Systems, devices, and methods for electron beams for plasma heating

Abstract

A long-pulse, high-power electron beam using a plasma emitter for plasma heating includes an arc plasma source, an electron optical system consisting of a system of accelerating grids, a beamline including a magnetic system for providing effective electron beam shaping, transport, and ultimately injection into a plasma confinement device of interest, a plasma generator coil, a plasma emitter coil, a lens coil, and a beam transport coil. In one embodiment, the electron beam source further comprises a beam emitter configured to provide an annular beam.

Description

[Technical Field]

[0001] (CROSS-REFERENCE TO RELATED APPLICATIONS) This application claims priority to U.S. Provisional Patent Application No. 63 / 111,446, filed November 9, 2020, which is incorporated by reference in its entirety for all purposes.

[0002] (Technical field) FIELD OF THE INVENTION The embodiments described herein relate generally to electron beams, and more particularly to systems, devices, and methods for long-pulse, high-power electron beams using plasma emitters that promote plasma heating. [Background technology]

[0003] Field-reversed configurations (FRCs) belong to a class of magnetic plasma confinement topologies known as compact toroids (CTs). They exhibit a predominantly poloidal magnetic field and possess zero or small self-generated toroidal fields (see M. Tuszewski, Nucl. Fusion 28, 2033 (1988)). The appeal of such configurations is their simple geometry for ease of construction and maintenance, unlimited natural divertors to facilitate energy extraction and ash removal, and very high β (β is the ratio of the mean plasma pressure to the mean magnetic field pressure inside the FRC), i.e., high power density. The essence of a high β is for economical operation and for D-He 3 and pB 11 It is advantageous for the use of advanced non-neutron fuels such as

[0004] The conventional method for forming FRCs uses the field-reversed theta-pinch technique to generate a high-temperature, high-density plasma (see A.L. Hoffman and J.T. Slough, Nucl. Fusion 33, 27 (1993)). A variation on this is the transient trapping method, in which the plasma created in a theta-pinch "source" is almost immediately ejected at one end into a confinement chamber. The transitioning plasmoid is then trapped between two strong mirrors at the end of the chamber (see, e.g., H. Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191 (1995)). Once inside the confinement chamber, various heating and current drive methods can be applied, such as (neutral or neutralized) beam injection, rotating magnetic fields, RF or ohmic heating. This separation of source and confinement functions offers important engineering advantages for potential future fusion reactors. FRCs have proven to be highly robust and resistant to dynamic formation, transient, and violent capture events. Furthermore, they tend to support favorable plasma states (see, for example, H.Y. Guo, A.L. Hoffman, K.E. Miller, and L.C. Steinhauer, Phys. Rev. Lett. 92, 245001 (2004)). In the past decade, significant progress has been achieved by developing other methods for forming FRCs, namely, by fusing spheromaks with reverse helicity (see, for example, Y. Ono, M. Inomoto, Y. Ueda, T. Matsuyama, and T. Okazaki, Nucl. Fusion 39, 2001 (1999)), and by driving the current with a rotating magnetic field (RMF), which also provides additional stability (see, for example, I.R. Jones, Phys. Plasmas 6, 1950 (1999)).

[0005] A drawback of previous FRC system designs is the lack of an efficient electron heating scheme other than neutral beam injection, which tends to have poor electron heating efficiency due to the mechanism of power decay on electrons through ion-electron collisions. One approach to electron heating of plasmas has been to use an electron beam. Efficient electron heating using an electron beam in an FRC system requires a long-pulse, high-power electron beam.

[0006] The challenges in generating long-pulse, high-power electron beams are primarily associated with cathode degradation resulting from high beam perveance and substantial beam space-charge effects. In many previous applications, cathodes are fabricated either from solid materials or from a system of grid electrodes forming a so-called plasma emitter. In both cases, high heat flux problems arise due to collisions of high-energy particles with the cathode's active surface. Beam space-charge effects can lead to the beam envelope rapidly expanding or collapsing with distance. Unless additional measures are taken, beam envelope behavior can also become extremely sensitive to ambient gas conditions along the beamline, making it virtually impossible to control the beam propagation and transport it to its final destination.

[0007] For the purpose of plasma heating in open plasma confinement configurations, electron beam injection can be performed along the axis of symmetry of the plasma confinement facility, but this involves the problem of transporting the beam into the confinement region through a magnetic plug, which imposes some specific requirements on the electron beam magnetic system and the (beam) plasma generator device.

[0008] As noted, the main disadvantage of previous approaches is cathode degradation, which leads to low pulse durations and low beam currents. Cathodes made from solid materials cannot withstand the high energy flux associated with heating and particle bombardment. Therefore, in previous approaches, pulse durations are typically limited to approximately 100 microseconds. For the same reason, the number of operating cycles is also limited to approximately 100 to 1,000 pulses before cathode replacement is necessary.

[0009] Additionally, in previous approaches, the beam current density, and therefore the beam space charge, is kept relatively small since space charge effects can be neglected while designing the beamline and during beam transport.

[0010] Improved systems, devices, and methods for facilitating long-pulse, high-power electron beams with plasma emitters for plasma heating are desired. [Prior art documents] [Non-patent literature]

[0011] [Non-Patent Document 1] M. Tuszewski, Nucl. Fusion 28, 2033 (1988) [Non-patent document 2] ALHoffman and JTSlough, Nucl.Fusion33,27(1993) [Non-patent document 3] H. Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191 (1995) [Non-patent document 4] HYGuo, ALHoffman, KEMiller, and LCSteinhauer, Phys.Rev.Lett.92,245001(2004) [Non-patent document 5] Y.Ono, M.Inomoto, Y.Ueda, T.Matsuyama, and T.Okazaki, Nucl.Fusion 39, 2001 (1999) [Non-patent document 6] IRJones,Phys.Plasmas 6,1950(1999) Summary of the Invention [Means for solving the problem]

[0012] Exemplary embodiments of systems, devices, and methods are provided herein for generating a long-pulse, high-power electron beam using a plasma emitter for plasma heating of FRC plasma. In exemplary embodiments, the electron beam includes an arc plasma source, an electron optical system consisting of a system of accelerating grids, a beamline including a magnetic system for providing effective electron beam shaping, transport, and ultimately injection into a plasma confinement device of interest, a plasma generator coil, a plasma emitter coil, a lens coil, and a beam transport coil.

[0013] Other systems, devices, methods, features, and advantages of the subject matter described herein will be, or will become, apparent to one of ordinary skill in the art upon examination of the following figures and detailed description. All such additional systems, methods, features, and advantages are intended to be included within this specification, be within the scope of the subject matter described herein, and be protected by the accompanying claims. Features of the exemplary embodiments should not be construed in any way as limiting the appended claims, even if those features are not expressly recited in the claims. The present invention provides, for example, the following. (Item 1) 1. A method for generating and sustaining a field-reversed configuration (FRC) plasma, the method comprising: forming an FRC around the plasma in a confinement chamber; injecting an electron beam axially into the FRC plasma from an electron beam source; maintaining the FRC plasma at a constant or near-constant value without decay by injecting a beam of fast neutral atoms from a neutral beam injector into the FRC plasma at an angle toward the midplane of the confinement chamber; A method comprising: (Item 2) The electron beam source comprises: an arc plasma source; an electron optical system comprising a system of accelerating grids; a beamline including a magnetic system configured to provide electron beam formation, transport, and injection into the FRC plasma; Item 1. The method according to item 1, comprising: (Item 3) Item 3. The method of item 2, wherein the electron beam source further comprises a beam emitter configured to provide an annular beam. (Item 4) Item 4. The method of item 3, wherein the beam emitter includes a multi-aperture emitter grid and a mask covering an aperture in a central region of the emitter grid. (Item 5) Item 4. The method of item 3, wherein the beam emitter includes a multi-aperture emitter grid and first and second masks covering apertures in a central region of the emitter grid and outer regions spaced apart from the central region. (Item 6) Item 6. The method of item 5, wherein the second mask has an inner profile shape that matches an outer profile shape of the first mask. (Item 7) The magnetic system comprises: a plasma generator coil; A plasma emitter coil; A lens coil; Beam transport coil and Item 3. The method according to item 2, comprising: (Item 8) Injecting the electron beam axially comprises: generating a plasma; expanding the plasma; and extracting electrons from the plasma; accelerating the extracted electrons; Item 1. The method according to item 1, comprising: (Item 9) The step of injecting a beam of fast neutral atoms comprises: adjusting the beam energies of the plurality of Neutral Beams between a first beam energy and a second beam energy, the second beam energy being different from the first beam energy; or adjusting beam energies of the plurality of neutral beams between a first beam energy and a second beam energy, the second beam energy being different from the first beam energy and higher than the first beam energy; or adjusting beam energies of the plurality of Neutral Beams between a first beam energy and a second beam energy, the second beam energy being different from the first beam energy, and the plurality of Neutral Beams switching between the first beam energy and the second beam energy for the duration of an implant shot; The method according to items 1-5, including one of the following: (Item 10) generating a magnetic field within the chamber using a quasi-DC coil extending around the chamber; or generating a magnetic field within the chamber using a quasi-DC coil extending around the chamber and generating a mirror magnetic field within the opposing end of the chamber using a quasi-DC mirror coil extending around the opposing end of the chamber. The method according to items 1 to 5, further comprising one of the following: (Item 11) The step of forming the FRC plasma includes: forming first and second forming FRC plasmas in first and second forming sections coupled to opposite ends of the confinement chamber; accelerating the forming FRC plasma toward a mid-plane of the chamber to form the FRC; The method according to items 1 to 5, comprising: (Item 12) 9. The method of claim 8, further comprising the step of inducing a magnetic flux surface of the FRC into a diverter coupled to an end of the forming section. (Item 13) 1. A system for generating and sustaining a field-reversed configuration (FRC) plasma, the system comprising: a containment chamber; and first and second diverters coupled to the first and second forming sections; first and second axial plasma guns operably coupled to the first and second divertors, the first and second formation sections, and the containment chamber; a plurality of neutral atom beam injectors coupled to the confinement chamber, the plurality of neutral atom beam injectors oriented to inject neutral atom beams toward a midplane of the confinement chamber at an angle less than perpendicular to a longitudinal axis of the confinement chamber; a magnetic system comprising: a plurality of quasi-DC coils positioned around the confinement chamber, the first and second forming sections, and the first and second divertors; a set of first and second quasi-DC mirror coils positioned between the confinement chamber and the first and second forming sections; and first and second mirror plugs positioned between the first and second forming sections and the first and second divertors; a gettering system coupled to the confinement chamber and the first and second diverters; one or more bias electrodes for electrically biasing open flux surfaces of the generated FRC, the one or more bias electrodes being positioned within one or more of the containment chamber, the first and second formation sections, and the first and second diverters; two or more saddle coils coupled to the containment chamber; one or more electron beams axially coupled to one or more of the first and second divertors; A system comprising: (Item 14) The electron beam an arc plasma source; an electron optical system comprising a system of accelerating grids; a beamline including a magnetic system configured to provide electron beam formation, transport, and injection into the FRC plasma; Item 11. The system according to item 10, comprising: (Item 15) Item 12. The system of item 11, wherein the electron beam further comprises a beam emitter configured to provide an annular beam. (Item 16) Item 16. The system of item 15, wherein the beam emitter includes a multi-aperture emitter grid and a mask covering an aperture in a central region of the emitter grid. (Item 17) Item 16. The method of item 15, wherein the beam emitter includes a multi-aperture emitter grid and first and second masks covering apertures in a central region of the emitter grid and outer regions spaced apart from the central region. (Item 18) Item 18. The method of item 17, wherein the second mask has an inner profile shape that matches an outer profile shape of the first mask. (Item 19) The magnetic system comprises: a plasma generator coil; A plasma emitter coil; A lens coil; Beam transport coil and Item 15. The system according to item 14, comprising: (Item 20) 1. A system for generating and sustaining a field-reversed configuration (FRC) plasma, the system comprising: a containment chamber; and first and second diverters coupled to the first and second forming sections; one or more of a plurality of plasma guns, one or more bias electrodes, and first and second mirror plugs, wherein the plurality of plasma guns include first and second axial plasma guns operably coupled to the first and second diverters, the first and second forming sections, and the confinement chamber, wherein the one or more bias electrodes are positioned within one or more of the confinement chamber, the first and second forming sections, and the first and second diverters, and the first and second mirror plugs are positioned between the first and second forming sections and the first and second diverters; a gettering system coupled to the confinement chamber and the first and second diverters; a plurality of neutral atom beam injectors coupled to the confinement chamber and oriented perpendicular to the axis of the confinement chamber; a magnetic system including a plurality of quasi-DC coils positioned around the confinement chamber, the first and second formation sections, and the first and second divertors, and a set of first and second quasi-DC mirror coils positioned between the confinement chamber and the first and second formation sections; one or more electron beams axially coupled to one or more of the first and second divertors; Equipped with The system is configured to generate an FRC without attenuation and maintain the FRC while the neutral beam is injected into the plasma. (Item 21) The electron beam an arc plasma source; an electron optical system comprising a system of accelerating grids; a beamline including a magnetic system configured to provide electron beam formation, transport, and injection into the FRC plasma; Item 21. The system of item 20, comprising: (Item 22) Item 22. The system of item 21, wherein the electron beam further comprises a beam emitter configured to provide an annular beam. (Item 23) Item 23. The system of item 22, wherein the beam emitter includes a multi-aperture emitter grid and a mask covering an aperture in a central region of the emitter grid. (Item 24) Item 23. The method of item 22, wherein the beam emitter includes a multi-aperture emitter grid and first and second masks covering apertures in a central region of the emitter grid and outer regions spaced apart from the central region. (Item 25) Item 25. The method of item 24, wherein the second mask has an inner profile shape that matches the outer profile shape of the first mask. (Item 26) The magnetic system comprises: a plasma generator coil; A plasma emitter coil; A lens coil; Beam transport coil and Item 23. The system according to item 22, comprising: (Item 27) an electron beam, the electron beam comprising: an arc plasma source; an electron optical system comprising a system of accelerating grids; a beamline including a magnetic system configured to provide electron beam formation, transport, and injection into a plasma confinement device of interest; The electron beam comprises: (Item 28) The electron beam an arc plasma source; an electron optical system comprising a system of accelerating grids; a beamline including a magnetic system configured to provide electron beam formation, transport, and injection into the FRC plasma; Item 28. The system of item 27, comprising: (Item 29) Item 29. The system of item 28, wherein the electron beam further comprises a beam emitter configured to provide an annular beam. (Item 30) The magnetic system comprises: a plasma generator coil; A plasma emitter coil; A lens coil; Beam transport coil and Item 30. The system of item 29, comprising: (Item 31) 30. The system of claim 29, wherein the beam emitter includes a multi-aperture emitter grid and a mask covering an aperture in a central region of the emitter grid. (Item 32) 30. The method of claim 29, wherein the beam emitter includes a multi-aperture emitter grid and first and second masks covering apertures in a central region of the emitter grid and outer regions spaced apart from the central region. (Item 33) Item 33. The method of item 32, wherein the second mask has an inner profile shape that matches the outer profile shape of the first mask. [Brief explanation of the drawings]

