^^, ^^) = local flux point remaining from the source Assuming a mid-point analysis once more alongside a one-dimensional analysis for simplification – which we’re allowed to do according to the symmetry of a spherical source, generates the system of a linear set of elements as shown in Figure A16. It follows from Equation that: ^^ ^^ = ^^0^^∙ ^^^^∙ ^^ ∙ For simplicity: ^^^^∙ ^^ = N ^^ = Number of atoms within the described elemental volume This implies, for the fission in the immediate adjacent node one length away: Equation 14: Fission in 1st adjacent node ^^0∙ ^^ ∙ ^^ ^^^^1= 4 ^^ ^^2To justify the removal of those neutrons from the flux “tunnel” the neutrons used to generate the fission event must be subsequently divided by the cross-sectional area of the “tunnel” with respect to the original source: Equation 15: Source neutrons removed from source tunnel, the first node ^^1^^0∙ ^^^^∙ ^^ Similarly for a nodal element that is the Equation 16: Source neutrons removed from source tunnel, the second node ^^2^^0∙ ^^^^∙ ^^ Continuing to an “n-th” node: Equation 17: Source neutron removed from source tunnel, N-th node ^^ ^^ ^^0∙ ^^^^∙ ^^ To visually illustrate this, Figure A17 effect for spherical sources. As the distance increases from a source node, the cross-sectional flux density decreases proportionally; thus, the number of reaction events and the number of neutrons that can be subtracted from the source tunnel due to those events also decrease. Expanding upon Equation 13 with only fission as a reaction: ^^ −^^1^^2^^^^ Equation 18: First law series ^^ ^^ ∙ ^ ^ ^^0^ ∙ N 1 1 1 ^0 ^^The series sum present in Euler’s basil problem which has a definite convergence answer if we seek to evaluate the disappearance point of the flux (i.e. where a nodal source no longer has any effect): Equation 19: Sum of all elements 1 1 1 1 ^^4Substituting in Equation 19: ^^0^^0∙ ^^^^∙ N ^^4 Equation 20: Maximum flux radii ∙ ^^ Equation 21: Maximum flux radii with ∙ ^^ Second law of local Criticality functions We now deal with a full expanded view of the principle of localised criticalities. In Figure A18, which repeats Figure A2, two identical elements are adjacent to one another. These two elements are homogenous, fissionable materials with element one undergoing a nuclear reaction to produce neutrons. The control of this initial source reaction is entirely independent of the system and will continue to bombard the target element at a constant rate. It should be expected that any neutron source is inherently spherical in nature, thus creating a source function of element one: Equation 22: Spherical source function ^^ ^^0 Equation 22 is constant for all spherical sources to a 2D flux field for neutrons emanating from the source a radial distance “r” away. It’s important to note that the above equation does not apply for values where the denominator function is less than one, that is to say: 4 ^^ ^^2≮ 1 ^^ ≮1 √ 4 ^^ ^^ ≮ 0.282 Assuming a mid-point analysis for element two (where “r” is equal to “l”), the fission events generated from element one as a source: ^^ ^^0 Neutrons generated from this fission event a secondary, spherical, source of neutrons. This new source impacts element one similarly to create: ^^ ∙ ^^ ^^ ^^ ^^2,1 And, assuming the two elements are a 1: ^^ ∙ ^^2∙ ^^^2 ^ To transform this into a source, in to source: Equation 23: Mirrored source function ^^2∙ ^^2∙ ^^^2 ^ Equation 23 may combine with the source to a combined source multiplication function: Equation 24: Source multiplication ^^2∙ ^^2∙ ^^^2 ^ This new source is then used in a repeating function as these neutrons impact element two in the same manner: ^^2∙ ^^2∙ ^^2 ^^We can then conclude this 222 ^^ ^^ ∙ ^^ ∙ ^^^^ Where “n” is considered the time step same as the original source function. Equation 12 establishes the time-dependent equation. Equation 25: time-dependent source multiplication equation 2 ^^ ∙ ^^^2 ^^ ^^ ∙2^ It may be necessary, as discussed in accuracy, to expand the accuracy beyond a simple singular reciprocating function and expand to a secondary or tertiary reciprocating function. In this case, the mirrored neutron’s effects are considered significant enough to be considered in Equation 12. The requirements for “significant” are outlined within the zeroth law. Equation 32 outlines an expanded notation for multiplication factors to increase the accuracy of a solution. Equation 26: Mirrored source addition extended and expanded ^ ∙ ^^ ∙ ^^^2 ^ ^^ ∙ ^^ ∙ ^^^2 2 ^ ^^ ∙ ^^ ∙ ^^^2 3 ^ ^^ ∙ ^^ ∙ ^^^2 n ^2 2 2 2 2 2 2 2^For a greatly. Figure A19 represents a system of 6 equally adjacent elements surrounding a source element. Since the material is homogenous, Equation 25 would become: 2 ^^ ∙ ^^^2 ^^ ^^ ∙2^ This can be extended to group to a source node, for example as shown in Figure A20. Figure A20 displays twelve elements of equidistance from the source element (red). Equation 25 now becomes: ^^ ^^2∙ ^^2∙ ^^^2 ^ And finally, to complete a 3-by-3 of equidistance from the source element (red). Equation 25 now becomes: ^^ If the source element was this would suggest a source function of: Equation 27: Cubic source ^^ Equation 27 no of semi- transparency. For metallic Uranium-238 this is the 21stnode. This suggests that a circle with a diameter of 41cm is the maximum area of effect for the source function. Once computed, this summation creates the local criticality value of the particular element. In general: Equation 28: General second law mirror Σ^^η2∙ σ2∙ Nρ2 Third Law of Interaction Accuracy While the universe is to expand that chaos, it is not random. This law aims to justify the tug-of-war between accuracy and computational ability; or rather, usefulness. During the introductory basics Equation 12 established the time step for source multiplication of two adjacent nodes, equation shown below: 2 ^^ ^^2∙ ^^2∙ ^^^^Where: ^^2∙ ^^2∙ ^^^2 ^ To become: ^^^^= ^^0[1 + ^^1] ^^ “M” designates the “mirrored multiplication factor” of a source emitted from node one, which causes a fission event in a second node, and the neutrons generated from the node two fission generates a subsequent fission event in the first node – these neutrons are then added to the original source. For large source fluxes, it may become necessary to peer a step lower and isolate the primary mirror- generated neutrons to assess a secondary mirror-generated set of neutron events – i.e. to analyse “M1” as a source of neutrons and find its mirrored multiplication factor to establish an “M2” which is then positively added to the time dependant source equation as a third source. Equation 29: Mirrored multiplication addition ^^1= ^^0+ ^^1^^0+ ^^2^^0^^2∙ ^^2∙ ^^^2 ^ Replacing the source function neutron events “M1”: Equation 30: Secondary mirrored event source ^^2∙ ^^2∙ ^^^2 ^ These neutron events are then become: ^^2∙ ^^2∙ ^^^2 ^ ^^2∙ ^^2∙ ^^^2 ^ Which implies: 2 ^ ∙ ^^^2 ^ ^^ ∙ ^^ ∙ ^^^2 2 ^^ ∙ ^2 2 2^The logic implies that one reached: Equation 31: Mirrored source addition extended ^^1= ^^0+ ^^1^^0+ ^^2^^0+ ^^3^^0…+ ^^^^^^0Equation 32: Mirrored source addition extended and expanded 22^2 ^2 2∙ ^^^2 2 ^ ^^2∙ ^^2∙ ^^^2 3 ^ ^^2∙ ^^2∙ ^^^2 n ^^ ∙ ^^ ∙ ^^ ^^ ∙ ^^^The zero or an arbitrary value that is essentially zero. This point of “arbitrary zero” is set by application; while, large reactor cores may possess large flux fields whereby an accuracy whereby the last “Mn” value that is in the vicinity of 1E-9 is a necessity as a flux of 1E15 exists and 1E6 neutron events is a reasonable justification to be zero while values higher cannot be “justifiably zero”, another application that uses a laboratory-sized source in the vicinity of 1E7 cannot operate at an “Mn” value of 1E-9 as this would create an impossible level of accuracy as it predicts partial events and not whole events. The maximum level of accuracy is therefore designated by: Equation 33: the third law 1 ≤ ^^ ^^0^^If a value exists which is justifiably zero but is above the zeroth’s base: Equation 34: Arbitrary point third law ^^^^^^ Where: ^^^^≥ 1 ^^^^= justifiably zero value point Continuing this vein of logic, there is also a “justifiably zero” point for primary level mirror functions; an element which is in the area of effect of the first law, whose effect as a mirror, would be negligible. Equation 35: Boundary mirror layer ^^2∙ ^^2∙ ^^^2 ^ Where; ^^^^= Mirror boundary ^^^^= Number of elements on the boundary ^^^^= Distance to the boundary And thus, by applying the third law; Equation 36: Third law mirror boundary 1 ^^ Equation 37: Third law arbitrary value ^^^^^^ Fourth Law of Neutron Field Superposition Once a local criticality function has been created, and the maximum area of effect has been established through the first law, a neutron source effect field can be predicted to grant all the neighbouring fuel elements an individual source function. An illustration of a neutron source mesh grid is shown in Figure A22. In the example shown in Figure A22, the red block indicates the source element, and the blue blocks represent elements within the mirror effect region, with only primary mirror effects, that will directly increase the local criticality of the source node and, the yellow region indicates elements effected by the source element but that do not contribute to the mirror effect. The source function, as shown in the second law for the three-dimensional cube, equates to Equation 27 as a function of time; ^^ This equation now governs the fission effect of all the elements within the neutron field. For elements one nodal length away (see Figure A23 which is a copy of Figure A19): ^^1= ^^ ∙ ^^1^^ ∙ ^^ ∙ ^^ ^^^^ ^^1= 4 ^^ ^^2^^^^∙ ^^^^∙ ^^ ^^ ^^ Equation 38: Neutron source nodal length away t From to the source node; Equation 39: Neutron source function of an element root-2 nodal length away t Continuing; Equation 40: Neutron source function of an element root-3 nodal length away t In Equation 41: Neutron source function of an element a distance "r" from the source t ^^^^∙ ^^ ∙ ^^^∙ ^^ η2∙ σ2∙ N2 η2∙ σ2∙ N2 η2∙ σ2∙ N2 S^^( ^^) =^[1 + 6 ∙ρ+ 12 ∙ρ+ρ] 4 ^^( ^^ ^^)2(4πl2)2228 ∙ 22(4π(√2l) ) (4π(√3l) ) Once each element has established an individual source function, it too can be analysed individually according to the neutron field it creates. In the example in Figure A24, the red block indicates the source element under investigation, and blue – once again – represents elements within the mirror effect region, with only primary mirror effects, that will directly increase the local criticality of the source node and, the yellow region indicates elements effected by the source element but that do not contribute to the mirror effect, green represent newly-added elements that were previously out of the field and, grey represent the original source node. To revise, the source function in this node is a two-dimensionally diagonal node (Equation 39); t Thus, ^^ ^^( ^^) = 4 ^^ ^^2Which becomes; Equation 42: Neutron flux field generation from a field root-2 away from the primary source t The the second law which implies, for a cubic mirror, that; ^^ So is now source : t This Equation 43: Source function of an element root-2 nodal length away with the second law 2t The again evaluated from basic principles; ^^1= ^^ ∙ ^^1^^^^∙ ^^^^∙ ^^ ^^1= 4 ^^ ^^2^^^^∙ ^^^^∙ ^^ ^^ ^^ which is now; Equation 44: Neutron source function of an element one nodal length away on the 2nd plane 2t Equation 45: Neutron source function of an element root-2 nodal length away on the second plane 2 2 plane 2 2 2 In the nodal lengths from the new plane with the effect from plane two being represented in Equation 45 The effects of this source would naturally be additive to the original source; yes, the effect of a mirror has already been taken into account in the creation of Equation 27, but what hasn’t been taken into account is the change in how that mirror increases in its local criticality over time due to its neighbouring elements – and subsequent mirror effects they generate. The neutron fields are superimposed on one another, additively, and thus for this example, after two fields have been computed, the source function of the original primary source becomes; ^^ Due to this particular example, it is easy to deduce the superimposed total source function by a simple symmetric analysis; six nodes are a distance one elemental node length away, twelve are a distance√2 elemental node lengths away and, eight are a distance√3 elemental node lengths away. The source function, after superimposing all twenty-one flux fields that are directly adjacent to the source element, creates; ^^ Equation 2: Superimposed cubic source function from “blue-zone” adjacent to the original source node ^^ ^^2∙ ^^2∙ ^^ ^2^ ^^2∙ ^^2∙ ^^ ^2^ ^^2∙ ^^2∙ ^^ ^2^^^∙ ^^^^∙ ^^ 2 For simplicity’s sake let’s assign it to be its own variable, where: Equation 48: Cubic mirror function η2∙ σ2∙ Nρ2 η2∙ σ2∙ Nρ2 η2∙ σ2∙ Nρ2 and thus, Equation 49: Simplified superimposed cubic source function from “blue-zone” adjacent to the original source node (see Figure A25): ^^ ∙ ^ 2 ^^^^^∙ ^^ 6 12 8 Analysing a fields. The red element is, once again, the target of analysis. From the summation of neutron fields one and two: Equation 50: Source function from source plane, a nodal distance root-8 away t 2 2 η2∙ σ2∙ Nρ] (4π(√3l) ) only change being the distance from the source: Equation 51: Source function of an element root-8 nodal lengths away with the second law 2t Upon analysis of a five-by-five-by-five element cube presents a set of distances from the centre (source) element: • 6 centre faces of nodal distances 2 with four elements accompanying a distance√5 and four elements of a distance√6 in addition to those. • 12 edges of nodal distances√8 and two accompanying elements√9 = 3 away. • 8 corner elements √12 away. In Figure A22 the example also indicates a number of elements just beyond the cube. This includes: i. 6 centre elements a distance 3 away with four elements accompanying of a distance √10 and an additional four at a distance of √11. In total, the new superimposed source function of neutron planes one and two become: Equation 52: Superimposed cubic source function from “blue-zone” adjacent and "yellow-zone" second adjacent to the original source node ^^ ^^2∙ ^^2∙ ^^ ^2^ ^^2∙ ^^2∙ ^^ ^2^ ^^2∙ ^^2∙ ^^ ^2^^^ ^^2 the following super imposed equation: Equation 53: general 4th-law source element function ^^ 2 ^ ∙ ^^^^∙ ^^ Σ^^^^Once the 4th-law value for the element. To construct source functions within the “green-zone” – i.e. elements unaffected within the source plane but are affected by the 2nd-degree plane - the starting source is a result of all of the superimposed planes. From the general equation, Equation 53: Equation 54: 3rd neutron plane starting source ^^ ∙ ^^ 2 ^^∙ ^^ Σ^^^From the second law ^^ Where : η2∙ σ2∙ Nρ2 η2∙ σ2∙ Nρ2 η2∙ σ2∙ Nρ2 Which implies: Equation 553: 3rd plane starting source including 2nd law ^^ ∙ ^^ 2 ^^∙ ^^ Σ^^^^When computing the effect Equation 45 and Equation 46): Equation 56: 3rd plane source effects on a neighbouring fuel element at a distance "r" from the element ^^ ∙ ^^ 3 2 ^^∙ ^^ 1 Σ^^^^The above source is also subject to 2ndlaw mirror effects: Equation 574: 3rd plane source effects on a neighbouring fuel element a distance "r" from the element with second law effects ^^ ∙ ^^ ∙ ^^ 3 ^^1 Σ^^^^When superimposed to planes 1 and 2. Equation 58: general 4th-law source element function for the superposition of planes 3 and 4 2 2 ^^^^ ∙ ^^^^∙ ^^ Σ^^^^ ∙ ^^^^∙ ^^ Σ^^^^The i. Source multiplied by 2ndlaw mirror effect. ii. Construction of neutron plane [1] from the source. iii. Effects of prior neutron plane establish the source functions of neighbouring elements. iv. Source functions from the prior step establish a new neutron plane [2]. v. Old neutron [1] and new neutron [2] planes superimpose additively. vi. These planes are marked as “fixed”. vii. New plane effects [2] have extended beyond that of the old plane [1], these sources become a 3rdplane [3]. viii. Repeat the cycle till system-wide local criticalities are established. Fifth Law Neutron Field Collapse Upon shut down, the original source is equated to zero. According to all of the equations, the individual source functions collapse to zero as the entire system is based around an independent source. To establish the time necessary for collapse; ^^(^^)= ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^(^^ − 1) ^^Where