[0014] The accompanying drawings, incorporated herein as part of the present specification, illustrate present exemplary embodiments and, together with the general description given above and the detailed description of exemplary embodiments given below, serve to explain and teach the principles of the present invention.

[0015] [Figure 1] FIG. 1 illustrates particle confinement in the present FRC system under high performance FRC regime (HPF) compared to conventional FRC regime (CR) and compared to other conventional FRC experiments.

[0016] [Figure 2] FIG. 2 illustrates the components of the present FRC system and the magnetic topology of the FRCs that can be produced in the present FRC system.

[0017] [Figure 3A] FIG. 3A illustrates the basic layout of the present FRC system from a top view, including the preferred arrangement of the central containment vessel, formation section, divertor, neutral beam, electrodes, plasma guns, mirror plugs, and pellet injector.

[0018] [Figure 3B] FIG. 3B illustrates the central confinement vessel as viewed from above, showing the neutral beam positioned at an angle that is perpendicular to the long axis of symmetry within the central confinement vessel.

[0019] [Figure 3C] FIG. 3C illustrates the central confinement vessel from above, showing the neutral beam positioned at an angle that is less than perpendicular to the long axis of symmetry within the central confinement vessel and directed to inject particles toward the midplane of the central confinement vessel.

[0020] [Figure 3D] 3D and 3E illustrate top and perspective views, respectively, of the basic layout of an alternative embodiment of the present FRC system, including a preferred arrangement of a central confinement vessel, forming section, inner and outer divertors, a neutral beam positioned at an angle less than perpendicular to the long axis of symmetry within the central confinement vessel, electrodes, plasma guns, and mirror plugs. [Figure 3E] 3D and 3E illustrate top and perspective views, respectively, of the basic layout of an alternative embodiment of the present FRC system, including a preferred arrangement of a central confinement vessel, forming section, inner and outer divertors, a neutral beam positioned at an angle less than perpendicular to the long axis of symmetry within the central confinement vessel, electrodes, plasma guns, and mirror plugs.

[0021] [Figure 4] FIG. 4 illustrates a schematic of the components of a pulsed power system for the forming section.

[0022] [Figure 5]FIG. 5 illustrates an isometric view of an individual pulsed power forming skid.

[0023] [Figure 6] FIG. 6 illustrates an isometric view of the forming tube assembly.

[0024] [Figure 7] FIG. 7 illustrates a partial cross-sectional isometric view of the Neutral Beam system and key components.

[0025] [Figure 8] FIG. 8 illustrates an isometric view of the neutral beam arrangement on the confinement chamber.

[0026] [Figure 9] FIG. 9 illustrates a partial cross-sectional isometric view of a preferred arrangement of a Ti and Li gettering system.

[0027] [Figure 10] 10 illustrates a partial cross-sectional isometric view of a plasma gun mounted within a divertor chamber. The associated magnetic mirror plug and divertor electrode assembly are also shown.

[0028] [Figure 11] FIG. 11 illustrates a preferred layout of annular bias electrodes at the axial ends of the containment chamber.

[0029] [Figure 12] Figure 12 illustrates the evolution of the excluded magnetic flux radius in the FRC system, obtained from a series of outer diamagnetic loops in two field-reversed theta-pinch forming sections and a magnetic probe embedded inside the central metallic confinement chamber. The time is measured from the moment of synchronous field reversal in the forming source, and the distance z is given relative to the axial mid-plane of the machine.

[0030] [Figure 13]Figures 13A, 13B, 13C, and 13D illustrate data from a representative non-HPF non-sustained discharge on the present FRC system. Shown as a function of time are the excluded magnetic flux radius at the mid-plane (Figure 13A), the six-code line-integrated density from the mid-plane CO2 interferometer (Figure 13B), the Abel-transformed density radial profile from the CO2 interferometer data (Figure 13C), and the total plasma temperature from pressure equilibrium (Figure 13D).

[0031] [Figure 14] FIG. 14 illustrates the excluded magnetic flux axial profile at selected times for the same discharge of the present FRC system shown in FIGS. 13A, 13B, 13C, and 13D.

[0032] [Figure 15] FIG. 15 illustrates an isometric view of a saddle coil mounted outside the containment chamber.

[0033] [Figure 16] 16A, 16B, 16C, and 16D illustrate the correlation between injected neutral beam FRC lifetime and pulse length. As shown, longer beam pulses produce longer-lived FRCs.

[0034] [Figure 17] 17A, 17B, 17C, and 17D illustrate the individual and combined effects of different components of the FRC system on the FRC performance and acquisition of the HPF regime.

[0035] [Figure 18]Figures 18A, 18B, 18C, and 18D illustrate data from a representative HPF unsustained discharge on the FRC system. Shown as a function of time are the excluded magnetic flux radius at the mid-plane (Figure 18A), the six-code line-integrated density from the mid-plane CO2 interferometer (Figure 18B), the Abel-transform density radial profile from the CO2 interferometer data (Figure 18C), and the total plasma temperature from pressure equilibrium (Figure 18D).

[0036] [Figure 19] Figure 19 illustrates the magnetic flux confinement as a function of electron temperature (Te), which represents a graphical representation of the newly established superior scaling scheme for HPF discharges.

[0037] [Figure 20] FIG. 20 illustrates the FRC lifetime as a function of pulse length for non-angled and angled injected neutral beams.

[0038] [Figure 21] 21A, 21B, 21C, 21D, and 21E illustrate the pulse length of the angled injected neutral beam and the lifetime of the FRC plasma parameters of plasma radius, plasma density, plasma temperature, and magnetic flux corresponding to the pulse length of the angled injected neutral beam.

[0039] [Figure 22] 22A and 22B illustrate the basic layout of a compact toroid (CT) injector.

[0040] [Figure 23] 23A and 23B illustrate the central containment vessel and show the CT injector mounted thereon.

[0041] [Figure 24] 24A and 24B illustrate the basic layout of an alternative embodiment of a CT injector having a drift tube coupled thereto.

[0042] [Figure 25] FIG. 25 illustrates a cross-sectional isometric view of the Neutral Beam System and key components for tunable energy beam output.

[0043] [Figure 26] FIG. 26 is a schematic diagram illustrating a Neutral Beam system with adjustable energy beam output.

[0044] [Figure 27] FIG. 27 is a schematic diagram illustrating the axial position control mechanism of the FRC plasma within the containment vessel (CV).

[0045] [Figure 28] FIG. 28 is a flow diagram of a general sliding mode control scheme.

[0046] [Figure 29] FIG. 29 is a composite graph of an example of a sliding mode axial position control simulation.

[0047] [Figure 30] FIG. 30 is a composite graph of an example of a sliding mode axial position control simulation.

[0048] [Figure 31] FIG. 31 is a schematic diagram of an electron beam source converted from an ion source.

[0049] [Figure 32] FIG. 32 is a graph of simulation results showing electron beam extraction and acceleration from a plasma.

[0050] [Figure 33] FIG. 33 is a partial schematic of the electron optical system.

[0051] [Figure 34] 34A and 34B are schematic diagrams of an embodiment of a plasma grid with a mask for producing a hollow beam.

[0052] [Figure 35] FIG. 35 is a schematic diagram showing axial electron beam injection into a plasma containment system.

[0053] [Figure 36] FIG. 36 is a schematic perspective view showing an electron beam mounted on a divertor of a plasma containment system.

[0054] It should be noted that the figures are not necessarily to scale, and that elements of similar structure or function are generally represented by like reference numerals throughout the figures for illustrative purposes. It should also be noted that the figures are intended only to facilitate explanation of the various embodiments described herein. The figures do not necessarily illustrate every aspect of the teachings disclosed herein, nor do they limit the scope of the claims. DETAILED DESCRIPTION OF THE INVENTION

[0055] Before the present subject matter is described in detail, it is to be understood that this disclosure is not limited to particular embodiments described, as such may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting, since the scope of the present disclosure will be limited only by the appended claims.

[0056] The present embodiments provided herein are directed to systems and methods that facilitate the formation and maintenance of FRCs with particle, energy, and magnetic flux confinement as well as excellent stability. Some of the present embodiments are directed to systems and methods that utilize a neutral beam injector with adjustable beam energy capability to facilitate the formation and maintenance of FRCs with elevated system energy and improved sustainability. Some of the present embodiments are directed to systems and methods that facilitate both radial and axial FRC plasma stability and axial position control of the FRC plasma along the axis of symmetry of the FRC plasma confinement chamber independent of the axial stability characteristics of the FRC plasma equilibrium. Some of the present embodiments are also directed to high-power electron beams for plasma heating in magnetic plasma confinement systems.

[0057] Representative examples of the embodiments described herein, examples of which utilize many of these additional features and teachings, both separately and in combination, will now be described in more detail with reference to the accompanying drawings. This detailed description is intended merely to teach those skilled in the art further details for practicing preferred aspects of the present teachings and is not intended to limit the scope of the invention. Thus, combinations of features and steps disclosed in the following detailed description may not be necessary to practice the invention in its broadest sense, but instead are taught only to specifically illustrate representative examples of the present teachings.

[0058] Furthermore, various features of the representative examples and dependent claims may be combined in ways not specifically and explicitly recited to provide additional useful embodiments of the present teachings. In addition, it is expressly noted that all features disclosed in the description and / or claims are intended to be disclosed separately and independently from one another, not only for the purposes of the original disclosure, but also for the purposes of limiting the claimed subject matter, independent of any combination of features in the embodiments and / or claims. It is also expressly noted that the designation of any range of values ​​or group of entities discloses all possible intermediate values ​​or intermediate entities, not only for the purposes of the original disclosure, but also for the purposes of limiting the claimed subject matter.

[0059] A discussion of systems and methods for forming and maintaining high-performance FRCs with superior particle, energy, and magnetic flux containment as well as superior stability over conventional FRCs is provided before turning to systems and methods that promote both radial and axial FRC plasma stability and axial position control of the FRC plasma along the axis of symmetry of the FRC plasma confinement chamber. Such high-performance FRCs offer a pathway to a variety of applications, including compact neutron sources (for medical isotope production, nuclear waste cleanup, materials research, neutron radiography, and tomography), compact photon sources (for chemical production and processing), mass separation and enrichment systems, and light nuclei fusion cores for future energy generation.

[0060] Various auxiliary systems and modes of operation have been explored to evaluate whether a superior confinement scheme exists in FRCs. These efforts have led to the breakthrough discovery and development of the high-performance FRC paradigm described herein. According to this new paradigm, systems and methods combine numerous novel ideas and tools to not only significantly improve FRC confinement but also provide stability control without negative side effects, as illustrated in FIG. 1. As discussed in more detail below, FIG. 1 depicts particle confinement in the FRC system 10 described below, operating according to a high-performance FRC scheme (HPF) for forming and maintaining FRCs, as opposed to operating according to a conventional scheme (CR) for forming and maintaining FRCs, and as opposed to particle confinement according to conventional schemes for forming and maintaining FRCs used in other experiments (see FIGS. 2 and 3). This disclosure will provide an overview and details of the innovative individual components of the FRC system 10 and method, as well as their collective effects.

[0061] (FRC system) (Vacuum System) 2 and 3 depict schematic diagrams of the present FRC system 10. The FRC system 10 includes a central containment vessel 100 surrounded by two diametrically opposed reversed-field theta-pinch forming sections 200, and two divertor chambers 300 beyond the forming sections 200 for controlling neutral density and impurity contamination. The present FRC system 10 contains an ultra-high vacuum and -8 It was constructed to operate at a typical base pressure of 1000 Torr. Such vacuum pressures require careful initial surface preparation of all parts prior to assembly, including a 24-hour 250°C vacuum bake and hydrogen glow discharge clean, as well as the use of dual pump mating flanges, metal O-rings, and high-purity internal walls between mating parts, as well as physical and chemical cleaning.

[0062] The reversed-field theta-pinch forming sections 200 are standard field-reversed theta-pinch (FRTP) but with an advanced pulsed-power forming system (see Figures 4-6), discussed in detail below. Each forming section 200 is fabricated from standard opaque industrial-grade quartz tubing featuring a 2-millimeter inner lining of ultra-high-purity quartz. The containment chamber 100 is fabricated from steel and allows for multiple radial and tangential ports, which also serve as flux conservers on the timescale of the experiments described below and limit fast magnetic transients. Vacuum is created and maintained within the FRC system 10 using a set of dry scroll roughing pumps, turbomolecular pumps, and cryogenic pumps. Magnetic System

[0063] Magnetic system 400 is illustrated in FIGS. 2 and 3. FIG. 2 illustrates, among other features, FRC magnetic flux and density contours (as a function of radial and axial coordinates) associated with an FRC 450 producible by FRC system 10. These contours were obtained by 2D resistive Hall MHD numerical simulations using code developed to simulate systems and methods corresponding to FRC system 10 and are in close agreement with measured experimental data. As seen in FIG. 2, FRC 450 consists of a torus of closed field lines in the interior 453 of FRC 450 inside section line 451 and an annular edge layer 456 on open field line 452 just outside section line 451. Edge layer 456 coalesces into jet 454 over the length of the FRC, providing a natural diverter.

[0064] The main magnetic system 410 includes a series of quasi-DC coils 412, 414, and 416, which are positioned at specific axial positions along the components, namely, the confinement chamber 100, the forming section 200 of the FRC system 10, and the divertor 300. The quasi-DC coils 412, 414, and 416 are powered by quasi-DC switching power supplies and produce a basic magnetic bias field of approximately 0.1 T within the confinement chamber 100, the forming section 200, and the divertor 300. In addition to the quasi-DC coils 412, 414, and 416, the main magnetic system 410 includes quasi-DC mirror coils 420 (powered by switching power supplies) between opposite ends of the confinement chamber 100 and its adjacent forming section 200. The quasi-DC mirror coils 420 provide a magnetic mirror ratio of up to 5 and can be independently excited for balanced shaping control. Additionally, a mirror plug 440 is positioned between each forming section 200 and each divertor 300. The mirror plug 440 comprises a compact quasi-DC mirror coil 430 and a mirror plug coil 444. The quasi-DC mirror coil 430 includes three coils 432, 434, and 436 (fed by switching sources) that produce an additional induction field and focus a magnetic flux surface 455 toward a small-diameter passage 442 that passes through the mirror plug coil 444. The mirror plug coil 444, which wraps around the small-diameter passage 442 and is fed by an LC pulsed power circuit, produces a strong magnetic mirror field of up to 4 T. The purpose of this overall coil arrangement is to tightly bundle and guide the magnetic flux surface 455 and the end-charged plasma jet 454 into the remote chamber 310 of the divertor 300. Finally, a set of saddle coil "antennas" 460 (see FIG. 15) are located outside the containment chamber 100, two on either side of the mid-plane, fed by DC power supplies. The saddle coil antennas 460 can be configured to provide a quasi-static magnetic dipole or quadrupole field of approximately 0.01 T for rotational instability control and / or electron current control. The saddle coil antennas 460 can flexibly provide a magnetic field that is either symmetric or asymmetric with respect to the mid-plane of the machine, depending on the direction of the applied current.

[0065] (Pulse-type power generation system) The pulsed power shaping system 210 operates on a modified theta-pinch principle. There are two systems, each supplying power to one of the shaping sections 200. Figures 4-6 illustrate the main building blocks and arrangement of the shaping system 210. The formation system 210 consists of a modular pulsed power arrangement consisting of individual units (=skids) 220, each of which energizes a portion of the coil 232 of a strap assembly 230 (=strap) wrapped around a formation quartz tube 240. Each skid 220 consists of a capacitor 221, an inductor 223, a high-speed, high-current switch 225, and associated trigger 222 and dump circuitry 224. Overall, each formation system 210 stores 350-400 kJ of energy and provides up to 35 GW of power for forming and accelerating FRCs. The coordinated operation of these components is achieved via state-of-the-art trigger and control systems 222 and 224, enabling synchronized timing between the formation systems 210 on each formation section 200 and minimizing switching jitter to within tens of nanoseconds. The advantage of this modular design is its flexible operation: FRCs can be formed in situ, accelerated and injected (= static formation) or simultaneously formed and accelerated (= dynamic formation).

[0066] (Neutral Beam Injector) A neutral atomic beam 600 is deployed on the FRC system 10, providing heating and current drive as well as generating fast particle pressure. As shown in Figures 3A, 3B, and 8, individual beam lines comprising neutral atomic beam injector systems 610 and 640 are positioned around the periphery of the central confinement chamber 100 and inject fast particles tangentially (at an angle perpendicular or orthogonal to the longitudinal axis of symmetry within the central confinement chamber 100) into the FRC plasma with impact parameters such that the target capture zone is well within the demarcation line 451 (see Figure 2). Each injector system 610 and 640 is capable of injecting up to 1 MW of neutral beam power into the FRC plasma with particle energies between 20 and 40 keV. Systems 610 and 640 are based on a positive ion multi-aperture extraction source and utilize geometric focusing, inertial cooling of the ion extraction grid, and differential pumping. Aside from the use of different plasma sources, systems 610 and 640 are distinguished primarily by their physical designs, which accommodate their respective mounting locations, providing side and top injection capabilities. Typical components of these neutral beam injectors are specifically illustrated in FIG. 7 for side injector system 610. As shown in FIG. 7, each individual neutral beam system 610 includes an RF plasma source 612 at the input end (which is replaced by an arc source in system 640) with a magnetic shield 614 covering the end. An ion optics source and acceleration grid 616 is coupled to the plasma source 612, and a gate valve 620 is positioned between the ion optics source and acceleration grid 616 and the neutralizer 622. A bending magnet 624 and an ion dump 628 are located between the neutralizer 622 and an aiming device 630 at the exit end. The cooling system includes two cryocoolers 634, two cryopanels 636, and an LN2 shroud 638. This flexible design allows operation over a wide range of FRC parameters.

[0067] An alternative configuration for the neutral atom beam injector 600 injects fast particles tangentially into the FRC plasma, but at an angle A less than 90° relative to the longitudinal axis of symmetry within the central confinement vessel 100. These types of beam injector 615 orientations are shown in FIG. 3C. Additionally, the beam injectors 615 on either side of the central confinement vessel 100's midplane can be oriented to inject their particles toward the midplane. Finally, the axial positions of these beam systems 600 can be chosen closer to the midplane. These alternative injection embodiments facilitate more central refueling options, which provide better beam coupling and higher capture efficiency of injected fast particles. Furthermore, depending on the angle and axial position, this arrangement of the beam injectors 615 allows for more direct and independent control of the axial elongation and other properties of the FRC 450. For example, injecting the beam at a shallow angle A relative to the vessel's longitudinal axis of symmetry will create an FRC plasma with a longer axial extension and lower temperature, while choosing a more perpendicular angle A will lead to a shorter axial but hotter plasma. In this manner, the injection angle A and location of the beam injector 615 can be optimized for different purposes. In addition, such angling and positioning of the beam injector 615 allows higher-energy beams (generally more favorable for depositing more power with less beam dispersion) to be injected into a lower magnetic field that would otherwise be required to capture such beams. This is due to the fact that it is the azimuthal component of energy that determines the fast ion trajectory scale (which becomes progressively smaller as the injection angle relative to the vessel's longitudinal axis of symmetry is reduced at a constant beam energy). Furthermore, injection angled toward the midplane and an axial beam position close to the midplane improve beam-plasma coupling during injection, even if the FRC plasma contracts or otherwise shrinks axially.

[0068] 3D and 3E , another alternative configuration of FRC system 10 includes an inner diverter 302 in addition to angled beam injector 615. The inner diverter 302 is positioned between the formation section 200 and the confinement chamber 100 and is configured and operates substantially similarly to the outer diverter 300. The inner diverter 302, which includes fast-switching magnetic coils, is effectively inactive during the formation process, allowing the forming FRCs to pass through the inner diverter 302 as they translate toward the midplane of the confinement chamber 100. Once the forming FRCs enter the confinement chamber 100 through the inner diverter 302, the inner diverter is activated and operates substantially similarly to the outer diverter, isolating the confinement chamber 100 from the formation section 200.