Equation 28: Σ^^η2∙ σ2∙ Nρ2 The mirror functions are the only and, therefore, are also the only measure for chain fission collapse. Discussion The first and second laws are both built upon the basic understanding of spherical sources, neutron multiplicity through chain fission and basic geometry. The inaccuracies of the method arrive at two key locations; the simplification of cubic elements into dimensionless point sources and the use of superposition to establish a system-wide relationship. The reason for both comes from the computational ability to track the locations of individual particles within the fuel material. For more accurate applications, nodal elements may have their dimensional units changed to reflect a smaller cube (changing the cm standard unit to mm) but I warn against this: this method already pushes the boundary on modern computational ability, utility-sized reactor cores computed down to the millimetre could require months of computations to compute even with modern technology. For the argument that using superposition effectively doubles the mirror effect there is the following rebuttal: From Equation 47: ^^ ^^2∙ ^^2∙ ^^ ^2^ ^^2∙ ^^2∙ ^^ ^2^ ^^2∙ ^^2∙ ^^ ^2^^^ ^^2 account twice is thus invalid. In practice this second half of the equation is always substantially less than the first (see Figure A26). The red line (Equation 47) represents the growth in source function for U238 under a source value of one and included the 4th-law superposition of the “blue zone” elements. The blue line is the latter half of the equation – the superimposed function: ^^ ∙ ^^ ∙ ^ 2 ^^^ 6 12 8 At original source value, as seen in Figure A20. This represents 0.357% of the total multiplication as a potential source of error. The trade-off is a system-wide function creation that allows for the geometric influence of a source and the ability to identify local criticalities without drastically increasing complexity. Single Stage ADS Source Embodiments of the present invention utilise a single stage ADS source, i.e. one material in the source bulb to be irradiated by protons. Using the proton fission interaction data from Isaev, et al., 2008, the following flux source equations have been derived from first principles: Equation 59: ADS neutron source ^^^^ ^^ ^^= ^^^^∙ ^^ ∙ ^^^^ ^^∙ ^^^^ ^^ ^^ ^^ ^^ ^^^^^^= ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ 22^^ ^^ ^^ ^^ ^^ ∙ 4.833 ∙ 10 ^^ ^^3 ^^^^ ^^ ^^= 1.217 ∙ 1015 ^^⁄^^This source flux effectively means that 7.22% of all protons within the beam line interact with the target plate with the intended reaction. It’s interesting to note that Equation 59, when used according to the volume of 1cm3, is consistent with MCNP and FLUKA simulations. Below is a table based on 500 ^A proton beam current (simple multiplication for higher beam currents may be done): Neutron source (n / s) Target (500 ^A) 26.5 MeV 62.9 MeV Figure A28 illustrates these results. Each of the above actinide elements has its respective advantages and disadvantages. Considering the multiplicities of a fast neutron reactor, even a minor change in neutron source has an enormous effect on the reactor flux as it expands through the material. The “highest flux” may not actually be the best choice when we bring into account melting point and reactor core temperature, cost / availability of the material and material hazard challenges. A summary of these properties is below: A. Target Melting Point Key Advantage Key Disadvantage From the above table, Th232 and U238 are favoured on technical and commercial criteria (at least at current material prices and availability) with U238 having a significant flux advantage over Th232. Preferred but non-limiting example of U238 will be discussed in more detail For the purpose of giving a fuller explanation of a preferred embodiment further experimental flux proceedings discussed herein will be conducted using the U238 tungsten alloy at about 3% tungsten (typically from 1% up to 10%). However the invention is explicitly not intended to be limited to only this particular material or alloy. The considerations and modelling herein can be extended to other materials as the skilled reader will appreciate. Where a material has not been selected herein because it is expensive and / or rare it will be appreciated that technically it could still be used, albeit at a price. Energy and material costs may change so that a less preferred material becomes more favourable. Similarly security concerns can be addressed as needed. Where a factor is that the melting point is low, this can be addressed either by alloying to increase melting point, for example with a metal such as tungsten, and / or by accepting operating constraints due to a lower acceptable core operating temperature – this may reduce possible thermal output from a given size core and / or require higher coolant flows but still be useful. Where the multiplication factor is lower, this can be addressed within the limits of what is practically and commercially acceptable by allowing longer flux buildup times and / or by core design with more and denser material. There comes a point where the multiplication factor is so low it becomes undesirable to build a practical reactor and control becomes more problematic but the skilled reader will appreciate that even a highly suboptimal design well outside the preferred parameters exploiting this inventive disclosure may still provide benefits as compared to conventional energy generation. The skilled person will also appreciate from the disclosure herein that factors inter-relate so that for example if the density of “useful” atoms in the material is high and cross-section is high the amount of material needed can be smaller than with a less “efficient” material choice so small compact cores and larger “lazier” core designs are both possible. Thus whilst other materials may be more expensive or have drawbacks, the invention does not exclude operating productive if currently less desirable arrangements of materials and physical layouts. Direct Proton Fast-Fission Neutron Source Mirror Functions For the source, it's imperative to choose a fast fission fuel with a high cross-section and atomic density to best take advantage of the second law mirror effect. According to Cross Section Evaluation Working Group (CSEWG) the fast fission cross-section for U238 is 0.6 barn, while the cross-section for Th232 is 0.2 barn within the working region of about 1-2 MeV where neutron multiplicity energies have a similar energy output for an input and output neutrons (i.e. the same energy neutron is ejected as received, continuing the cycle). The atomic density of Uranium and Thorium is 0.04833E24 atoms / cm2and 0.03039E24 atoms / cm2respectively, meaning, Uranium-238 has an atomic density of 1.6 times greater than thorium-232. The combination of both a lower atomic density and cross-section creates the following dilemma when evaluated according to the first and second laws: From the first law, Equation 20: ∙ ^^4^^ ^^ℎ232 = cm (78th element out of bounds) − ∙ ∙ ∙4= From the second law for a cubic mirror function, Equation 27: ^^ And the fourth a effects and only accounting for “blue zone” immediate, Equation 47: ^^ ^^2∙ ^^2∙ ^^ ^2^ ^^2∙ ^^2∙ ^^ ^2^ ^^2∙ ^^2∙ ^^ ^2^^^ ^^2 Figure A29. After 10000 seconds (just under three hours of irradiation) the source multiplier has only increased by about 1.12. Expanding to 100000 seconds (just under 28 hours) creates the graph shown in Figure A30. What’s of greater concern is the significantly small multiplier for the second plane source, see Figure A31. This indicates that a significant increase in fuel or time under constant irradiation may be required to achieve a meaningful level of activity with thorium alone as a primary fuel source. In comparison, Uranium-238 produces the following multiplier in Figure A32. Alongside a second plane, the source multiplier is shown in Figure A33. In general, if the requirements are to make a compact unit – such as an SMR – Uranium is the better choice as it would require far less fuel with a far shorter start-up time. If the goals are to create a large utility, with far less numerous shutdowns and a less constrained space requirement, Thorium is a viable fuel option. Two stage Neutron ADS source Preferred embodiments of the present invention utilise a two-stage neutron source in which protons from a particle accelerator impinge on a first material to produce neutrons that go on to impinge on a second material. The previous section discussed a source that was conducting direct proton fission on a target material where the target material is also fissionable under fast neutrons. For direct proton fission, the minimum requirement is 26.7 MeV on target (Isaev et. al., 2008). To achieve this, a minimum of a 35 MeV particle accelerator is required as the beamline would need to pass through a window that separates the Uranium and the LBE coolant. A 35 MeV cyclotron is a costly investment in two ways; the amount of low-carbon steel required to make the magnet can drain a local supply chain (increasing production time) and the financial investment grows exponentially for every MeV that a particle accelerator is capable of. That is not to say that a commercially viable reactor cannot be made and indeed one can, particular for higher power applications. However at present the most commonly produced particle accelerator is a 15 MeV cyclotron designed for the medical industry to produce PET drugs. This is under the threshold minimum for direct proton fission. It would be a yet further and independently advantageous step if a system taking advantage of the multiplication discussed above could be made to function with excitation deriving from such a source, or a cyclotron with energy below 20MeV. According to a further innovative aspect, this can be achieved. Medical cyclotron sources are can be used with a refinement. 15MeV is adequate to excite a lithium-7-based neutron ADS source, the threshold for which is 1.88 MeV. Lithium-7 does have a fast neutron reaction with a minimum threshold of 2.47 MeV, reaching a peak interaction cross-section of 0.6 barns at 7.5 MeV (Hernandez & Pereslavtsev, 2018). Within the upper echelon of neutron production, Lithium-7 will likely begin to degrade over time if at the centre of a fast-fission reactor core. Another concern is the lack of a “primary” mirror effect in terms of the second law, instead, the source unit will have to have lithium surrounded by fast-fissionable material to generate any source multiplication. If the energy value of the inbound proton is carefully regulated, the Lithium-7 source unit will favour the Lithium-7 (p, n) reaction creating Berylium-7 – which will decay back into Lithium-7 with a half-life of 53 days. The fast-neutron reaction, with a minimum threshold of 2.47 MeV, will be the only destruction of the Lithium-7 source unit due to this unique circular decay function. For this reason, the Lithium, or equivalent material in the ignition bulb is preferably replaceable (with the reactor shut down) without disturbing the fuel or the coolant. We now determine how the fundamental principles of accelerator-driven design would view a non- proton fissionable source, consider Figure A34, a repeated mesh grid. From the second law, Equation 27 as a function of time; ^^ The mirror source now to one, ^^^^ ^^7( ^^) = ^^0 In doing so, the immediate fuel (every block in Figure A27 except the red source node) is impacted differently: From first principles: ^^ ^^ ^^ ^^ ∙ ^^ ∙ ∙0 As a source function of volume ^^ ^^ ∙ ∙ ^^ ∙0 Because this is a fast fissionable may place: Equation 60: Source function of an element a distance "r" from the ADS source element ^^^^( ^^) = ^^ ∙ ^^ ∙ ^^ Examining all 20 neighbouring elements produces the following result for the source body: ^^ multiplication plot, see Figure A36. It would require 5 hours before an effect is noticeable. It is worth mentioning that this is before the fourth law superposition of the neutron fields. If the immediate fuel is switched to Thorium-232, we would expect a far slower build-up – see Figure A35. The system requires nearly three times as long to build up a meaningful level of source multiplication. Fundamental Theory Of Accelerator-Driven Fission Applied Winding Number The total number of times C circles z 0, counted with multiplicity, is referred to as the winding number of a closed curve C in the complex plane. It can be mathematically stated as the integral of the curve’s argument over the curve, normalized by 2 ^^: ^^ ^^ In this case, dz represents the z along curve C. An integer winding number gives the curve a topological invariant, or property that does not change even while the curve is continuously deformed. To determine whether a point is inside or outside of a polygonal mesh in the complex plane, utilize the winding number. To do this, one can build intricate curves from the mesh’s vertices to the target point and then calculate each curve’s winding number. The point is inside the mesh if the sum of the winding numbers for all the curves is non-zero, and outside the mesh, if the sum is zero. This technique, known as the "winding number algorithm," is popular and effective for determining whether a point is within or outside of a polygonal mesh because it only involves quickly calculating the winding numbers of each curve. The result is solid and trustworthy because the winding number is a topological invariant, meaning that it is unaffected by ongoing mesh deformations. Node Initialization First, the code needs to create a mesh of nodes, assigning to each node if it is fuel or not. This is done by loading the stl meshes using the numpy-stl module and getting the number of nodes that will be required in the x,y, and z directions. The meshes are then centered on the nodes. By splitting the code up into processes, using the multiprocessing module in python, for each x coordinate, the code can be run on multiple cores and therefore save computational time. Each process then iterates through the y and z coordinates calculating the winding number for each node. To improve the speed each point’s coordinates are compared to the minimum and maximum coordinates of the mesh. If the point lies outside of these bound it is not necessary to calculate the winding number as the point cannot be inside the mesh. Multiplicities Of Nodes For each step of the code, the same optimization is done in the initializing of the nodes (splitting the code into processes for each x-coordinate). In order to optimize further concept from the First Law Of Semi Transparency is used to eliminate calculations if the node is outside the area of effect. First, the multiplicities for the source node are calculated. This is done using the concepts from the Second Law Of Local Criticality Functions and iterating through each of the nodes and calculating their contribution. Next, the first plane is calculated using the concepts from the Fourth Law Of Neutrons Field Superposition. For this part the code iterates through each of the nodes treating it as the secondary source then it iterates through the nodes again calculating each of the nodes’ contribution to the secondary source’s multiplicity. These multiplicities are then added together for each secondary source. After the first plane, the second plane is calculated using once again the concepts from the Fourth Law Of Neutrons Field Superposition. For this part the code iterates through each of the nodes treating it as the secondary source then it iterates through the nodes again calculating how the secondary source affects the nodes’ multiplicity. These multiplicities are then added together for each node. Once this has been done the multiplicities can be used to predict how the system will respond. List Of Assumptions Neutron Spectrum Produced By Fission Neutrons in the fast spectrum between 1.5 – 5 MeV are considered to be the only neutrons produced by fission. In reality this is consistent with the vast majority of all neutrons produced in fission by both Uranium-238 and Thorium-232. A lack of data exist for the neutron spectrum for fission in Th232 and it is assumed to similar to U238. Average secondary neutron energy is shown in Figure A50 (First moments (average energies) of 235,238U and 239Pu prompt fission neutron spectra for endf / B-VII.0 calculated with the Los Alamos model

[0069] in comparison with those of endf / B-VI. Fission Cross Sections Cross section Element value Reasoning Thorium- 0.15 barn From the data collected from the cross-section working group, the 232 cross section for Thorium-232 fast fission to be 0.15 barn between 1.5- 5 MeV fast neutrons. Uranium- 0.6 barn From the data collected from the cross section working group, the cross 238 section for Uranium-238 fast fission is fairly consistent at 0.6 barn between 1.5-5 MeV fast neutrons. Plutonium- 1.8- 2.2 From the data collected from the cross section working group, the cross 239 barn section for Plutonium fast fission is inconsistent with a range between 1.8 barn and 2.3 between 1.5-5 MeV fast neutrons. Fission Multiplicities Neutron Multiplicity Element value Reasoning Thorium- 2.3 Evaluation of the prompt neutron multiplicities for Th232 232 suggested that a conservative 2.3 neutrons per fission for the average energy produced. Uranium- 2.5 Evaluation of the prompt neutron multiplicities for U238 238 suggested that a conservative 2.5 neutrons per fission for the average energy produced. Plutonium- 3.2 Evaluation of the prompt neutron multiplicities for Pu239 239 suggested that a conservative 3.2 neutrons per fission for the average neutron energy produced. Figure A51 shows neutron multiplicities in prompt fission of Thorium 232. Figure A52 shows the fission and capture cross section of Uranium 238. Figure A53 shows neutron multiplicities in prompt fission of Uranium 238. Figure A54 shows prompt fission neutron multiplicities in Plutonium 239. Atomic Density Of Fuel Atoms Element (xE24) / cm^3 Reasoning Thorium- 0.03039 Assumed to be 100% of the density and not alloyed to another 232 metal. Uranium- 0.04833 A multiplier of 0.97 was also used in conjunction with this value 238 to simulate the need for at least one alloy. Plutonium 0.04983 Assumed to be 100% of the density and not alloyed to another metal. ADS Neutron Source We accurately predict the neutron source that could be expected from both a single step ads source (direct proton induced fission) and a two-step ads source whereby the target is Lithium-7 (targeting the (p,n) reaction). ads Neutron Source Source Source Type rate (n / s) Reasoning Direct proton 1.217 Calculated at 500 mA of 26.5 MeV protons on direct proton bombardment ⋅ 1015fission of U238. (single-step) Light atom target 1 ⋅ 1013Calculated at 500 mA of 2.25-13 MeV protons using a cross (Li-7 (p,n), two-step) − 4 section of 0.3 barn. This is the lower limit of the reaction as the ⋅ 1013peak interaction is 0.58 barn, but the 0.3 barn was found to be more consistent over the spectrum of 2.25 – 13 MeV Figure A11 shows the reactions of Lithium-7 under proton bombardment. Effect Of Lead andLBE On Neutron Spectrum have no effect on the neutron spectrum. This assumption is based on a very low cross section of absorption and scattering by the coolant as well as, due to the high atomic weight of the coolant, a scattering event would result in a minimal change in neutron energy. It was determined that, on average, 135.91cm of coolant would be required to slow a neutron down to the point where it would no longer be useful – assuming a 2 MeV average and a 1.5 MeV minimum energy to be functionally “useful” for fission. This is in comparison to a 34.49cm mean free path for Uranium and 219.37 cm for Thorium. Such an assumption reduces computational complexity but is inaccurate for larger cores. The size of the trinity series cores is 30cm in radius and 45cm for rose-3 cores – well within the maintenance distance for a “no moderation” assumption. ( ^^ − 1)2^^ + 1 (208 − 1)2208 + 1 ^^ ^^ ^^ ^^ ^^ lbe Properties Melting point 125°C / (+ / -400K) Boiling point 1660°C / (+ / -1930K) Thermal conductivity + / -20W / mK (varies) Heat capacity 134J / kgK at 1500K (varies) Neutron scattering cross-section 6.9 barns Neutron absorption cross-section 1.5 mbarns Density 11.065 g / cm^3 Build Up Of Fission Product Material Effects Moderation A review of the most common fission products of Th232 and U238 has been conducted. The analyses took a weighted total, capture and total scattering cross section of the isotopes with available data – 44.3% and 62.8% of all fission products for Th232 and U238 respectively. The weighted, adjusted, total scattering cross section (assuming 100% of the material) is shown at the bottom of each table and again in the analyses of each core type. In order to accurately represent the most pessimistic of effects, Mo-95 was assumed to be 100% of all atoms when considering the scattering effects – as it’s the lightest atom – while maintaining the adjusted total scattering cross section. Additionally, the fission products are assumed to have scattered evenly throughout the cores coolant which then establishes the atomic density accordingly. Fission WIMS U-238 Total Weighted Capture Weighted Total Weighted product ID Scattering 42-Mo- 4095 5,13E-02 7,864 4,03E-01 0,3244 1,66E-02 7,5396 3,87E-01 95 43-Tc- 99 4099 6,24E-02 9,126 5,69E-01 0,658 4,10E-02 8,468 5,28E-01 44-Ru- 4101 6,21E-02 7,78 4,83E-01 0,7557 4,69E-02 7,0243 4,36E-01 101 45-Rh- 4103 0,00E+00 8,321 0,00E+00 0,7325 0,00E+00 7,5885 0,00E+00 103 45-Rh- 4105 4,09E-02 8,321 3,41E-01 0,7325 3,00E-02 7,5885 3,11E-01 105 47-Ag- 4109 2,52E-03 8,335 2,10E-02 0,6336 1,59E-03 7,7014 1,94E-02 109 54-Xe- 4131 3,29E-02 7,878 2,59E-01 0,2781 9,14E-03 7,5999 2,50E-01 131 54-Xe- 5134 7,46E-02 7,878 5,87E-01 0,2781 2,07E-02 7,5999 5,67E-01 134 54-Xe- 4135 2,69E-04 7,878 2,12E-03 0,2781 7,47E-05 7,5999 2,04E-03 135 54-Xe- 4136 6,68E-02 7,878 5,27E-01 0,2781 1,86E-02 7,5999 5,08E-01 136 55-Cs-133 4133 6,73E-02 8,01 5,39E-01 0,5251 3,53E-02 7,4849 5,04E-01 55-Cs-134 4134 6,46E-09 7,316 4,73E-08 1,16 7,49E-09 6,156 3,98E-08 55-Cs-135 5135 3,71E-07 7,366 2,73E-06 0,2272 8,43E-08 7,1388 2,65E-06 55-Cs-137 4137 6,23E-02 7,366 4,59E-01 0,2272 1,41E-02 7,1388 4,44E-01 60-Nd- 4143 4,62E-02 11,26 5,20E-01 0,3606 1,66E-02 10,8994 5,03E-01 143 60-Nd- 4145 3,87E-02 12,17 4,71E-01 0,5222 2,02E-02 11,6478 4,51E-01 145 62-Sm- 6147 0,00E+00 15,01 0,00E+00 1,246 0,00E+00 13,764 0,00E+00 147 62-Sm- 4149 0,00E+00 14,61 0,00E+00 2,27 0,00E+00 12,34 0,00E+00 149 62-Sm- 4150 3,29E-08 12,26 4,03E-07 0 1,62E-08 11,7673 3,87E-07 150 62-Sm- 4151 7,99E-03 12,56 1,00E-01 2,943 2,35E-02 9,617 7,69E-02 151 62-Sm- 4152 5,30E-03 11,22 5,95E-02 0,4856 2,57E-03 10,7344 5,69E-02 152 63-Eu- 5151 0,00E+00 13,39 0,00E+00 3,987 0,00E+00 9,403 0,00E+00 151 63-Eu- 5152 2,92E-14 13,39 3,91E-13 3,987 1,16E-13 9,403 2,75E-13 152 63-Eu- 4153 4,15E-03 10,78 4,47E-02 2,555 1,06E-02 8,225 3,41E-02 153 63-Eu- 4154 8,25E-11 11,9 9,82E-10 3,09 2,55E-10 8,81 7,27E-10 154 63-Eu- 4155 1,42E-03 11,21 1,59E-02 1,507 2,13E-03 9,703 1,37E-02 155 64-Gd- 2154 0,00E+00 11,41 0,00E+00 2,905 0,00E+00 8,505 0,00E+00 154 64-Gd- 2155 0,00E+00 11,41 0,00E+00 2,905 0,00E+00 8,505 0,00E+00 155 64-Gd- 2156 7,60E-04 11,41 8,68E-03 2,905 2,21E-03 8,505 6,47E-03 156 64-Gd- 2157 4,14E-04 11,41 4,72E-03 2,905 1,20E-03 8,505 3,52E-03 157 64-Gd- 2158 1,85E-04 11,41 2,11E-03 2,905 5,37E-04 8,505 1,57E-03 158 66-Dy- 160 1,89E-11 10,71 2,02E-10 0,7471 1,41E-11 9,9629 1,88E-10 160 66-Dy- 161 1,22E-05 10,73 1,30E-04 1,847 2,24E-05 8,883 1,08E-04 161 66-Dy- 162 3,41E-06 10,98 3,74E-05 0,449 1,53E-06 10,531 3,59E-05 162 66-Dy- 163 2,03E-06 10,81 2,20E-05 1,13 2,30E-06 9,68 1,97E-05 163 66-Dy- 164 1,25E-06 10,13 1,26E-05 0,2194 2,74E-07 9,9106 1,24E-05 164 Total 6,28E-01 5,42E+00 3,14E-01 5,10E+00 Adjust 1E0 8,62E+00 4,99E-01 8,12E+00 Fission WIMS ID Th-232 Total Weighted Capture Weighted Total Weighted product Scattering 42-Mo- 95 4095 5,75E-02 7,864 4,52E-01 0,3244 1,87E-02 7,5396 4,34E-01 43-Tc- 99 4099 2,98E-02 9,126 2,72E-01 0,658 1,96E-02 8,468 2,53E-01 44-Ru-101 4101 7,14E-03 7,78 5,55E-02 0,7557 5,39E-03 7,0243 5,01E-02 45-Rh-103 4103 6,15E-11 8,321 5,11E-10 0,7325 4,50E-11 7,5885 4,66E-10 45-Rh-105 4105 5,25E-04 8,321 4,37E-03 0,7325 3,85E-04 7,5885 3,99E-03 47-Ag-109 4109 6,60E-04 8,335 5,50E-03 0,6336 4,18E-04 7,7014 5,08E-03 54-Xe-131 4131 1,62E-02 7,878 1,28E-01 0,2781 4,51E-03 7,5999 1,23E-01 54-Xe-134 5134 5,20E-02 7,878 4,10E-01 0,2781 1,45E-02 7,5999 3,96E-01 54-Xe-135 4135 1,02E-04 7,878 8,04E-04 0,2781 2,84E-05 7,5999 7,75E-04 54-Xe-136 4136 5,54E-02 7,878 4,37E-01 0,2781 1,54E-02 7,5999 4,21E-01 55-Cs-133 4133 4,02E-02 8,01 3,22E-01 0,5251 2,11E-02 7,4849 3,01E-01 55-Cs-134 4134 3,04E-10 7,316 2,22E-09 1,16 3,53E-10 6,156 1,87E-09 55-Cs-135 5135 3,72E-08 7,366 2,74E-07 0,2272 8,45E-09 7,1388 2,65E-07 55-Cs-137 4137 5,73E-02 7,366 4,22E-01 0,2272 1,30E-02 7,1388 4,09E-01 60-Nd-143 4143 6,63E-02 11,26 7,47E-01 0,3606 2,39E-02 10,8994 7,23E-01 60-Nd-145 4145 5,45E-02 12,17 6,63E-01 0,5222 2,85E-02 11,6478 6,35E-01 62-Sm-147 6147 0,00E+00 15,01 0,00E+00 1,246 0,00E+00 13,764 0,00E+00 62-Sm-149 4149 0,00E+00 14,61 0,00E+00 2,27 0,00E+00 12,34 0,00E+00 62-Sm-150 4150 1,45E-09 12,26 1,78E-08 0 7,14E-10 11,7673 1,71E-08 62-Sm-151 4151 3,64E-03 12,56 4,57E-02 2,943 1,07E-02 9,617 3,50E-02 62-Sm-152 4152 7,55E-04 11,22 8,48E-03 0,4856 3,67E-04 10,7344 8,11E-03 63-Eu-151 5151 0,00E+00 13,39 0,00E+00 3,987 0,00E+00 9,403 0,00E+00 63-Eu-152 5152 0,00E+00 13,39 0,00E+00 3,987 0,00E+00 9,403 0,00E+00 63-Eu-153 4153 3,10E-04 10,78 3,34E-03 2,555 7,92E-04 8,225 2,55E-03 63-Eu-154 4154 2,20E-13 11,9 2,62E-12 3,09 6,80E-13 8,81 1,94E-12 63-Eu-155 4155 3,62E-05 11,21 4,05E-04 1,507 5,45E-05 9,703 3,51E-04 64-Gd-154 2154 2,69E-21 11,41 3,06E-20 2,905 7,80E-21 8,505 2,28E-20 64-Gd-155 2155 0,00E+00 11,41 0,00E+00 2,905 0,00E+00 8,505 0,00E+00 64-Gd-156 2156 2,69E-05 11,41 3,07E-04 2,905 7,82E-05 8,505 2,29E-04 64-Gd-157 2157 9,32E-06 11,41 1,06E-04 2,905 2,71E-05 8,505 7,93E-05 64-Gd-158 2158 4,64E-06 11,41 5,30E-05 2,905 1,35E-05 8,505 3,95E-05 66-Dy-160 160 4,87E-14 10,71 5,22E-13 0,7471 3,64E-14 9,9629 4,85E-13 66-Dy-161 161 1,45E-07 10,73 1,55E-06 1,847 2,68E-07 8,883 1,29E-06 66-Dy-162 162 7,98E-08 10,98 8,76E-07 0,449 3,58E-08 10,531 8,40E-07 66-Dy-163 163 4,63E-08 10,81 5,01E-07 1,13 5,24E-08 9,68 4,49E-07 66-Dy-164 164 2,03E-08 10,13 2,06E-07 0,2194 4,46E-09 9,9106 2,01E-07 Total 4,43E-01 3,98E+00 1,77E-01 3,80E+00 Adjust 1E+0 8,99E+00 4,01E-01 8,59E+00 Core Core Mean Free Path by Percentage Fuel Burn UP Volume 10% Lethargy 20% Lethargy 30% Lethargy 40% Lethargy Mean Free Mean Free Mean Free Mean Free Path Path Path Path Th232 Experimental 294195 14948,75 7474,37 4982,92 3737,19 Rotating U238 Experimental 294195 9800,737 2450,18 3266,91 2450,18 Rotating Th232 Experimental 294195 40657,08 10164,3 13552,4 10164,3 Ext Rotating U238 Experimental Ext 294195 26655,7 6663,93 8885,23 6663,93 Rotating Th232 Experimental 294195 20328,48 5082,12 6776,16 5082,12 non-Rotating U238 Experimental 294195 13327,82 3331,95 4442,61 3331,95 non-Rotating Th232 Trinity 3E+06 53905,7 13476,4 17968,6 13476,4 U238 Trinity 3E+06 35341,8 8835,45 11780,6 8835,45 Th232 X5 3E+06 32328,73 8082,18 10776,2 8082,18 U238 X5 3E+06 21195,45 5298,86 7065,15 5298,86 Th232 Rose 3 1E+07 72492,47 18123,1 24164,2 18123,1 U238 Rose 3 1E+07 47527,71 11881,9 15842,6 11881,9 (^^ − 1)2^^ + 1 1 ^^^^ℎ232= (8.99 ^^ − 24)⋅ ^^^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^1 ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^^^ ^^ ^^⋅ ^^^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^, ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^= ^^ ^^ ^^ℎ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ℎ The results concluded that, between a 0-40% fuel burn up, at no point does the fission product build up ever get to a meaningful point to which they would have a moderation effect. Even the lowest distance of 3331,95cm far exceeds that of the core radius for even the largest core at 130 cm. Further information regarding fission predict cross sections can be found in “Review of ENDF / B-VI Fission-Product Cross Sections” by R.Q. Wright and R.E. MacFarlane prepared by Oak Ridge National Laboratory. Event Table For Assumptions That May Be Found To Be Inaccurate Assumption Potential outcome Level of possibility (1- Effect section, they are Atomic density Decreasing of atomic 75 – very likely, to be Slight reduction in Metallic core The metallic fuel according to some embodiments of the present invention may be referred to as rose core. This core separates fuel into a Tritosphere