[0069] (Pellet injector) To provide a means for injecting new particles and better control the particle inventory of the FRC, a 12-barrel pellet injector 700 (see, e.g., I. Vinyar et al., “Pellet Injectors Developed at PELIN for JET, TAE, and HL-2A,” Proceedings of the 26th International Conference on th Fusion Science and Technology Symposium, 09 / 27 to 10 / 01 (2010)) is utilized on the FRC system 10. Figure 3 illustrates the layout of the pellet injector 700 on the FRC system 10. Cylindrical pellets (D approximately 1 mm, L approximately 1-2 mm) are injected into the FRC at velocities in the range of 150-250 km / s. Each individual pellet has a mass of approximately 5 x 10 19 It contains hydrogen atoms, which is comparable to the amount of FRC particles.

[0070] (gettering system) It is well known that neutral halo gas is a significant problem in all confinement systems. Charge exchange and recycling (release of cold impurity material from the walls) processes can have devastating effects on energy and particle confinement. In addition, any significant density of neutral gas at or near the edge would lead to an immediate loss or at least a significant reduction in the lifetime of injected large-orbit (high-energy) particles (large orbits refer to particles with orbits on the scale of the FRC topology or at least with orbital radii significantly larger than the characteristic magnetic field gradient length), a fact that is detrimental to all energetic plasma applications, including fusion via auxiliary beam heating.

[0071] Surface conditioning is a means by which the deleterious effects of neutral gases and impurities can be controlled or reduced within a confinement system. To this end, the FRC system 10 provided herein employs titanium and lithium deposition systems 810 and 820 to coat the plasma-facing surfaces of the confinement chamber (or vessel) 100 and divertors 300 and 302 with Ti and / or Li films (tens of microns thick). The coating is achieved using evaporation techniques. Solid Li and / or Ti are evaporated and / or sublimated and sprayed onto nearby surfaces to form the coating. The source is either an atomic oven (for Li) 822 with an induction nozzle or a solid heated sphere with an induction shroud (for Ti) 812. The Li evaporator system typically operates in continuous mode, while the Ti sublimator is often operated intermittently between plasma operations. The operating temperatures of these systems exceed 600°C to obtain high deposition rates. To achieve sufficient wall coverage, multiple strategically arranged evaporator / sublimator systems are required. Figure 9 details a preferred arrangement of gettering deposition systems 810 and 820 within the FRC system 10. The coating acts as a gettering surface, effectively pumping atomic and molecular hydrogen species (H and D). The coating also reduces other typical impurities, such as carbon and oxygen, to insignificant levels.

[0072] (Mirror plug) As previously mentioned, the FRC system 10 employs sets of mirror coils 420, 430, and 444, as shown in Figures 2 and 3. The first set of mirror coils 420 are located at the two axial ends of the confinement chamber 100 and are excited independently of the DC confinement, shaping, and diverter coils 412, 414, and 416 of the main magnetic system 410. The first set of mirror coils 420 primarily serve to steer and axially contain the FRC 450 during fusion and provide balanced shaping control during sustainment. The first set of mirror coils 420 produces a nominally higher magnetic field (approximately 0.4-0.5 T) than the central confinement field produced by the central confinement coil 412. The second set of mirror coils 430, including three compact quasi-DC mirror coils 432, 434, and 436, is located between the forming section 200 and the divertor 300 and is driven by a common switched power supply. The mirror coils 432, 434, and 436, together with a more compact pulsed mirror plug coil 444 (fed by a capacitive power supply) and a physical constriction 442, form a mirror plug 440 that provides a narrow, low-gas-conductivity path with very high magnetic fields (2-4 T, with a rise time of approximately 10-20 ms). The most compact pulsed mirror coil 444 is compact in radial dimensions, with a bore of 20 cm and similar length, compared to the meter-plus-scale bore and pancake design of the confinement coils 412, 414, and 416. The purposes of the mirror plug 440 are manifold: (1) the coils 432, 434, 436, and 444 tightly bundle and guide the magnetic flux surface 452 and the edge-charged plasma jet 454 into the remote diverter chamber 300. This ensures that the exhaust particles properly reach the diverter 300 and that there is a continuous magnetic flux surface 455 that traces from the open field line 452 region of the central FRC 450 to the diverter 300; and (2) the physical constriction 442 in the FRC system 10, through which the coils 432, 434, 436, and 444 allow the passage of the magnetic flux surface 452 and the plasma jet 454, but provides an obstruction to the neutral gas flow from the plasma gun 350 located in the diverter 300.Similarly, constriction 442 prevents backflow of gas from formation section 200 to divertor 300, thereby reducing the number of neutral particles that need to be introduced into the entire FRC system 10 when beginning FRC startup; (3) the strong axial mirror produced by coils 432, 434, 436, and 444 reduces axial particle losses, thereby reducing the diffusivity of collimated particles on the open field line.

[0073] In an alternative configuration shown in FIGS. 3D and 3E, a set of thin, reduced diameter coils 421 are positioned between the inner diverter 302 and the forming section 200.

[0074] (axial plasma gun) The plasma flow from the gun 350 mounted within the divertor chamber 310 of the divertor 300 is intended to improve stability and neutral beam performance. The gun 350 is mounted axially inside the chamber 310 of the divertor 300, as shown in Figures 3 and 10, and produces plasma that flows along an open field line 452 within the divertor 300 toward the center of the confinement chamber 100. The gun 350 operates with a high-density gas discharge within the washer stack channel and is designed to generate a multi-kiloampere fully ionized plasma for 5-10 ms. The gun 350 includes pulsed magnetic coils that match the output plasma flow to the desired size of the plasma within the confinement chamber 100. The technical parameters of the Gun 350 are characterized by a channel with an outer diameter of 5-13 cm and an inner diameter of up to approximately 10 cm, providing a discharge current of 10-15 kA at 400-600 V, with an internal magnetic field of 0.5-2.3 T.

[0075] The gun plasma flow can penetrate the magnetic field of the mirror plug 440 and flow into the formation section 200 and the confinement chamber 100. The efficiency of plasma transmission through the mirror plug 440 increases with decreasing distance between the gun 350 and the plug 440 and by making the plug 440 wider and shorter. Under reasonable conditions, the gun 350 can transmit plasma at a rate of about 1000 keV through the mirror plug 440 of 2-4 T, with high ion and electron temperatures of about 150-300 eV and about 40-50 eV, respectively. 22 The gun 350 is capable of delivering protons / second, providing significant replenishment of the FRC edge layer 456 and overall improvement in FRC particle containment.

[0076] To further increase the plasma density, a gas box could be utilized to inject additional gas into the plasma stream from the gun 350. This technique allows the density of the injected plasma to be increased several times. In the FRC system 10, a gas box installed on the divertor 300 side of the mirror plug 440 improves the replenishment of the FRC edge layer 456, the formation of the FRC 450, and plasma line coupling.

[0077] Given all the adjustment parameters discussed above, and also taking into account that operation with only one or both guns is possible, it is readily apparent that a wide range of operating modes is available.

[0078] (bias electrode) Electrical biasing of the open flux planes provides a radial potential that causes azimuthal E×B motion, providing a control mechanism; similar to turning a knob, velocity shear can control not only the open field line plasma but also the actual rotation of the FRC core 450. To accomplish this control, FRC system 10 employs various electrodes strategically placed in various parts of the machine. Figure 3 depicts bias electrodes positioned at preferred locations within FRC system 10.

[0079] In principle, there are four classes of electrodes: (1) a point electrode 905 within the confinement chamber 100 that contacts a specific open field line 452 within the edge of the FRC 450 to provide localized charging; (2) an annular electrode 900 between the confinement chamber 100 and the forming section 200 to charge the far-edge flux layer 456 in an azimuthally symmetric manner; (3) a stack of concentric electrodes 910 within the divertor 300 to charge multiple concentric flux layers 455 (whereby layer selection is controllable by adjusting the coil 416 to adjust the divertor magnetic field to terminate the desired flux layer 456 on the appropriate electrode 910); and finally, (4) an anode 920 (see FIG. 10 ) of the plasma gun 350 itself (which captures the inner open flux surface 455 near the section line of the FRC 450). FIGS. 10 and 11 show some typical designs for some of these.

[0080] In all cases, the electrodes are driven by a pulsed or DC power supply at voltages up to about 800 V. Depending on the size of the electrodes and the magnetic flux surface being traversed, currents can be drawn in the kiloampere range.

[0081] (Non-sustainable operation of FRC system - conventional system) Standard plasma formation on the FRC system 10 follows the well-developed reversed-field theta-pinch technique. A typical process for starting an FRC begins by driving the quasi-DC coils 412, 414, 416, 420, 432, 434, and 436 to steady-state operation. The RFTP pulsed power circuit of the pulsed power formation system 210 then drives the pulsed rapid reversed-field coil 232, creating a temporary reverse bias of approximately 0.05 T within the formation section 200. At this point, a predetermined amount of neutral gas at 9-20 psi is injected into the two formation volumes defined by the quartz tube chambers 240 (north and south) of the formation section 200 via a set of azimuthally oriented discharge troughs in a flange located on the outer end of the formation section 200. A small-scale RF (approximately several hundred kilohertz) field is then generated from a set of antennas on the surface of the quartz tube 240 to create pre-ionization within the neutral gas column in the form of a localized seed ionization region. This is followed by applying a theta resonance modulation onto the current driving the pulsed fast reversed field coil 232, which leads to further comprehensive pre-ionization of the gas column. Finally, the main pulsed power bank of the pulsed power shaping system 210 is activated to drive the pulsed fast reversed field coil 232, creating a forward bias field of up to 0.4 T. This step can be time-sequenced, whereby a forward bias field is generated uniformly throughout the length of the shaping tube 240 (static shaping), or a continuous peristaltic field modulation is achieved along the axis of the shaping tube 240 (dynamic shaping).

[0082] During this entire formation process, the actual magnetic field reversal within the plasma occurs rapidly within approximately 5 μs. Multi-gigawatt pulsed power delivered to the forming plasma readily produces hot FRCs, which are then ejected from the forming section 200 by either time-sequential modulation of the forward magnetic field (magnetic peristalsis) or application of a temporarily increased current in the last coil of coil set 232 near the axially outer end of the forming tube 210 (which creates an axial magnetic field gradient pointing axially toward the confinement chamber 100). The two (north and south) formed FRCs thus formed and accelerated then expand into the larger diameter confinement chamber 100, with the quasi-DC coil 412 producing a forward bias field to control the radial expansion and provide a balanced external magnetic flux.

[0083] When the north and south forming FRCs arrive near the midplane of the confinement chamber 100, the FRCs collide. During the collision, the axial kinetic energy of the north and south forming FRCs is largely thermalized when the FRCs eventually merge into a single FRC 450. A large set of plasma diagnostics is available within the confinement chamber 100 to study the equilibrium of the FRCs 450. Typical operating conditions in the FRC system 10 produce a composite FRC with a section radius of about 0.4 m and an axial extension of about 3 m. Further characterization is performed using an external magnetic field of about 0.1 T, a magnetic field of about 5×10 19 m 3 and a total plasma temperature of up to 1 keV. Without any sustainment, i.e., heating and / or current drive by neutral beam injection or other auxiliary means, the lifetime of these FRCs is limited to approximately 1 ms, i.e., the intrinsic characteristic configuration decay time.

[0084] (Experimental data on non-sustained motion - conventional system) Figure 12 shows the radius of the dividing line r s The excluded flux radius r approximates ΔΦThe typical time evolution of plasmoids is shown to illustrate the dynamics of the theta-pinch fusion process in FRC450. Two individual plasmoids (northern and southern) are produced simultaneously and then merged together at supersonic speeds of about 250 km / s. Z , accelerate outward from their respective forming segments 200 and collide near the midplane at z=0. During the collision, the plasmoids contract axially and then rapidly expand radially and axially before finally merging to form FRC450. Both the radial and axial dynamics of the merging FRC450 are evidenced by detailed density profile measurements and bolometer-based tomography.

[0085] Data from a representative unsustained discharge of the FRC system 10 is shown as a function of time in Figures 13A, 13B, 13C, and 13D. The FRC is started at t=0. The excluded flux radius at the axial midplane of the machine is shown in Figure 13A. This data was obtained from an arrangement of magnetic probes located just inside the steel wall of the containment chamber, which measures the axial magnetic field. The steel wall is an excellent flux conserver on the time scale of this discharge.

[0086] The line-integrated density from a six-cord CO2 / He-Ne interferometer located at z = 0 is shown in Figure 13B. Taking into account the vertical (y) FRC displacement, as measured by bolometric tomography, the Abel transformation yields the density contours in Figure 13C. After some axial and radial oscillations during the first 0.1 ms, the FRC settles with a white density profile. This profile is quite flat, with substantial density on the axis, as required by typical 2D FRC equilibration.

[0087] The total plasma temperature, derived from pressure balance and in perfect agreement with the Thomson scattering spectroscopy measurements, is shown in Figure 13D.

[0088] Analysis of the entire excluded flux configuration shows that the shape of the FRC section line (approximated by the excluded flux axial profile) gradually evolves from a racetrack to an elliptical shape. This evolution, shown in Figure 14, is consistent with a gradual magnetic reconnection from two to a single FRC. In fact, rough estimates suggest that at this particular moment, about 10% of the two initial FRC fluxes reconnect during the collision.

[0089] The length of the FRC shrinks steadily during the FRC lifetime, from 3 to about 1 m. This shrinkage suggests that convective energy losses primarily govern the FRC confinement, as visualized in Figure 14. As the plasma pressure inside the dividing line decreases faster than the external magnetic pressure, the magnetic field line tension in the end regions compresses the FRC axially, restoring axial and radial equilibrium. For the discharges discussed in Figures 13 and 14, the FRC magnetic flux, particle loading, and thermal energy (about 10 mWb and 7 × 10 , respectively) decrease. 19 particles, and 7 kJ) decreases by roughly an order of magnitude within the first millisecond as the FRC equilibrium appears to decline.

[0090] (Sustained operation - HPF system) 12-14 are examples of decaying FRC characteristics without any sustainment. However, several techniques can be deployed on the FRC system 10 to further improve the FRC confinement (inner core and edge layers) for HPF systems and sustain configurations.

[0091] (neutral beam) First, fast (H) neutrons are injected into the beam from eight neutral beam injectors 600, and then injected into the B zThe beam of fast neutrons is injected perpendicular to the FRC 450. The fast ions, primarily created by charge exchange, have betatron orbits (with a primary radius much larger than the FRC topology or at least the characteristic magnetic field gradient length scale) that increase the azimuthal current of the FRC 450. After a certain fraction of the discharge (0.5-0.8 ms into the shot), a sufficiently large fast ion population significantly improves the stability and confinement properties of the inner FRC (see, e.g., M.W. Binderbauer and N. Rostoker, Plasma Phys. 56, part 3, 451 (1996)). Furthermore, from a sustainability perspective, the beam from the neutral beam injector 600 is also the primary means for driving the current and heating the FRC plasma.

[0092] In the plasma regime of the FRC system 10, fast ions are primarily decelerated by plasma electrons. During the initial stage of the discharge, the typical orbit-averaged deceleration time of fast ions is 0.3-0.5 ms, which primarily results in significant FRC heating of the electrons. Fast ions experience large radial deviations outside the separatrix because the inner FRC magnetic field is inherently low (average approximately 0.03 T compared to an external axial field of 0.1 T). Fast ions may be susceptible to charge exchange losses if the neutral gas density is very high outside the separatrix. Therefore, wall gettering and other techniques deployed on the FRC system 10 (such as the plasma gun 350 and mirror plug 440, which contribute to gas control, among other things) tend to minimize edge neutrons and allow the desired buildup of fast ion current.

[0093] (pellet injection) Once a significant fast ion population builds within the FRC 450, frozen H or D pellets are injected into the FRC 450 from the pellet injector 700, with a higher electron temperature and longer FRC lifetime, sustaining the FRC particle inventory of the FRC 450. The expected ablation timescale is short enough to provide a significant FRC particle source. This rate can also be increased by increasing the surface area of ​​the injected piece by breaking individual pellets into smaller fragments while they are in the barrel or injection tube of the pellet injector 700 and before entering the confinement chamber 100 (a step that can be achieved by increasing the friction between the pellet and the wall of the injection tube by tightening the bend radius of the final section of the injection tube just before entering the confinement chamber 100). By varying the fragmentation as well as the firing sequence and rate of the 12 barrels (injection tubes), it is possible to tune the pellet injection system 700 to provide exactly the desired level of particle inventory sustainment. This, in turn, helps maintain the internal dynamic pressure in the FRC 450 and its sustained operation and lifetime.

[0094] When the ablated atoms encounter significant plasma within the FRC 450, they become fully ionized. The resulting cold plasma components are then collisionally heated by the intrinsic FRC plasma. The energy required to maintain the desired FRC temperature is ultimately provided by the beam injector 600. In this sense, the pellet injector 700, together with the neutral beam injector 600, form a system that maintains stable conditions and sustains the FRC 4504.

[0095] (CT injector) As an alternative to pellet injectors, compact toroid (CT) injectors are provided primarily for refueling field-reversed configuration (FRC) plasmas. The CT injector 720 comprises a magnetized coaxial plasma gun (MCPG) and includes coaxial cylindrical inner and outer electrodes 722 and 724, a bias coil positioned inside the inner electrode 726, and an electrical breaker 728 on the end of the CT injector 720 opposite the discharge, as shown in FIGS. 22A and 22B. Gas is injected through a gas injection port 730 into the space between the inner and outer electrodes 722 and 724, from which a spheromak-shaped plasma is generated by the discharge and pushed out of the gun by the Lorentz force. As shown in FIGS. 23A and 23B, a pair of CT injectors 720 are coupled to the containment vessel 100 near and on opposite sides of the vessel's midplane to inject CT into the central FRC plasma within the containment vessel 100. The discharge end of the CT injector 720 is oriented toward the midplane of the containment vessel 100 at an angle to the longitudinal axis of the containment vessel 100 similar to the neutral beam injector 615 .

[0096] In an alternative embodiment, the CT injector 720 includes a drift tube 740 comprising an elongated cylindrical tube coupled to the discharge end of the CT injector 720, as shown in Figures 24A and 24B. As depicted, the drift tube 740 includes drift tube coils 742 positioned around and axially spaced therealong. A plurality of diagnostic ports 744 are depicted along the length of the tube.

[0097] Advantages of the CT injector 720 include (1) control and adjustability of particle load per injected CT, (2) high-temperature plasma is deposited (instead of cryogenic pellets), (3) the system can be operated in a repetition rate mode to allow for continuous refueling, and (4) the system can also restore some magnetic flux as the injected CT carries the embedded magnetic field. In an embodiment for experimental use, the inner diameter of the outer electrode is 83.1 mm and the outer diameter of the inner electrode is 54.0 mm. The surface of the inner electrode 722 is preferably coated with tungsten to reduce impurities originating from the electrode 722. As depicted, a bias coil 726 is mounted inside the inner electrode 722.

[0098] In recent experiments, ultrasonic CT translation velocities of up to about 100 km / s have been achieved. Other typical plasma parameters are as follows: electron density about 5 x 1021 m 3 , electron temperature about 30-50 eV, and particle population about 0.5-1.0 x 1,019. The high dynamic pressure of the CT allows the injected plasma to penetrate deep into the FRC and deposit particles inside the dividing line. In recent experiments, FRC particle refueling has resulted in approximately 10-20% of the FRC particle population being successfully delivered by the CT injector, demonstrating that refueling can be easily performed without disrupting the FRC plasma.

[0099] (Saddle coil) To achieve steady-state current drive and maintain the required ion current, it is desirable to prevent or significantly reduce electron spin-up due to electron-ion frictional forces (resulting from impacting ion-electron momentum transfer). The FRC system 10 utilizes an innovative technique to provide electron splitting by an externally applied stable magnetic dipole or quadrupole field. This is accomplished via an external saddle coil 460 depicted in FIG. 15. A transversely applied radial magnetic field from the saddle coil 460 induces an axial electric field within the rotating FRC plasma. The resulting axial electron current interacts with the radial magnetic field, exerting an azimuthal splitting force F on the electrons. θ =-σV eθ <│B r │ 2 For typical conditions in the FRC system 10, the applied magnetic dipole (or quadrupole) field required inside the plasma needs to be only on the order of 0.001 T to provide sufficient electron division. A corresponding external field of about 0.015 T is small enough not to cause significant fast particle losses or otherwise negatively affect confinement. In fact, the applied magnetic dipole (or quadrupole) field contributes to suppressing instabilities. Combining tangential neutral beam injection with axial plasma injection, the saddle coil 460 provides an additional level of control over current maintenance and stability.

[0100] (Mirror plug) The design of the pulsed coils 444 within the mirror plug 440 allows for the local generation of high magnetic fields (2-4 T) using moderate (approximately 100 kJ) volumetric energy. With regard to the magnetic field formation specific to this operation of the FRC system 10, all field lines within the formation volume pass through the constriction 442 in the mirror plug 440, and no plasma wall contact occurs, as suggested by the magnetic field lines in FIG. 2. Furthermore, the mirror plug 440, in conjunction with the quasi-DC divertor magnets 416, can be adjusted to direct the field lines onto the divertor electrode 910 or to diverge the field lines in an end-tip configuration (not shown). The latter improves stability and suppresses thermal conduction of parallel electrons.

[0101] The mirror plug 440 itself also contributes to neutral gas control. The mirror plug 440 allows for better utilization of the deuterium gas discharged into the quartz tube during FRC formation, because backflow into the divertor 300 is significantly reduced by the plug's low gas conductivity (only 500 L / s). Most of the discharged gas remaining inside the formation tube 210 is rapidly ionized. In addition, the high-density plasma flowing through the mirror plug 440 provides efficient neutral ionization and thus an effective gas barrier. As a result, most of the neutrons recycled within the divertor 300 from the FRC edge layer 456 do not return to the confinement chamber 100. In addition, neutrons associated with the operation of the plasma gun 350 (discussed below) will be largely confined to the divertor 300.

[0102] Finally, the mirror plugs 440 tend to improve FRC edge layer confinement. With a mirror ratio (plug / confining field) in the range of 20-40 and a length of 15 m between the north and south mirror plugs 440, the edge layer particle confinement time τ ∥ increases by at most one digit. ∥ Improvements in the FRC particle containment can be easily increased.

[0103] The radial diffusion (D) particle loss from the section volume 453 is proportional to the axial loss (τ ∥ ), then (2πr s L s )(Dn s / δ)=2πr s L s δ)(n s / τ ∥ ) and from there, the segregation density gradient length is given by δ = (Dτ ∥ ) 1 / 2 where r s、 L s , and n s are the segment radius, segment length, and segment density, respectively. The FRC particle confinement time is τ N =[πr s2 L s <n>] / [(2πr s L s )(Dn s / d)]=( <n> / n s )(τ ⊥ τ ∥ ) 1 / 2 where τ ⊥ =a 2 / D and a=r s In physics, τ ∥ The improvement in leads to an increase in δ (a decrease in the seismic density gradient and drift parameter) and therefore a reduction in FRC particle losses. The overall improvement in FRC particle confinement is s But τ ∥ Generally speaking, it is difficult to call it a quadratic equation, since it increases with .

[0104] τ ∥ Significant improvement in also requires that the edge layer 456 remain extremely stable (i.e., free of n=1 flutes, firehoses, or other MHD instabilities inherent in open systems). The use of the plasma gun 350 provides this desirable edge stability. In this sense, the mirror plug 440 and plasma gun 350 form an effective edge control system.