configuration with up to seven layers (or more) of “petals” or shells that substantially surround the ignition bulb. Each petal layer features 97% Uranium- 238, 3% Tungsten and comprises ribs or blades 5cm in depth and 2cm in height that is separated according to a constant angle for that layer. Every blade peers directly into the centre with a flat face of a height of 2cm, i.e. each blade is aligned with the ignition bulb so that its 2cm flat face is substantially perpendicular to a line between it and the ignition bulb. Figure A37 shows a side view and a top view of a rose core while Figure A38 shows an individual fuel Tritosphere. Addition Of Movement Concerning The 4th Law Each petal is supported by a tungsten support stem which is attached to a central base that allows each petal to move in layers: similar to the movement of a rose in bloom. The advantage of allowing each petal to move is related to the 4th law and the influence of distance on the establishment of neutron planes in terms of local criticalities: removing fuel elements out of the ability to establish a “mirror” overlap of neutron planes ensures the destruction of the local criticality function and thus a prompt shutdown or, forcing some layers to function entirely as irradiated passive fuel in a “subcritical” format. Natural Convection Dynamics The fuel arrangement attempts to allow adequate convection flow for pool heating of LBE coolant with the creation of blades that are angled with a flow trajectory upwards towards the centre and a plume directly after – a typical convection heating situation for elements in a fluid medium. While figures A37 and A38 show a horizontal fuel blade, it is preferred that the horizontal layer be removed or the rose core re-designed so that there is no horizontal blade. This is due to a potential of unfavourable pooling of superheated LBE that may become trapped under the fuel element. Passive Safety Feature – controlled meltdown Using a 97%-3% Uranium-Tungsten fuel provides a melting point of 1650°C while the LBE’s boiling point is 1660°C. Due to the nature of two-phase heating stagnating during the transition, it would require the Uranium to have fully liquified before the LBE would begin transitioning to a vapour: thus, remaining unpressurised. The density of liquid uranium is 17.3 g / cm3while LBE in a liquid state is 11 g / cm3and in the event of a meltdown, this would force the uranium to sink to the bottom of the chamber and out of range of the locally mirrored criticality (Nuclear Energy Agency 2015) (Okamoto, 2009). Once at the bottom, the Uranium 238 is within the cold zone of the LBE and will begin to rapidly solidify and will be in the range of irradiated fuel in a “subcritical” state. Naturally, this is a complete destruction of the unit but, according to the IAE international nuclear event scale (INES), ensures that even if every other safety feature failed the maximum INES event category reached is a partial level 4 with no environmental or public safety consequences – see Figure A39. A level four is a partial meltdown and release of reactor fuel resulting in exposure to radiation. The meltdown of the rose core lacks the latter –radiation exposure – but satisfies the first requirement. In a generation three pressurised water reactor, a meltdown would have caused an over- pressurisation of water within the vessel which would lead to a subsequent rupture of the containment vessel in the event of a disaster – Chernobyl. The lack of pressurisation, and self- destruction before allowing pressurisation, is a completely new approach. Metallic Core Concept – Trinity Figure A55 shows a side and top view of a three fuel-element design suitable for incorporation into the reactor shown in Figure 27. The Trinity core provides an improvement on the Rose core in respect of ease of manufacturing and improved performance. The Rose core features a number of unique components and requires quite a large reactor vessel due to the natural convection requirement of the coolant. By contrast the Trinity core features three spiral fins designed to direct coolant through the axis of the reactor to incorporate forced convection in the lead coolant, thus making the reactor far smaller. Additionally, the Trinity core means that the use of Thorium becomes a much more viable concept as the core is significantly denser at the centre of the reactor. By utilising Thorium and forced convection both complexity and cost are reduced as both of these areas require little research for adaption into a system. The shape of the spiral elements of the Trinity core may be defined by rotating a line about a point in an x-y plane while steadily increasing the value on the z-axis to define a 3-dimensional element. The rotation is preferably about one fifth of a full turn. Addition Of Movement With Reference To The 4th Law Spiral movement does not change the distances between nodes as the entire reactor is spinning about a symmetric axis. The addition of a mechanism of rotation adds complexity from an engineering stand point, but is an additional safety system that may directly impact the heat extraction rate rather than the fission rate – in the case of the Rose petals – which was already controlled by the accelerator. Forced Convection Dynamics Forced convection in lbe and lead have been modelled extensively. In many respects, this reduced the complexity as a pool boiling modal (required for Rose) would need to be created as a near-scale modal to be accurate. Forced convection drastically increases the heat transfer rate. Due to the shape of the reactor, fuel is forced through the axis of the core and heat transfer rate is directly proportional to the rotation of an external motor – which may be adjusted if the need for greater heat transfer arises. Passive Safety Feature – Controlled Meltdown If the Trinity system were to employ Thorium fuel, the coolant would also have to change to pure lead to account for the increased melting temperature of Thorium. Pure lead will evaporate at 1750°C while Thorium will become a liquid at 1755°C. The effect of this means that the lead coolant, in a forced convection system, will become a gas if Thorium reaches its melting temperature. Two phase cooling, simultaneous to the softening / melting of the surface level fuel will begin to remove additional heat from the reactor before a full meltdown begins. Damage to the reactor fuel is likely to occur but, a large heat transfer ability will supplement the rotating system bringing the reactor back into standard operating temperature ranges. The danger this possesses is the pressurisation of lead coolant. Measures need to be made to safeguard the over pressurisation of the vessel – either to activate a gas extraction system which then returns the gas as a liquid back to the core or, a direct lead gas coolant condenser inside the reactor. Metallic Core concept – Willow Run Figure A56 shows a side and top view of a five fuel-element design suitable for incorporation into the reactor shown in Figure 27. The Willow Run core was designed with the desire to improve the Rose core on the basis of ease of manufacturing. The Rose core features a large number of unique components and requires a larger reactor vessel due to the natural convection requirement. Willow run features five spiral fins designed to direct coolant through the axis of the reactor to incorporate forced convection in the lead coolant, thus making the reactor far smaller. Additionally, the use of Thorium as a fuel becomes a much more viable concept as the core is significantly denser at the centre of the reactor. The change over to Thorium and forced convection both reduce complexity and investment as both of these areas require little research for adaption into a system. The addition of two fuel fins relative to Trinity core, with a reduced angle, increased the heat transfer ability of the reactor core in a significant manner. This model is seen as a direct improvement on Trinity while still inheriting similar design difficulties around the rotation of the fuel element. Addition Of Movement With Reference To The 4th Law Spiral movement does not change the distances between nodes as the entire reactor is spinning about a symmetric axis. The addition of a mechanism of rotation adds complexity on an engineering standpoint but is an additional safety system that may directly impact the heat extraction rate rather than the fission rate – in the case of the Rose petals – which was already controlled by the accelerator. The decreased gap between fuel fins increased the overall heat transfer ability as the additional surface area was heavily influential. Forced Convection Dynamics Forced convection in lbe and lead have been modelled extensively. In many respects, this reduced the complexity as a pool boiling modal (required for Rose) would need to be created as a near-scale modal to be accurate. Forced convection drastically increased the heat transfer rate. Due to the shape of the reactor, fuel is forced through the axis of the core and heat transfer rate is directly proportional to the rotation of an external motor – which may be adjusted if the need for greater heat transfer arises. Passive Safety Feature – Controlled Meltdown If the Willow Run system were to employ Thorium fuel, the coolant would also have to adjust to pure lead to account for the increased melting temperature of Thorium. Pure lead will evaporate at 1750°C while Thorium will become a liquid at 1755°C. The effect of this means that the lead, in a forced convection system, will become a gas if Thorium reaches its melting temperature. Two phase cooling, simultaneous to the softening / melting of the surface level fuel will begin to remove additional heat from the reactor before a full meltdown begins. Damage to the reactor fuel is likely to occur but, a large heat transfer ability will supplement the rotating system bringing the reactor back into standard operating temperature ranges. The danger this possesses is the pressurisation of lead coolant. Measures need to be made to safeguard the over pressurisation of the vessel – either to activate a gas extraction system which then returns the gas as a liquid back to the core or, a direct lead gas coolant condenser inside the reactor. The benefit of the additional fins is the increased heat transfer dynamics. Future improvements may follow a similar path of decreasing the fin thickness while increasing the number of fins. A structural analysis of the rotating core will also become more and more necessary with the reduction of the fin thickness. Figure A57 shows a heat map simulation of a three ring Rose core from above and Figure A58 shows a side view. The Rose core has a very spread-out multiplicity heat map as shown in the figures. This is desirable because it means that the fuel will burn at roughly the same rate. The rise time is shown in Figure A59 which is longer than that for an equivalent Uranium core (Figure A62) but is still viable. Figures A60, A61 and A62 duplicate Figures A57 – A59 with Uranium as the fuel. At 25MW the Thorium Rose core has a projected life of 55.39 years and a half-life (when half the power output is reached) of 127.97 years. The Uranium Rose core is better at a projected life of 88.28 years and a half-life of 203.97 years. Figures A63, A64 and A65 duplicate Figures A57 – A59 for a Trinity core with Thorium as the fuel and Figures A66 – A68 have Uranium as the fuel. Trinity has a slightly less spread out heat-map as shown in the figures, therefore a larger core would be more desirable to increase the lifespan. However, Trinity has a faster rise time than rose as shown in Figures A65 and A68. At 25MW the Thorium Trinity core has a projected life of 9.66 years and a half-life of 22.32 years, the Uranium Trinity core is better at a projected life of 15.40 years and a half-life of 35.57 years. Note that lifespan is directly linked to the mass of fuel, therefore Rose cores last longer but require roughly 5 times more mass - which directly increases the cost of the unit. Figures A69, A70 and A71 duplicate Figures A57 – A59 for a Thorium Willow Run core, that is to say a five-element rotating core, while Figures A72 – A74 illustrate a Uranium core. From Figures A69, A70, A72 and A73 