[0105] (Plasma Gun) The plasma gun 350 improves the stability of the FRC exhaust jet 454 through magnetic field line coupling. The gun plasma from the plasma gun 350 is generated without azimuthal angular momentum, which proves useful for controlling FRC rotational instabilities. Thus, the gun 350 is an effective means for controlling FRC stability without requiring older quadrupole stabilization techniques. As a result, the plasma gun 350 makes it possible to exploit the beneficial effects of fast particles or, as outlined in this disclosure, access highly hybrid motion FRC regimes. Thus, the plasma gun 350 allows the system 10 to be operated with a saddle coil current that is just sufficient for electron splitting but below the threshold that would cause FRC instability (and / or lead to dramatic fast particle diffusion).

[0106] As mentioned in the discussion of mirror plugs above, τ ∥ If it can be greatly improved, the supplied gun plasma will be comparable to the edge layer particle loss rate (about 10 22 / s). The lifetime of the gun-produced plasma in the FRC system 10 is within the range of milliseconds. In fact, consider a gun plasma confined between the end mirror plugs 440 with a density of about 10 e about 10 13 cm 3 and an ion temperature of about 200 eV. The capture length L and the mirror ratio R are about 15 m and 20, respectively. The ion mean free path due to Coulomb collisions is λ ii about 6×10 3 cm, and since λ ii lnR / R < L, the ions are confined in a gas kinetic system. The plasma confinement time in this system is τ gd about RL / 2V s , about 2 ms, where V s is the ion sound speed. For comparison, the classical ion confinement time for these plasma parameters is τ c about 0.5τ ii (lnR+(lnR) 0.5 ), about 毫秒であろう。異常横断拡散は、原則として、プラズマ閉じ込め時間を短縮し得る。しかしながら、FRCシステム10では、ボーム拡散率を仮定する場合、ガンプラズマに対する推定される横断閉じ込め時間は、τ ⊥ >τ g about 2 ms. Therefore, the gun will provide a significant supply to the FRC edge layer 456 and an improvement in the overall FRC particle confinement.

[0107] Furthermore, the gun plasma flow can be turned on within approximately 150-200 milliseconds, allowing its use in initiating, translating, and fusing FRCs into the confinement chamber 100. When turned on at t approximately 0 (FRC main bank initiation), the gun plasma helps sustain this dynamically forming and fusing FRC 450. The combined particle load from the forming FRC and from the gun is sufficient for neutral beam trapping, plasma heating, and long-term persistence. When turned on between t -1 and 0 ms, the gun plasma can fill the quartz tube 210 with plasma or ionize gases exhaled into the quartz tube, thus enabling FRC formation with reduced, or perhaps even zero, exhaled gas. The latter may require a sufficiently cool forming plasma to allow for rapid diffusion of the reverse bias field. When turned on at t < -2 ms, the plasma flow is sufficient to allow neutral beam formation several tens of times prior to FRC arrival. 13 cm 3 1-3 m of the formation and confinement region of the formation section 200 and confinement chamber 100, with a target plasma density of 3 The plasma gun 350 may then be configured to fill a field volume of 1000 .0001. The formed FRC may then be configured to form a resulting containment vessel plasma. In this manner, the plasma gun 350 allows for a wide variety of operating conditions and parameter regimes.

[0108] (electrical bias) Controlling the radial electric field profile in the edge layer 456 is beneficial to FRC stability and confinement in several ways. The innovative biasing components deployed in the FRC system 10 allow for the application of various deliberate distributions of electric potential to open magnetic flux planes throughout the machine from areas well outside the central confinement region in the confinement chamber 100. In this way, radial electric fields can be generated across the edge layer 456 just outside the FRC 450. These radial electric fields then modify the azimuthal rotation of the edge layer 456 and affect its confinement via E×B velocity shear. Any differential rotation between the edge layer 456 and the FRC core 453 can then be conducted to the inside of the FRC plasma via shear. As a result, controlling the edge layer 456 directly affects the FRC core 453. Furthermore, because free energy in plasma rotation can also contribute to instabilities, this technique provides a direct means for controlling instability initiation and growth. In FRC system 10, appropriate edge biasing provides effective control of FRC core rotation as well as translation and rotation of open field lines. The locations and shapes of the various provided electrodes 900, 905, 910, and 920 allow control of different groups of magnetic flux surfaces 455 and at different and independent potentials. In this manner, a wide array of different electric field configurations and strengths is achieved, each of which can have different characteristic effects on plasma performance.

[0109] A key advantage of all these innovative biasing techniques is the fact that the behavior of the core and edge plasmas can be influenced from well outside the FRC plasma, i.e., without the need for any physical components to come into contact with the central hot plasma (which would have important implications for energy, magnetic flux, and particle losses). This has major beneficial impacts on the performance and all potential applications of the HPF concept.

[0110] (Experimental data - HPF operation) Injection of energetic particles using the beam from the Neutral Beam Gun 600 plays a key role in enabling the HPF regime. Figures 16A, 16B, 16C, and 16D illustrate this fact. A set of curves showing the correlation of FRC lifetime with beam pulse length is plotted. All other operating conditions were held constant for all discharges comprising this study. This data was averaged over many shots and therefore represents typical behavior. It is clear that longer beam durations produce longer-lived FRCs. This evidence in this study, as well as other diagnostics, demonstrates increased beam stability and reduced losses. The correlation between beam pulse length and FRC lifetime is not perfect because beam capture becomes inefficient below a certain plasma size; that is, as the FRC 450 shrinks in physical size, not all of the injected beam is intercepted and captured. The shrinkage of the FRC is primarily due to the fact that the net energy loss from the FRC plasma during the discharge (about 4 MW approximately midway through the discharge) is somewhat greater than the total power delivered into the FRC using the neutral beam (about 2.5 MW) for the particular experimental setup. Locating the beam closer to the midplane of vessel 100 would tend to reduce these losses and extend the FRC lifetime.

[0111] Figures 17A, 17B, 17C, and 17D illustrate the effect of different components for achieving the HPF regime. This shows a typical system of curves depicting the lifetime of the FRC 450 as a function of time. In all cases, a constant and moderate amount of beam power (approximately 2.5 MW) is injected throughout the duration of each discharge. Each curve is representative of a different combination of components. For example, operating the FRC system 10 without any mirror plug 440, plasma gun 350, or gettering from the gettering system 800 results in rapid onset of rotational instability and loss of FRC topology. Adding the mirror plug 440 alone delays the onset of instability and increases confinement. Utilizing the mirror plug 440 in combination with the plasma gun 350 further reduces instabilities and increases the lifetime of the FRC. Finally, adding gettering (in this case, Ti) in addition to the gun 350 and plug 440 produces the best results; the resulting FRC is free of instabilities and exhibits the longest lifetime. It is clear from this experimental demonstration that the perfect combination of components produces the best effect and provides a beam with the best target conditions.

[0112] As shown in Figure 1, the newly discovered HPF regime exhibits significantly improved transport behavior. Figure 1 illustrates the change in particle confinement time in FRC system 10 between the conventional regime and the HPF regime. As shown, the HPF regime provides an improvement of well over five times. In addition, Figure 1 details the particle confinement time in FRC system 10 compared to that in prior conventional FRC experiments. Relative to these other machines, the HPF regime of FRC system 10 improves confinement by a factor of 5 to approximately 20. Finally, and most importantly, the nature of the confinement scaling in FRC system 10 is significantly different from all previous measurements. Prior to the establishment of the HPF regime in FRC system 10, various empirical scaling laws were derived from data in prior FRC experiments to predict confinement time. All of these scaling laws primarily depended on the ratio R 2 / ρ i where R is the radius of the magnetic field null (a rough measure of the physical scale of the machine) and ρ i is the ion Larmor radius (a rough measure of the applied magnetic field) evaluated in an externally applied field. It is clear from Figure 1 that long-term confinement in a conventional FRC is only possible with large machine sizes and / or high magnetic fields. The operation of the FRC system 10 in the conventional FRC regime CR tends to follow those scaling laws, as shown in Figure 1. However, the HPF regime is significantly superior, demonstrating that significantly better confinement can be obtained without large machine sizes or high magnetic fields. More importantly, it is also clear from Figure 1 that, compared to the CR regime, the HPF regime offers improved confinement time while reducing the plasma size. Similar trends are evident for the flux and energy confinement times, as explained below, which also increase by more than 3 to 8 times in the FRC system 10. The breakthrough in the HPF regime therefore enables the use of moderate beam powers, lower magnetic fields, and smaller sizes to sustain and maintain FRC equilibrium in the FRC system 10 and future high-energy machines. These improvements combined result in lower operating and construction costs as well as reduced engineering complexity.

[0113] For further comparison, Figures 18A, 18B, 18C, and 18D show data from a representative HPF system discharge in FRC system 10 as a function of time. Figure 18A depicts the excluded flux radius at the midplane. For these longer time scales, the conductive steel wall is no longer a good flux conserver, and to properly account for flux diffusion through the iron, magnetic probes inside the wall are augmented with probes outside the wall. Compared to typical performance in conventional system CR, the HPF system operating mode exhibits over 400% longer lifetimes, as shown in Figures 13A, 13B, 13C, and 13D.

[0114] A representative trace of the line-integrated density is shown in Figure 18B along with its Abelian transform complement and in Figure 18C along with the density contours. Compared to the conventional FRC system CR, the plasma is more quiescent throughout the pulse, demonstrating very stable operation, as shown in Figures 13A, 13B, 13C, and 13D. The peak density is also slightly lower in the HPF shot, which is a consequence of the higher total plasma temperature (up to two times), as shown in Figure 18D.

[0115] For each discharge illustrated in Figures 18A, 18B, 18C, and 18D, the energy, particle, and flux confinement times are 0.5 ms, 1 ms, and 1 ms, respectively. At a reference time of 1 ms into the discharge, the plasma energy stored is 2 kJ, but the losses are about 4 MW, making this target highly suitable for neutral beam sustainment.

[0116] Figure 19 summarizes the full benefits of the HPF scheme in the form of newly established experimental HPF flux confinement scaling. As can be seen from Figure 19, based on measurements taken before and after t = 0.5 ms, i.e., at t ≤ 0.5 ms and t > 0.5 ms, the flux confinement (as well as particle confinement and energy confinement) scales at a given section radius (r s ) versus electron temperature (T e ) varies approximately as the square of T e This strong scaling, with a positive exponent (but not a negative exponent) of , is completely opposite to that exhibited by conventional tokamaks, where confinement is typically inversely proportional to some exponent of the electron temperature. The appearance of this scaling is a direct consequence of the HPF regime and large-orbit (i.e., orbits on the scale of the FRC topology and / or at least the characteristic magnetic field gradient length scale) ion population. Essentially, this new scaling substantially favors high operating temperatures, enabling reactors of relatively moderate size.

[0117] The advantages offered by the HPF system make it possible to achieve a neutral beam-driven FRC sustainment, or steady state, which means that global plasma parameters, such as plasma thermal energy, total particle number, plasma radius and length, as well as magnetic flux, can be sustained at reasonable levels without substantial decay. For comparison, Figure 20 shows data from a representative HPF system discharge in FRC system 10 as a function of time in plot A, and data for a projected representative HPF system discharge in FRC system 10 as a function of time in plot B. The FRC 450 is sustained without decay throughout the duration of the neutral beam pulse. For plot A, a neutral beam with a total power in the range of approximately 2.5 to 2.9 MW was injected into the FRC 450 for an active beam pulse length of approximately 6 ms. The plasma diamagnetic lifetime depicted in plot A was approximately 5.2 ms. More recent data indicates that a plasma diamagnetic lifetime of approximately 7.2 ms is achievable using an active beam pulse length of approximately 7 ms.

[0118] As described above with respect to Figures 16A, 16B, 16C, and 16D, the correlation between beam pulse length and FRC lifetime is not perfect because beam trapping becomes inefficient below a certain plasma size, i.e., not all injected beam is intercepted and trapped as the physical size of the FRC 450 shrinks. FRC shrinkage or decay is primarily due to the fact that the net energy loss from the FRC plasma during the discharge (approximately 4 MW at approximately the middle of the discharge) is somewhat greater than the total power delivered into the FRC using the neutral beam (approximately 2.5 MW) for the particular experimental setup. As described with respect to Figure 3C, beam injection angled from the neutral beam gun 600 toward the midplane improves beam-plasma coupling during the injection period, even if the FRC plasma contracts or otherwise shrinks axially. In addition, proper pellet refueling will maintain the required plasma density.

[0119] Plot B shows the results of a simulation performed using an active beam pulse length of approximately 6 ms and a total beam power from the neutral beam gun 600 of slightly more than approximately 10 MW. The neutral beams are assumed to inject H (or D) neutrons with particle energies of approximately 15 keV. The equivalent current injected by each beam is approximately 110 A. For plot B, the beam injection angle relative to the device axis was approximately 20°, and the target radius was 0.19 m. The injection angle can be varied within the range 15° to 25°. The beams are assumed to be injected azimuthally cocurrently. Not only the net lateral force, but also the net axial force from the neutral beam momentum injection is assumed to be minimized. Similar to plot A, fast (H) neutrons are injected from the neutral beam injector 600 into one FRC 450 from the moment the north and south forming FRCs fuse within the confinement chamber 100.

[0120] The underlying simulations for plot B use a coupled set of transport equations for all plasma species to model two-way loss processes, as well as a multidimensional Hall MHD solver for the background plasma and equilibrium and a full-kinetic Monte Carlo-based solver for the energetic beam components and all scattering processes. The transport components are experimentally calibrated and extensively benchmarked against experimental databases.

[0121] As shown by plot B, the steady-state diamagnetic lifetime of FRC450 will be the beam pulse length. However, it is important to note that the key correlation plot B shows that the plasma or FRC begins to decay at the time the beam is turned off, not before. The decay will be similar to that observed during the discharge, which is not beam-assisted (probably about 1 ms beyond the beam-off time), and is simply a reflection of the characteristic decay time of the plasma, which is driven by intrinsic loss processes.

[0122] Turning to Figures 21A, 21B, 21C, 21D, and 21E, the experimental results illustrated in the figures demonstrate the achievement of FRC persistence or steady state driven by an angled neutral beam. That is, global plasma parameters such as plasma radius, plasma density, and plasma temperature, as well as magnetic flux, are sustained at a constant level without decay relative to the NB pulse duration. For example, such plasma parameters remain essentially constant for approximately 5+ ms. Such plasma performance, including persistence features, has a strongly correlated NB pulse duration, and diamagnetism remains even several milliseconds after NB termination due to accumulated fast ions. As illustrated, plasma performance is limited only by pulse length constraints arising from finite stored energy in the associated power supplies of not only the NB injector but also many other critical system components.

[0123] (Neutral Beam Adjustable Beam Energy) As described above with respect to Figures 3A, 3B, 3C, 3D, 3E, and 8, a neutral atomic beam 600 is deployed on the FRC system 10 to generate high-velocity particle pressure as well as provide heating and current drive. The individual beam lines comprising the neutral atomic beam injector system 600 are positioned around the periphery of the central confinement chamber 100 and are preferably angled, as shown in Figures 3C, 3D, and 3E, to inject neutral particles toward the midplane of the confinement chamber 100.

[0124] To further improve FRC persistence and demonstrate FRC scaling to high plasma temperatures and increased system energies, the present FRC system 10 includes a neutral beam injector (NBI) system 600 with increased power and extended pulse lengths, e.g., for illustrative purposes only, up to 30 ms pulse lengths, at approximately 20+ MW power. The NBI system 600 includes multiple positive ion-based injectors 615 (see FIGS. 3D and 3E ) and features a flexible, modular design, with some of the NBI injectors 615, e.g., four of the eight NBI injectors 615, having the ability to adjust the beam energy from an initial lower beam energy to an increased beam energy (e.g., from approximately 15 keV to approximately 40 keV) at a constant beam current during a shot. This capability of the NBI injectors 615 is desirable for achieving more efficient heating and resulting pressurization of the plasma core 450. In particular, this capability enables highly desirable performance improvements at peak energy operating levels compared to lower energy levels. For example, (i) up to two times the heating power, (ii) approximately one-fifth reduction in charge exchange losses, and (iii) up to two times the heating efficiency. Additionally, the continuously variable beam energy producible by the NBI injector 615 allows optimal matching of the trajectory parameters of the injected and then trapped fast ions to the instantaneous magnetic pressure profile during the ascent process. Finally, the fast ramp rate enabling ascent durations of 0.1 to 10 ms, along with the fast (approximately 1 ms or less) adjustment capability of the beam energy and power of the NBI injector 615, provides an additional effective "control knob," i.e., a controllable feature for plasma shaping and active feedback control of the plasma via modulation of the beam energy and power.

[0125] Sufficient heating power is required to enable heating and pressurization of the FRC 450, both sustained and ramping to high plasma temperatures and elevated system energy. Assuming a sufficiently low loss rate, the rate of ramp is primarily a function of the amount of power that can be deposited into the FRC core 450 by the NBI injector 615 at any given time. A higher primary neutral beam power through the injection port is therefore always desirable.

[0126] Furthermore, the effective heating rate resulting from the NBI injector 615 is a complex interaction between the injected beam properties and the current, sustained instantaneous profile of the magnetic field across the FRC core 450, as well as the temperature, electron and ion densities, and neutral concentrations of all species. Of these, the magnetic field profile is carefully varied on sub-millisecond timescales by the control system during ascent, while the dynamic pressure-related profile evolves through turbulence in the energy as well as inherent variations deriving from self-organization processes and the plasma deposited by the injection process. Beam tunability provides a means to most optimally adapt to these fluctuating conditions.

[0127] For example, the charge exchange cross section (i.e., the probability of electron capture by fast ions to form neutral atoms) is a strong function of beam energy. For the 15-40 keV range, the main charge exchange rate decreases significantly as a function of beam energy. Therefore, at any given level of magnetic field, energy retention in the plasma is highest when injecting particles at the highest energy compatible with such magnetic field level (among other things, this requires that the energy of the injected particles results in a trapped ion orbit radius that fits within the inner walls of the confinement system).

[0128] Another example of a profile effect on overall heating efficiency concerns where power is deposited. Higher beam energy will typically lead to relatively higher energy deposition at the FRC periphery compared to the core. Raising the magnetic field but keeping the beam energy the same will result in tighter trapped ion trajectories and correspondingly higher power coupling into the FRC core plasma. These facts, in turn, significantly affect energy retention as well; for example, energy deposited at the periphery is much more easily transported out of the system along the open field line structure, while energy deposited in the core is lost relatively more slowly due to lower cross-field transport times. Therefore, close coordination of magnetic field gradients and appropriate increases in beam energy is desirable.

[0129] The beam system 600 is designed for fast voltage ramping in the range of 0.1 to 10 ms. This offers the potential to increase ion and electron temperatures by a factor of 2 and 10, respectively, on timescales shorter than typical macroscopic instability growth times. Thus, plasma stability is fundamentally increased, as are operational reliability and repeatability.

[0130] A variable voltage rise time of 0.05–1 ms provides a sufficiently rapid response time so that the beam can be utilized as part of an active feedback system. In this way, beam modulation can be used to control macro- and microstability. For example, temporarily shifting the radial power deposition profile by varying the beam energy (and thereby shifting the radial energy deposition pattern) can affect pressure gradients that can equilibrate the onset of unstable plasma modes. The FRC system 10 shown in Figures 3D and 3E utilizes this capability, along with fast magnetic feedback, to control internal tilts, rotation rates, drift wave generation, and other operating scenarios.

[0131] 25 depicts an illustration of an NBI injector 615 of the present FRC system 10. The NBI injector 615, in an exemplary embodiment, is shown to include an arc driver 650; a plasma box 651; an ion optics system 652 comprising triodes or tetrodes of extraction and acceleration grids; a aiming gimbal 653; an arc evaporator 655, e.g., a Ti arc evaporator, a cryogenic pump 656 having a surface structure, e.g., a ribbed surface structure, configured for increased cryogenic pumping, and a neutralizer 654 comprising a deflection magnet 656 for removing non-neutralized ions; and a collimating aperture 658 containing an insertable calorimeter 659 for intermittent beam characterization, diagnostics, and recalibration.

[0132] More specifically, referring to FIG. 26, the implementation of the adjustable beam system is preferably based on a triode type ion optical system (=IOS) 660, as shown. The concept is an acceleration - deceleration scheme. As illustrated in FIG. 26, the first grid G1 is set to voltage V1, while the second grid G2 is set to voltage V2, and the final grid G3 is set to voltage V3. The extracted ions are first accelerated to energy E1 = e×(V1 - V2) while traversing the gap between G1 and G2 (where e here refers to the charge of the ion). They are then decelerated in the gap between G2 and G3 such that E2 = E1+e×(V2 - V3). The voltages are typically adjusted such that V1 > V2 < V3. Based on suitable individual power supplies PS1, PS2, PS3, the grid voltages can be gradually adjusted during the pulse to vary the output of the emitted ions 662. For example, to initiate a beam pulse of hydrogen atoms, the operating voltages can be adjusted to V1 = 15 kV, V2 = - 25 kV, and V3 = 0 V. The initial beam ions are then first accelerated to 40 keV and then will emerge from the IOS with an energy of 15 keV. In the second half of the pulse, the power supply can be switched to provide V1 = 40 kV, V2 = - 1 kV, V3 = 0 V. The beam deceleration in the second gap will then effectively disappear and will result in an output beam energy of approximately 40 keV. Each of the power supplies is individually controllable and provides suitable voltage modulation. The initial beam ions are extracted from the scale of a standard arc or RF - based plasma source PS. After emerging from the IOS 660, the beam ions 662 traverse a neutralizer 664, and the fast ions are converted to neutral ions by charge exchange with electrons released from the cold neutral gas present within the neutralizer 664. Appropriate cryogenic pumping prevents the neutral gas from leaking out of the downstream orifice of the neutralizer 664. At the end of the neutralizer, there is also a suitable bending magnet 666 that provides removal of the non - neutralized fast ions 663 and an ion dump 668 associated with absorbing the fast ions and their energy.The emerging atomic beam 670 is then passed through a suitable aperture 6720 to reduce beam divergence and provide a well-collimated stream of neutral atoms towards the core of the reactor.

[0133] In an alternative version, the IOS is based on a tetrode design. In this case, the IOS consists of four grids with the same acceleration-deceleration principle as described for the triode case. Those skilled in the art will readily recognize the similarities between the system components and operating principles. The introduction of the fourth grid provides further fine-tuning possibilities and overall more operating flexibility.

[0134] The exemplary embodiments provided herein are described in US Provisional Patent Application No. 62 / 414,574, which application is incorporated herein by reference.

[0135] (Plasma stability and axial position control) Conventional solutions to FRC instabilities typically provide axial stability at the expense of radial instability, or radial stability at the expense of axial instability, but not both. Primarily, an equilibrium in which the plasma position is stable laterally or radially has the desired property of axisymmetricity at the expense of axial instability. In view of the foregoing, embodiments provided herein are directed to systems and methods that facilitate both radial and axial stability of the FRC plasma and axial position control of the FRC plasma along the axis of symmetry of the FRC plasma confinement chamber that is independent of the axial stability characteristics of the FRC plasma equilibrium. However, the axial position instability is actively controlled using a set of external axisymmetric coils that control the FRC plasma axial position. The systems and methods provide feedback control of the FRC plasma axial position independent of the stability characteristics of the plasma equilibrium by using nonlinear control techniques that affect the voltages applied to a set of external coils concentric with the plasma.