it can be seen that Willow Run is shown to have a well spread out heat-map. Willow Run is shown in Figures A71 and A74 to have a longer rise time. This is expected to be due to the angle of the blade, allowing less of the blade to be influenced by the source bulb. At 25MW the Thorium Willow Run core has a projected life of 16.06 years and a half-life of 37.11 years, the Uranium Willow Run core is better at a projected life of 25.60 years and a half-life of 59.15 years. Heat Transfer Methodology The on Eutectic Alloy And properties, Materials Compatibility, Thermal- Hydraulics And Technologies Extensive use of the Handbook on Lead-bismuth Eutectic Alloy and Lead Properties, Materials Compatibility, Thermal-hydraulics and Technologies was conducted to construct a simplistic thermal capability modal of the ade system. In the case of the Rose core, it was concluded that a mock system would be necessary to conduct such a thermal capacity modal, and thus a model was not conducted, while the Trinity cores underwent a forced convection modal with the available data from the handbook. The Handbook on Lead-bismuth Eutectic Alloy and Lead Properties, Materials Compatibility, Thermal-hydraulics and Technologies – or “handbook” – is a compilation of research from the last century on the heat transfer ability of Lead, LBE and Bismuth. The handbook was compiled by the Nuclear Energy Agency – a group of 31 countries – for the sole purpose of reviewing metallic alloys for the use of cooling nuclear systems. The handbook was peer-reviewed and published in 2015 and data from this handbook will be used exclusively for the thermal model as it, in itself, projects the most accurate data collection the science possess. Trinity Models – Forced Convection Of Lead And lbe The trinity models have the ability to rotate through the forced, external, power of a motor. Due to the shape of the fuel fins / elements, the core functions as an axial flow turbine undergoing heat transfer at the surface of the fins. To produce a basic numerical modal of this, the gap between the fins was assumed to be a circular pipe of diameter with a centre along the midpoint of the fuel (200mm radius from the centre of the core) with the size of the pip being determined by the distance between the fuel pieces. Figure A75 shows a Trinity Three Pipe Modal and Figure A76 shows a Trinity five Pipe Modal illustrate this pseudo pipe formation. The fluid flow rate is dictated by rpm, which then in tern dictates the heat transfer rate. Fluid velocity is governed by the following equation: 2 ^^ ^^ ^^ ^^ ⋅⋅ ^^ And Figure A77 shows the fluid velocity equation vectors where: ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^^^ ^^ ^^ ^^ ^^ ^^= 200 ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ℎ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ The exit angle for trinity three and five are 30° and 15° respectively. From the establishment of the fluid velocity, the Reynolds number could be established; ^^ ^^ ^^ ^^ ^^ = ^^ Where; $$L=Length\ of\ the\ reactor\ core\big$$ ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ $$v=fluid\ velocity\big$$ ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ The Length of the reactor core is 720mm and the data for the dynamic viscosity and density was taken from the handbook at 1000k; ^^^^ ^^= 10200 ^^ ^^ / ^^3^^^^ ^^ ^^= 9850 ^^ ^^ / ^^3^^^^ ^^= 1.325 ^^ − 3 ^^^^ ^^ ^^= 1 ^^ − 3 Once the Reynolds number was established, the Péclet number could be established through the equation; ^^ ^^ = ^^ ^^ ⋅ ^^ ^^ The Prandtl number was taken as the chemical constant at 700°C to be 0.01 and 0.009 for Lead and lbe respectively. Figure A78 shows the density of melted LBE versus temperature and Figure A79 shows the dynamic viscosity of melted LBE versus temperature at normal pressure. Figure A80 shows the Molecular Prandtl number as a function of temperature for different fluids. Once the Péclet number has been established, the Nusselt number can be established through the equation: ^^ ^^ = 3.3 + 0.02(^^ ^^)0.8this is equation 10.78 from the handbook and may be used for both lbe and Lead (Nuclear Energy Agency, 2015). This equation assumes a uniform wall temperature. The reason behind assuming a uniform wall temperature is that this scenario is more likely than a uniform heat flux due to the nature of the ade point source. With the established Nusselt number, the heat transfer coefficient may be established through the assumption of the fin as acting as a coolant pipe; ^^ ^^ ⋅ ^^ ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ The diameter of the pipe comes from Figure A75 and Figure A76 where trinity three possesses a 167.8mm diameter and trinity five possesses a 126.8mm diameter. The thermal conductivity of Lead and lbe has been established as 20 W / mK and 17 W / mk respectively. Figure A81 shows Thermal Conductivity Of Molten Lead, Bismuth And lbe Versus temperature. From the heat transfer coefficient, the thermal heat transfer rate could be established through the law of cooling: Q = hA(Ts− Tf)A = surface area Trinity 5 has a surface area of 2,9583m3 and Trinity 3 has a surface area of 1,77498m3 respectively. A high standard operating temperature of the core would be 1300°C, this is a point before Thorium would exhibit material deformation. An upper 1500°C is also displayed – this refers to an “emergency” temperature in which the fins are experiencing material deformity. Figure A82 shows a graph of heat transfer capability versus r.p.m. for the three (Trinity) and five (Willow Run) cores at the two different temperatures and for lead and LBE coolant. Thermal Cycle Figure A83 shows a thermal cycle having twin Rankine with reheat and re-gen as an alternative to those shown in Figures A45 and A46. The calculations are as follows: Net Power Output: ^^^^^^ ^^ = 10500 ^^ ^^ Turbine efficiency: ^^^^= 0.4 Boiler efficiency: ^^^^ ^^ ^^ ^^ ^^ ^^= 0.9 Pump efficiency: ^^^^= 0.8 Turbine compression ratio: ^^^^= 4 State 1: ^^1= 540° ^^ = 813.15 ^^ ^^1= 12 ^^ ^^ ^^ From State 1 using steam tables: ℎ1= 3455.781 ^^ ^^ / ^^ ^^ ^^ ^^1= 6.629 ^^ ^^ / ^^ ^^ ^^ ℎ ^1− ℎ ^2State 2s: ^^ ^^2=1= 3 ^^ ^^ ^^ ^^^^^^2 ^^= ^^2= 3 ^^ ^^ ^^ ^^2 ^^= ^^1From State 2s using steam tables: ℎ2 ^^= 3042.386 ^^ ^^ / ^^ ^^ ^^ State 2 using turbine efficiency equation: ℎ2= ℎ1− ^^^^×(ℎ1− ℎ2 ^^)= 3290.423 ^^ ^^ / ^^ ^^ ^^ State 2 using steam tables: ^^2= 525.95° ^^ = 699.1 ^^ State 3: ^^3is assumed to return to ^^1: ^^3= ^^1= 540° ^^ = 813.15 ^^ ^^3= ^^2= 3 ^^ ^^ ^^ From state 3 using steam tables: ℎ3= 3547.041 ^^ ^^ / ^^ ^^ ^^ ^^3= 6.62 ^^ ^^ / ^^ ^^ ^^ ℎ − ℎ ^^3 4State 4s: ^^4 ^^= ^^3From State 4s using steam tables: ℎ4 ^^= 3106.79 ^^ ^^ / ^^ ^^ ^^ State 4 using turbine efficiency equation: ℎ4= ℎ3− ^^^^×(ℎ3− ℎ4 ^^)= 3290.423 ^^ ^^ / ^^ ^^ ^^ State 4 using steam tables: ^^4= 348.35° ^^ = 721.5 ^^ For Boiler: ^^ − 4 − 5 = ^^7−8ℎ4− ℎ5= ℎ8− ℎ7Assume State 5 is a saturated vapor: ^^5= ^^4From steam tables: ℎ5= 2765.64 ^^ ^^ / ^^ ^^ ^^ Assume State 6 is a saturated liquid: ^^6= ^^5From steam tables: ℎ6= 709.38 ^^ ^^ / ^^ ^^ ^^ ^^6= 2.02 ^^ ^^ / ^^ ^^ ^^ State 7s: ^^7 ^^= ^^6From steam tables: ℎ7 ^^= 721.85 ^^ ^^ / ^^ ^^ ^^ ℎ7 ^− ℎ ^^^ 6State 7 using equation [eq:Pump ℎ7 ^^− ℎ6^^ ^^ ^^ ^^ From equation [eq:Boiler ℎ8= ^^^^ ^^ ^^ ^^ ^^ ^^(ℎ4− ℎ5)+ ℎ7= 1269.74 ^^ ^^ / ^^ ^^ ^^ ^^^^ ^^ ^^= ^^^^[ℎ2− ℎ1]+ ^^^^[ℎ4− ℎ3]+ ^^^^[ℎ7− ℎ6]^^^^= 29.4 ^^ ^^ / ^^ ^^^^ ^^= ^^^^[ℎ1− ℎ8] + ^^^^[ℎ3− ℎ2] = 71834.79 ^^ ^^ Safety Systems And Decommissioning of the rose core, it is designed to use the thermodynamics of two-phase heat transfer to strategically destroy fuel elements before allowing the lbe coolant to vaporize – thus ensuring no pressurization of the reactor core. During a phase change, the temperature of the medium stays constant and this, in combination with Newton’s law of cooling, ensures that the vaporization of lbe is impossible. “The rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings while under the effects of a breeze”– Newton’s law of cooling ^^ = ℎ ^^( ^^1− ^^2) In the event of a runaway reaction (where all active control systems have failed), and the Uranium- Tungsten alloy approaches its melting temperature of 1650°C, the fuel elements cannot heat the lbe beyond this temperature of 1650°C – which is below the vaporization point of lbe at 1660°C. Once in a liquid state, the Uranium-Tungsten alloy will sink to the bottom of the chamber due to the density difference between the alloy and the lbe medium. The alloy will also separate into tungsten and Uranium respectively. Uranium will solidify at 1132°C in the cooler lbe (return temperature of 480°C) and will also be out of range of the neutron field planes established in the 4th law – creating only irradiated fuel with no mirror effects. If the entire core melts down and is out of range of the source bulb’s mirror field, the reaction rate becomes entirely subcritical at the bulb with a very low flux field – even at utility-scale, this irradiation amount is only a few kilowatts. This is how the reactor core was designed from the start - with failure in mind. Every other reactor before this attempts to stop a runaway reaction and over-pressurization by reinforcing stopgaps from that event, but the rose core started with failure and accepted it. This mantra change is imperative in passive safety and is the primary passive safety element – natural laws of thermodynamics. Active Safety The most obvious is the control of the particle accelerator: varying the input or shutting it down entirely will reduce / collapse the neutron mirror fields in a highly predictable way. This, in itself, is also a passive safety element as the shutdown of electrical power is typically the first occurrence in the event of a disaster: floods, electrical short, terrorism, etc. The reactor core does not feature control rods; the particle accelerator is the control. Every law of fission, neutron reaction dynamics, and thermodynamics actively oppose this reactor core from functioning without the particle accelerator. The rate of reaction is monitored via neutron detectors embedded in the shielding and will be the first indication of an increased reaction rate. When the reactor is running near the desired energy rate, the beamline intensity is varied rhythmically to balance the core in the vicinity of the desired output. All of this is done with no human input and will all be automatic. To protect equipment – a potential financial loss not a potential exposure risk – the following measures are available: 1. Fire suppression systems may be installed near all of the electronics with a preference for protecting the cyclotron. 2. Cycle pressure and temperature systems to monitor for any unexpected change or loss in pressure triggering an immediate shutdown. 3. 4-hour backup power for all control systems to adequately monitor the shutdown process. 4. Radiation detection monitors surrounding both thermal cycles – a spike in radiation will trigger an immediate shutdown. Breach Of Containment lbe, at room temperature, is solid. This allows for fission products to be encased within this solid in the event of a breach of containment of the lbe closed cycle. Shut down of the reactor also closes the leak point as it, too, would cool to a solid allowing for the unit to be repaired safely. Regulation regulations, Uranium-238 is classified as low-level nuclear waste, and the destruction of this waste is labeled under waste treatment. In the view of industry experts there is a possibility of classifying the ade reactor as a waste destruction device rather than a reactor core which will make implementation drastically easier than a generation three – or even a generation four – reactor. Decommissioning and lbe heat exchanger are designed to be repository ready. The purpose of this is to simplify the decommissioning process in that the entire unit is placed into retirement without the need to process and separate waste or destroy components. Each reactor core has a large half-life. The reactor may continue beyond a single half-life, but it is theorized that the unit’s structure may have integrity problems after one half-life (69.3% material remaining). Every fission event creates a local discontinuity within the material and, while each member is not load-bearing, the weight itself at such a point may become too much to hold and crack under the thermal stress. It may be recommended to construct a specialized facility for decommissioned units. Test Cores Figure A84 shows a test core having a non-rotating natural convection impeller with Thorium fuel. Figures A85 and A86 show the heatmaps and Figure A87 shows the output power. Figures A88 and A89 shows the heatmaps and Figure A90 the output for the test core with Uranium fuel. The heat-maps in figures A85, A86, A88 and A89 show the multiplicities inside the test cores, as expected the outside of edges have the lowest multiplicities while those closest to the source bulb have the highest. The heat-map also shows that the shape of the source bulb has low effect on the distribution of multiplicities, but that it instead only requires fuel to be close to the source node, allowing for the mirror effect to increase the source node’s multiplicity. In figures A87 and A90 it can be seen that Thorium takes roughly 6 hours longer to reach 1MW compared to Uranium which only takes about an hour to reach 1 MW. Thorium however might be a better candidate for test core due to availability, cost and the slower rise allowing for more control and better data capture due to the lower data capture frequency required. Forced Convection Test Cores Figure A91 shows a rotating fuel micro reactor assembly and Figure A92 shows various views of the fuel elements. Figures A93, A94 and A95 show the corresponding heat maps and power output for Thorium fuel. Figures A96, A97 and A98 show the corresponding heat maps and power output for Uranium fuel. Figure A99 shows a control system graph for a core (thorium shown but the principle is valid for all fuels) in which the reactor output is varied up and down in response to demand. This has particular application to the transport field as it allows a ship or train to “throttle back” on the output of the reactor when the vessel is not moving or is moving very slowly. The technique is, of course, usable in all applications. By using neutron detectors the neutrons per second can be monitored, Figure A99 shows a diagram for the response of the system. By setting a desired upper and lower limit, shown in the figure by upper 1 and lower, the output can be controlled by changing the accelerator current. Upper 2 is a safety limit, if this limit is reached the power to the accelerator is cut until troubleshooting and operator re-activation occurs. By using hysteresis between levels lower and upper 1, a balance can be struck between the response of the control loop, activation and de-activation of the accelerator and thermal strain on the components of the reactor. The same can be done for a lower power, idle state, for example 10% power. ^^ ^^ ^^ ^^ ^^ 1 is replaced by ^^ ^^ ^^ ^^ ^^ 1  ^^ ^^ ^^ ^^, ^^ ^^ ^^ ^^ ^^ by ^^ ^^ ^^ ^^ ^^  ^^ ^^ ^^ ^^ and ^^ ^^ ^^ ^^ ^^ 2 with ^^ ^^ ^^ ^^ ^^ 2  ^^ ^^ ^^ ^^. The ^^ ^^ ^^ ^^ ^^ 2  ^^ ^^ ^^ ^^ is proportionally much higher than that of the normal ^^ ^^ ^^ ^^ ^^ 2. The idle state allows for less fuel consumption and heat that needs to be dumped while still shortening the startup time from the idle level. As can be seen from the lower idle and upper 1 idle levels, a much tighter control of the idle level can be maintained. Figure A100 shows reactor ramp up for a Thorium 5-layer core. Figure A101 shows reactor ramp up for thorium trinity rose core. These are times (in seconds) related to startup and idle Uranium Rose Source Bulb time to 0.15MW = 9216 Thorium Rose Source Bulb time = 61654 Thorium Rose Source Bulb Trinity time = 24264.0 Thorium Rose Source Bulb Trinity time = 29776 Thorium Rose Source Bulb Trinity time = 31965 Thorium Rose Source Bulb Trinity time = 5512 Thorium Rose Source Bulb Trinity time = 7701 Thorium Rose Source Bulb X5 time = 28944.0 Thorium Rose Source Bulb X5 time = 34452.0 Thorium Rose Source X5 time = 36612 Thorium Rose Source Bulb X5 time to = 5508.0 Thorium Rose Source Bulb X5 time to 1-25MW = 7668 Figure A102 shows various views of an alternative fuel arrangement comprising 24 elements and suitable for use in the reactor of Figure 27, preferably a large reactor. Control Systems Figure 103 shows two possible placements for neutrons detectors. Neutron Detectors can either be placed inside the fuel cell or above the fuel cell under the capstone. This is possible because there is no neutron shielding between the top of the fuel cell and the capstone. Figure A104 shows the steam cycle for the fuel cell, temperature and pressure sensors are placed at 1-4 a high temperature sensor is placed at ^^^^. In case off shutdown the backup power needs to be able to power the system for at least 2 restarts, 2 hour cool down period and power the compressor and inter-cooler fans during this time. Figure A105 shows a block diagram of a control system for the fuel cell. As explained previously, neutron detectors will be used to monitor the neutrons per second, this will then be fed into an analogue controller and fuel cell control software or a PID controller. The analogue controller’s sole purpose is to monitor the neutrons per second and if it is above the ^^ ^^ ^^ ^^ ^^ 2 safety limit shown in Figure A99 it will shut down the accelerator. The fuel cell control software will also monitor the neutrons per second and keep it within the desired range. If the ^^ ^^ ^^ ^^ ^^ 2 limit is sensed by the software it to can cut power to the accelerator. A mechanical shutoff is also needed. If any of the three systems cut power to accelerator this is communicated to the analogue controller, control software and steam cycle controller, this then allows for the bypass valve to be activated protecting the turbine, the inter-cooler fans are also set to max speed and mass flow in the steam cycle is increased to allow for better cooling. The fuel cell temperature sensor feeds into the analogue controller, fuel cell software and steam cycle controller. The fuel cell software and steam cycle controller can communicate and together keep the fuel cell temperature within the desired range, this is done by either changing the desired neutrons / second, mass flow in the steam cycle or increasing the inter-cooler fan speed. If the fuel cell temperature is too high the same shutoff sequence is used as the one used in the neutron sensor. The steam side pressure and temperature sensors also have max values that can cause the shutdown protocol to be initiated. The steam side pressure and temperatures sensors are fed into the steam cycle controller, the controller keeps these two values within the desired range. If pressure is to high the blow-off valve can be activated, the blow-off valve also has a mechanical limit after which it will release pressure. The pressure is released into a tank, this allows for the water to be used to refill the loop if needed. Entrance breach, Restart and Fire Safety If the fuel cell is breached or fire is detected the shutdown procedure is triggered. In the case of fire CO2are deployed to automatically extinguish the fire. If the fuel cell needs to be restarted a master key must be given to the system, the person with this key must ensure that it is safe for the fuel cell to be restarted. Idle State The idle state control system is very similar to that of the normal operating conditions except for the upper and lower limits that are changed and the bypass valve is set to bypass the turbine at all times. All other safety and control methods are kept in place. Inherent safety of the innovative design The benefits of the design of inherent safety will be appreciated. Whereas a conventional nuclear reactor requires positive damping of neutrons to prevent thermal runaway, with the current design it is simply a matter of switching off power to the accelerator to stop the reaction almost instantly. An “emergency off” capability which does not require positive action or mechanical components is thus readily provided. Moreover in less extreme scenarios the reaction rate can be precisely modulated by varying the accelerator input with a much faster response time several orders of magnitude more responsive than physically moving bulky and sometimes fragile control rods. Finally, even if the control system were to fail catastrophically in a frankly unforeseeable way such that it continues to deliver full power despite increasing reactor temperature and if somehow all emergency off devices failed to cut power, the melting of the fuel elements, which cannot ever themselves form a super-critical self- sustaining reaction even if all condensed into one, itself serves to reduce reactor power. Power Output The of a system-wide 4thlaw analysis is computationally intensive and time-consuming for such a large core. Investigations have revealed that the following simplification can be made to give a useful determination of expected output for planning purposes without requiring the extra complexity: i. Layers of the core beyond the source bulb are analysed as passive irradiated fuel. ii. The source bulb undergoes a full analysis under the same dimensions of Equation 52. iii. The source bulb equation referenced in the above point is the only time-dependent equation for the reactor dynamics in both start-up and shutdown. iv. The rose core is analysed as an average density within a spherical zone – i.e. no gaps exist between fuel blades but the mass is the same as if there were gaps. Chain fission neutrons are seen as travelling “outward” from the centre and are added to the flux as it attempts to escape the centre. To describe a spherical flux without loss we simply describe the total number of neutrons distributed over the surface area of that sphere, hence: Equation 61: Spherical Flux Without Loss ^^^^ Equation 62: Neutron Attenuation ^^(^^)= ^^^^∙ ^^−Σ∙ ^^While scattering – and subsequently diffusion – are irrelevant, absorption cross-sections do need to be taken into account. Combining Equation 61 and Equation 62: Equation 63: Spherical Flux with Absorption ^^ ∙ ^^−Σa ^^^^ ^^where: ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ( ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^) ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ℎ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ Σa= ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ The python code was intended to take a material change in spherical layers. A function was then made to account for this as shown in Figure A40. “SpFluxU” is a function for neutrons passing through a spherical layer of U238 and similarly “SpFluxLBE” is for LBE. Both functions output a field value in “neutrons / s.cm2”. These functions are continuously recalled through layers of materials as you can normalise a later material layer using a simple volume equation: 4 ^^^ ^^ ^^ ^^= ^^ ∙ ^^34 ^ − ^^ ∙ ^^33^^3^^Where: ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^^^3^^ ^^ ^^ ^^ ^^ ^^= ^^3^^− ^^3^^Equation 64: Normalised Radius 3 ^^^^ ^^ ^^ ^^ ^^ ^^=√^^3^^− ^^3^^Using this simple equation and a flux normalisation you may continuously re-input into the spherical flux equation. Figure A41 is an excerpt from the code that computes the fission reaction rate in the material. “IgnBall” is the target source plate function whereby the source created by the proton-induced fission gets taken as an input. Further fissions may take place within the ball and this is calculated by taking the average of the flux over three points within the sphere and multiplying that by the standard reaction equation: Equation 65: Fission Reaction Rate ^^ = ^^ ∙ ^^^^∙ ^^^^238 ^^∙ ^^ Where: ^^ = ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ Function “Ring1” computes the fission rate in the first ring of fission material. Between every fuel ring, a layer of LBE is designated to run as a free-flow coolant. The normalisation equations now take heavy effect in the function. “rn1” takes the volume of LBE and normalises the radius to compute back into the earlier “SpFluxLBE” function with “S_norm1” as the normalised flux in neutrons per second. Flux normalization is done by multiplying the flux exiting the last layer by the surface area of that layer, with the addition of multiplying the fission reaction rate of the previous fuel layer by three (see line 11 in Figure 11A). The multiplicity of three is derived from the cross-section evaluation group’s date on Uranium fast fission and aims to be a good conservative estimate considering the high neutron energies exiting the ADS flux. The fission cross-section is taken to be 1 barn – the average for the fast fission group. Once the neutrons exiting the LBE layer are computed, the flux within the fuel layer is once again normalised and recomputed with “rn2” and “S_norm2”. The average is taken between entrance flux and the flux at the outer edge and this average is once again used as in Equation 65 in line 16. The volume for these fuel rings is “hard-coded” from the 3D CAD evaluation of the respective petals The functions shown in the code have been replicated to host up to 7 fuel layers and total several hundred lines of python code. The following table identifies the fuel mass by layer according to one embodiment of the present invention. Layer Mass (grams) Total mass (grams) In one embodiment of the present invention, an output of 5MWe is provided, that is to say 5MW of electricity. With an output of 5MWe, the thermal output of the core would need to be in the range 12-14 MWt to adequately supply the electrical demand after system efficiencies. Figure A37 is a 3- layer rose core with a lithium-7 source designed for a compact power delivery system. At 14 MWt this configuration has a 230-year half-life with a 16-hour start-up time (see Figure A42). Figure A43 is a comparable graph for a 7 layer core with a single stage. Figure A44 shows a single tritosphere for a 3-layer core. The largest configuration described for the Rose core is a seven-layer single-stage reactor. The maximum output, while still maintaining a half-life above 100 years, is 135 MWt at a half-life of 104 years. After thermal efficiencies, this core will generate approximately 50 MWe. If a larger facility is desired, it is recommended to add additional layers in the same configuration, in the range of 8-10 layers. Increasing the number of layers improves efficiency. However the individual core becomes large and maintenance if needed is complicated. Alternatively multiple cores can be co-located and indeed can be powered and controlled from a single accelerator source. Thermal to electrical conversion considerations Those skilled in the art of power station and nuclear reactor design in particular are familiar with arrangements for extracting heat with flows of multiple MW from a high temperature source at several hundred degrees (up to approaching 1000C) to provide useful electrical output. This disclosure will not therefore concentrate on that so as not to re-invent the wheel, or steam turbine. An important consideration though is the very high temperature regime the embodiments allow, potentially improving thermodynamic efficiency. A practical consideration is that materials should be used which can withstand the high temperatures of the coolant (LBE) without softening. Inconel® 600 is a suitable material used in heat exchangers with a melting point of about 1350 degrees C and tungsten or titanium-tungsten alloys can be used for higher temperatures up to 3000C. The following examples are purely for illustration and not intended to be limiting. The primary purpose of the disclosure is to show that the thermal power generated can be comfortably handled using largely off-the shelf conventional components without excessive physical or practical issues arising. Of course for efficiency an optimised heat exchanger will likely be made for a particular application. Example of steam power generation a closed cycle LBE to an open cycle steam power generator. As illustrated: i. Hot LBE at 1000°C ii. Cooled LBE (500° - 600°) iii. Open feedwater at 300k iv. 10 MPa compressed water v. Superheated steam, 10 MPa (500°C – 600°C) vi. Exhaust steam to atmosphere The detailed outlet values and heat transfer is dependent on the scale of the reactor facility. The heat exchanger is a counter flow (outlet of LBE at the inlet of steam) orientation to best take advantage of the high-temperature variance between the two working fluid cycles. INCONEL® 600 variants are recommended for use with service temperatures of up to 1200°C and many of these variants are currently in use in the nuclear industry. For a mobile SMR application, it may become necessary to implement a closed-loop steam cycle and a third open-loop air-cooling system to ensure that the exhaust steam from the turbine is adequately cooled back to saturated water. Figure A46 shows this three-working-fluid system and will be the focus of analyses. A Siemens® SST-200 turbine was chosen as the steam turbine with inlet parameters of 10 MPa and 500°C. Due to the unique nature of an ultra-high temperature LBE heat source, it is possible to have the entire system in the superheated steam region – drastically improving thermal efficiencies. Designing the entire steam cycle to be in the superheated region allows for steam to be treated as an ideal gas. The NTU method for heat exchangers also applies as no two-phase heat transfers exist. Turbine energy balance: Equation 66: Polytropic temperature relationship - turbine ^^(^^−1)^^ ^^ 0.8(1.33−1) 10 1.33 ^^6= (500 + 273) [ ] − 273 = 216.42° ^^ 100 Equation 67: turbine power ^^^^= ^^^^^^(ℎ5− ℎ6) ^^^^5200 ^^ ^^ ^^ The compressor unit is a multistage process to supply steam at 10 MPa at 350°C. The NTU method for the LBE-steam heat exchanger is as follows: Assuming a counterflow shell and tube arrangement with C = 0.5: Equation 68: non-dimensional heat transfer coefficient (NTU) ^^ ^^^^ ^^Since: Equation 69: NTU max heat transfer ^^^^ ^^= ^^^^ ^^( ^^ℎ ^^ ^^− ^^^^ ^^ ^^) For safety considerations, the LBE heat transfer: ^^^^ ^^= ^^^^ ^^ ^^^^^^ ^^ ^^ ^^Thus: Equation 70: LBE mass flow ^^^^ ^^ ^^ ^^ ^^^^^^^^^^ ^^ ^^ ^^ ^^^^ ^^ ^^= 0.5 ^^^^ ^^ ^^ ^^12.77 ∙ 2000 ^^^^ ^^ ^^= 0.5 = 87.16 ^^ ^^ 146.5⁄^^ Equation 71: Heat transfer to steam ^^^^ ^^ ^^ ^^ ^^= ^^(ℎ5− ℎ4)^^^^ ^^ ^^ ^^ ^^= 12.77(3373.6 − 2923.4)= 5.75 ^^ ^^ LBE heat transfer: Equation 72: LBE heat transfer ^^^^ ^^ ^^= ^^^^ ^^ ^^ ^^ ^^= ^^^^ ^^(^^1− ^^2) ^^ ^^ =^^ ^^ ^^ ^^ ^^2^^1− ^^^^ ^^5750 ^^2= 1000 − = 549.7°C 146.5 ∙ 87.16 Effectiveness: Equation 73: NTU effectiveness ^^ ^^ ^^^^ ^^ ^^ ^^ ^^ ^^ = = 0.693 146.5 ∙ 87.16(1000 − 350) NTU = 1.3 Basic dimensions of the heat exchanger: Equation 74: Nusselt number from heat transfer in a pipe ℎ ^^ ^^ ^^ = = 4.364 ( ^^ ^^ ^^) ^^ ^^ ^^ ^^ 4.364 ∙ 15 ℎ = = = 1309.2 ^^ / ^^2^^ ^^ 50 ^^ − 3 Assuming: ℎ = ^^ Equation 75: NTU relation to the surface area ^^ ^^ ^^ ^^ ^^ ^^^^ 87.16 ^^ = ^^ ^^ ^^ ∙^^= 1.3 ∙ = 12.68 ^^2 1309.2 For a pipe of diameter 50mm: Equation 76: Surface area of a pipe ^^ = ^^ ^^ ^^ ^^ 12.68 ^^ = = = 80.7 ^^ ^^ ^^ ^^(50 ^^ − 3) It is recommended that increasing the number of pipes will condense the system. Overall, 80.7m of piping is rather small, and won't impact the feasibility of a condensed SMR. Reactor Vessel Material Figures A47, A48 and A49 are from a 2017 study on Ferro-Boron (Iron and boron mixture) which identifies the degree of shielding provided by various levels of ferro-boron content. The traditional amount of 1m on concrete “with boron” has been the standard for a long time but thinking has changed more recently. The use of a lead-based alloy as coolant is a partial shielding for gamma rays (not neutrons) so a combination of 35cm Concrete at a Ferro-boron content of 50% (FeB-2 in the graphs) and the coolant’s 15 cm radius beyond the core is more than sufficient as a shielding material. Passive Safety The rose core is designed to use the thermodynamics of two-phase heat transfer to strategically destroy fuel elements before allowing the LBE coolant to vaporise – thus ensuring no pressurisation of the reactor core. During a phase change, the temperature of the medium stays constant and this, in combination with Newton’s law of cooling, ensures that the vaporisation of LBE is impossible. “The rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings while under the effects of a breeze” – Newton’s law of cooling ^^ = ℎ ^^( ^^1− ^^2) In the event of a runaway reaction (where all active control systems and emergency off systems have failed), and the Uranium-Tungsten alloy approaches its melting temperature of 1650°C, the fuel elements cannot heat the LBE beyond this temperature of 1650°C – which is below the vaporisation point of LBE at 1660°C. Once in a liquid state, the Uranium-Tungsten alloy will sink to the bottom of the chamber due to the density difference between the alloy and the LBE medium. Uranium will solidify at 1132°C in the cooler LBE (return temperature of 480°C) and will also be out of range of the neutron field planes established in the 4thlaw – creating only irradiated fuel with no mirror effects. If the entire core melts down and is out of range of the source bulb’s mirror field, the reaction rate becomes entirely subcritical at the bulb with a very low flux field – even at utility-scale, this irradiation amount is only a few kilowatts. This is how the reactor core was designed from the start - with complete safety in mind. Every other reactor prior to this attempts to stop a runaway reaction and over-pressurisation by reinforcing stopgaps from that event, but the rose core concept started with the possibility of an “unforeseeable” failure and embraced it. This mantra change is imperative in passive safety and the primary passive safety element relies on natural laws of thermodynamics rather than man-made mechanisms to provide a shutdown. LBE, at room temperature, is solid. This allows for fission products (of which there are fewer of any concern in any event) to be encased within this solid in the event of a breach of containment of the LBE closed cycle. Shut down of the reactor also closes the leak point as it, too, would rapidly cool to a solid allowing for the unit to be repaired safely. This contrasts with a pressurised water reactor which will explode and scatter steam and water over a wide area and disappear into the environment. Active Safety The most straightforward element of active safety is the control of the accelerator: varying the input or shutting it down entirely will reduce / collapse the neutron mirror fields rapidly in a highly predictable way. This, in itself, is also a passive safety element as the shutdown of electrical power is typically the first occurrence in the event of a disaster: floods, electrical short, terrorism etc. The reactor core does not feature control rods; the particle accelerator provides the control. Every law of fission, neutron reaction dynamics and thermodynamics actively oppose this reactor core from functioning without the particle accelerator. The rate of reaction is monitored via neutron detectors embedded in the shielding and will be the first indication of an increased reaction rate. When the reactor is running near the desired energy rate, the beamline intensity is varied rhythmically to balance the core in the vicinity of the desired output. All of this can readily be done automatically with no human input. Moreover the rapid response time allows more sophisticated control algorithms to be deployed which predict future neutron flux based on reactor state and temperature and measured or predicted load and can proactively adjust beam to give fine control. This proactive modelling can be performed in addition to parallel fail-safes which simply reduce excitation as temperature increases, for example reducing at a first temperature threshold and shutting down at a second threshold. To protect equipment – a potential financial loss not a potential exposure risk – the following measures are to be put in place: I. Fire suppression systems should be installed near all of the electronics with a preference for protecting the cyclotron. II. Cycle pressure and temperature systems should monitor for any unexpected change or loss in pressure triggering an immediate shutdown. III. 4-hour backup power is sufficient for all control systems to adequately monitor the shutdown process, which can be provided by a simple UPS. IV. Radiation detection monitors surrounding both thermal cycles – a spike in radiation should trigger an immediate shut-down. However it should be noted that there is not much radiation as compared to a conventional reactor.

Claims

CLAIMS 1. A power source comprising: an ignition region comprising a target material arranged to receive a flux of protons and generate neutrons in response thereto; a reactor core containing a sub-critical quantity of actinide material arranged as a structure having at least one layer around the ignition region, wherein the actinide material comprises at least Thorium or Uranium and generates insufficient neutrons by spontaneous fission in the absence of the flux of protons to the ignition region to maintain a critical or super-critical reaction; a coolant containing at least one metal; an accelerator arranged to supply a flux of protons having an energy of between 4MeV and 200MeV to the target material in the ignition region, a window in the reactor core to permit the passage of said flux of protons unimpeded by coolant or actinide material; a control arrangement to control the power of the proton flux to modulate reactor core power.

2. A power source as claimed in claim 1, wherein the beam current of the flux of protons is at least 100µA.

3. A power source as claimed in claim 1, wherein the beam current of the flux of protons is at least 250µA.

4. A power source as claimed in claim 1, wherein the beam current of the flux of protons is at least 500µA 5. A power source as claimed in any preceding claim, wherein the control arrangement is arranged to model future neutron flux based on a measure of reactor state and to modulate the proton flux power based on said model.

6. A power source as claimed in any one of the claims 1 to 5, wherein the ignition region comprises a first material responsive to proton bombardment at energies below 20MeV to generate neutrons within a first energy range and a second material responsive to the neutrons in the first energy range to generate neutrons in a second energy range.

7. A power source as claimed in claim 6, wherein the accelerator is arranged to provide a flux of protons having an energy between 4MeV and 15MeV.

8. A power source as claimed in claim 6 or claim 7, wherein the first material in the ignition region comprises Lithium-7.

9. A power source as claimed in any one of the claims 1 to 5, wherein the ignition region comprises an actinide material responsive to the flux of protons.

10. A power source as claimed in claim 9, wherein the accelerator is arranged to provide a flux of protons having an energy of between 15MeV and 100MeV 11. A power source as claimed in claim 6, wherein the accelerator is arranged to provide a flux of protons having an energy of between 15MeV and 50MeV.

12. A power source as claimed in any one of the preceding claims, wherein the actinide material comprises at least 80% by weight of Thorium, and at least 1% of another metal selected from Iron, Nickel, Magnesium and Uranium.

13. A power source as claimed in claim 12, wherein the another metal comprises at least iron.

14. A power source as claimed in claim 12, wherein the another metal comprises at least nickel.

15. A power source as claimed in claim 12, wherein the another metal comprises at least magnesium.

16. A power source as claimed in claim 12, wherein the another metal comprises at least uranium.

17. A power source as claimed in any of the claims 12 to 16, wherein the proportion of the another metal is selected to cause the melting point of the actinide material to be below a predetermined value.

18. A power source as claimed in any one of the preceding claims, wherein the reactor vessel further contains means for forced distribution of coolant within the vessel.

19. A power source as claimed in claim 18, wherein the means for forced distribution of coolant comprise means for forced convection of coolant.

20. A power source as claimed in claim 19, wherein the means for forced convection of coolant comprises an impeller.

21. A power source as claimed in claim 19, wherein the means for forced convection of coolant comprise at least one element of actinide material rotatable about an axis.

22. A power source as claimed in claim 21, wherein the elements of actinide material are arranged evenly around the axis.

23. A power source as claimed in claim 22, comprising three elements of actinide material.

24. A power source as claimed in claim 22, comprising twelve fuel elements.

25. A power source as claimed in any one of the claims 21 to 24, wherein the fuel elements are shaped to promote the movement of coolant within the container.

26. A power source as claimed in claim 18, wherein the means for forced distribution of coolant comprises a pump external to the reactor vessel.

27. A power source as claimed in claim 26, wherein the means for forced distribution comprise a forced convection heat transfer generated by the coolant flow of an axial flow pump.

28. A power source as claimed in claim 26, wherein the means for forced distribution comprise an electromagnetic pump.

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