[0136] The embodiments presented herein utilize the axially unstable balance of the FRC to stabilize or control axial instability while enhancing radial stability. In this way, both axial and radial stability can be obtained. A control method is designed to radially or laterally stabilize the FRC plasma at the expense of axial instability by modifying the external or equilibrium magnetic field, and then instantly restore the FRC plasma position toward the midplane of the confinement chamber by acting on the radial field coil currents while minimizing overshoot and / or oscillations around the midplane. An advantage of this solution is that it reduces the complexity of the actuators required for control. Compared to conventional solutions involving multiple degrees of freedom, the method of the embodiments presented herein reduces the complexity of the control problem along the FRC plasma rotation axis, which has one degree of freedom.

[0137] The combination of coil current waveform, fueling, and neutral beam power generated in an axially unstable plasma defines a plasma control scenario that places the plasma in an axially unstable regime. This scenario can be preprogrammed using prior knowledge from simulation or experiment, or controlled feedback to maintain an axially unstable equilibrium. The plasma position should be controlled independently of the equilibrium stability characteristics during discharge; for example, the control scheme should function to its limits for either an axially stable or an axially unstable plasma. The most axially unstable plasma that can be controlled has a growth time comparable to the vessel skin time.

[0138] Turning now to systems and methods for facilitating both radial and axial stability of an FRC plasma and axial position control of the FRC plasma along the axis of symmetry of an FRC plasma confinement chamber, FIG. 27 shows a simplified schematic illustrating an exemplary embodiment of an axial position control mechanism 510. Shown within confinement chamber 100, a rotating FRC plasma 520 has a plasma current 522 and an axial displacement direction 524. A balance field (not shown) is produced within chamber 100 by a symmetric current component, such as quasi-DC coil 412 (see FIGS. 2, 3A, 3D, and 3E). The balance field produces no net force in the axial displacement direction 524, but can be tuned to produce a stable plasma in either the transverse / radial or axial direction. For purposes of the embodiments presented herein, the balance field is tuned to produce a transverse / radial stable FRC plasma 520. As described above, this leads to axial instability and, therefore, axial displacement of the FRC plasma 520 in the axial displacement direction 524. As the FRC plasma 520 moves axially, it induces currents 514 and 516, which are antisymmetric, i.e., in opposite directions, within the walls of the confinement chamber 100 on either side of the midplane of the confinement chamber 100. The FRC plasma 520 will induce these types of current components both within the vessel and in the external coil. These antisymmetric current components 514 and 516 produce radial fields that interact with the toroidal plasma current 522 and produce forces that oppose the movement of the FRC plasma 520; the result of this force is that it slows down the plasma axial displacement. These currents 514 and 516 gradually dissipate over time due to the resistivity of the confinement chamber 100.

[0139] Radial field coils 530 and 531 disposed around containment chamber 100 on either side of the mid-plane provide additional radial field components due to currents 532 and 534 induced in opposite directions in coils 530 and 531. Radial field coils 530 and 531 may comprise axially symmetric coil pairs that may be positioned inside or outside containment vessel 100. Radial coils 530 and 531 are shown positioned outside containment vessel 100, similar to quasi-DC coils 412 (see FIGS. 2, 3A, 3D, and 3E). Each of coils 530 and 531, or pairs of coils, may carry different currents than the coils on either side of the mid-plane, but the currents are antisymmetric with respect to the mid-plane of containment vessel 100, and along the mid-plane, B z ≠0, B r = 0. Radial field coils 530 and 531 generate complementary radial field components that interact with toroidal plasma current 522 and produce an axial force that, in turn, pushes the plasma backward toward the midplane of confinement chamber 100.

[0140] The control mechanism 510 includes a control system configured to act on radial field coil currents to instantly restore the plasma position toward the machine midplane while minimizing overshoot and / or oscillations near the midplane. The control system includes a processor operably coupled to the radial field coils 530 and 531, the quasi-DC coil 412, their respective power supplies, and other components (e.g., magnetic sensors, etc.) to provide plasma position, plasma velocity, and active coil current measurements. The processor may be configured to perform the calculations and analyses described herein and may include or be communicatively coupled to one or more memories including non-transitory computer-readable media. It may include processor- or microprocessor-based systems, including systems using microcontrollers, reduced instruction set computers (RISC), application-specific integrated circuits (ASICs), logic circuits, and any other circuits or processors capable of performing the functions described herein. The above is merely exemplary and thus is not intended to limit in any way the definition and / or meaning of the terms “processor” or “computer.”

[0141] The functions of the processor may be implemented using either software routines, hardware components, or a combination thereof. The hardware components may be implemented using a variety of technologies, including, for example, integrated circuits or discrete electronic components. The processor unit typically includes readable / writable memory storage devices and typically also includes hardware and / or software for writing to and / or reading the memory storage devices.

[0142] The processor may include a computing device, an input device, a display unit, and an interface, for example, for accessing the Internet. The computer or processor may include a microprocessor. The microprocessor may be connected to a communication bus. The computer or processor may also include memory. The memory may include random access memory (RAM) and read-only memory (ROM). The computer or processor may also include a storage device, which may be a hard disk drive or a removable storage drive, such as a floppy disk drive, an optical disk drive, etc. The storage device may also be other similar means for loading computer programs or other instructions into the computer or processor.

[0143] The processor executes a set of instructions stored in one or more storage elements to process input data. The storage elements may also store data or other information as desired or needed. The storage elements may be in the form of information sources or physical memory elements within a processing machine.

[0144] The problem of controlling the position of an axially stable or unstable FRC configuration using a radial field coil actuator is solved using a branch of nonlinear control theory known as sliding mode control. A linear function of the system state (sliding surface) serves as the error signal with the desired asymptotically stable (sliding) behavior. The sliding surface is designed using Lyapunov theory to demonstrate asymptotic stability over a wide range of FRC dynamic parameters. The proposed control scheme can then be used for both axially stable and unstable plasmas without the need to retune the parameters used in the sliding surface. This property is advantageous because, as described above, the equilibrium may need to transition between axially stable and axially unstable equilibria at different phases of the FRC discharge.

[0145] The configuration of the control scheme 500 is shown in Figure 28. A low-pass filter limits the switching frequency within the desired control bandwidth. A digital control loop is assumed, requiring sampling and signal transmission with one sample delay. The error signal (sliding surface) is a linear combination of the coil current, plasma position, and plasma velocity. The plasma position and velocity are obtained from external magnetic measurements. The current in the active coil system can be measured by standard methods.

[0146] Coil current and plasma position are required to implement position control. Plasma velocity is required to improve performance, but is optional. A nonlinear function of this error signal (relay control law) generates separate voltage levels for every pair of power supplies connected to the mid-plane symmetric coils. The mid-plane symmetric coils are supplied with relay voltages of equal magnitude but opposite sign. This creates a radial field component, restoring the plasma position towards the mid-plane.

[0147] To demonstrate the feasibility of the control scheme, an accurate plasma model is used to simulate the plasma dynamics. The model utilizes the magnet geometry. The plasma current distribution corresponds to an axially unstable equilibrium with a growth time of 2 ms when only the plasma and vessel are considered. The power supplies are assumed to operate at discrete voltage levels, typically in 800 V steps.

[0148] Figure 29 shows several plasma control simulations highlighting the relationship between the voltage applied to the coils and the plasma position settling time, along with the coil peak current and ramp rate required to return the 20 cm axially displaced plasma to the mid-plane. These sliding-mode axial position control simulation examples are launched at 0.3 T using four pairs of outer trim coils. The four examples are shown corresponding to power supplies with discrete voltage levels in steps of 200 V (black squares), 400 V (black circles), 800 V (black triangles), and 1600 V (open squares). For all four examples, the control bandwidth is 16 kHz and the sampling frequency is 32 kHz. The plasma position (top), current in the outermost coil pair (center), and coil current ramp rate (bottom) are shown. The plasma displacement is allowed to become unstable until it reaches 20 cm. At this point, feedback control is applied.

[0149] Simulation results show the following: A coil ramp rate of 0.5 MA / sec is sufficient to return the plasma to the mid-plane within 1.5 ms (black square trace), requiring a 200V power supply. 2.2.3ms to return the plasma to the mid-plane (black circular trace), a coil ramp rate of 1 MA / sec is sufficient, requiring a 400V power supply. 3.1. A coil ramp rate of 2 MA / sec is sufficient to return the plasma to the mid-plane within 3 ms (black triangle trace), requiring an 800 V power supply. 4. A coil ramp rate of 4 MA / sec is sufficient to return the plasma to the mid-plane within 1.0 ms (white square trace), requiring a 1600 V power supply.

[0150] The peak currents for all trim coils for the third case studied above (2 MA / s ramp rate) are also shown as a function of trim coil position in Figure 30. A sliding mode axial position control simulation example is run at 0.3 T using a power supply with three levels (+800 V, 0, -800 V), four pairs of external trim coils using a 16 kHz control bandwidth and a 32 kHz sampling rate. A coil ramp rate of 2 MA / s is required to return the plasma to the midplane within 1.3 ms. The peak currents required in all coil pairs are less than 1.5 kA. The actual switching frequency required (approximately 2 kHz) is well below the control system bandwidth.

[0151] The control system can be implemented with a target surface that is a function of only coil current and plasma velocity, without plasma position. In this case, the axial position control loop provides only stabilization of the axial dynamics, not control. This means that the plasma is in a metastable state and can drift slowly along its axis. Position control is then provided using an additional feedback loop that controls the plasma gap between the plasma section and the vessel, thus simultaneously performing plasma shape and position control.

[0152] Another plasma confinement device in which a similar control system is used is the tokamak. To maintain plasma confinement, the plasma current in a tokamak must be kept between lower and upper limits, which are approximately proportional to the plasma density and the toroidal field, respectively. To operate at high plasma densities, the plasma current must be increased. At the same time, the poloidal field must be kept as low as possible, thus ensuring a q safety factor greater than q = 2. This is achieved by elongating the plasma along the mechanical axis, allowing for large plasma currents (and thus high plasma densities) without increasing the boundary magnetic field above its safety limit. These elongated plasmas are unstable along the mechanical axis (known as the vertical direction in tokamak terminology) and also require a plasma stabilization mechanism. Vertical plasma position control in a tokamak is also restored using a set of radial field coils and is therefore very similar to the RFC position control problem. However, the reasons for requiring stabilization in tokamaks and FRCs are different. In tokamaks, plasma vertical instability is a cost imposed for operating at high plasma currents, requiring plasma stretching to operate with high toroidal fields. In FRCs, plasma instability is a cost imposed for obtaining transverse stability. Tokamaks have a toroidal field that stabilizes the configuration, and therefore they do not require transverse stabilization.

[0153] (Electron beam for plasma heating) Turning to Figures 31-25, an exemplary embodiment of a high-power electron beam for plasma heating in a magnetic plasma confinement system is presented. In the exemplary embodiment, the electron beam provides a maximum electron current of approximately 100-120 A at approximately 30 kV acceleration voltage with a pulse duration of approximately 6-10 ms. Electrons are extracted and accelerated from the plasma emitter by nested multi-aperture accelerating grids. The beam is transported to an injection port in a grounded drift tube. The electron plasma emitter is immersed in an external axial magnetic field, providing conditions for axial injection into a plasma confinement system with a high magnetic field. An exemplary embodiment of an electron beam source with a plasma emitter that facilitates the generation of a long-pulse, high-power electron beam for heating an FRC plasma is presented herein.

[0154] As shown in FIG. 31 , an exemplary embodiment of an electron beam 750 includes an arc plasma source 754, an electron optical system 770 consisting of a system of nested accelerating grids, and a beamline including a magnetic system 760 for providing effective electron beam shaping, transport, and ultimately injection into a plasma confinement device of interest. As depicted in FIG. 31 , the magnetic system 760 includes a plasma generator coil 762, a plasma emitter coil 764, and, as further depicted in FIG. 36 , a beam transport coil 766. As depicted in FIG. 31 , the arc plasma source 754, e.g., an arc plasma generator, is positioned to produce plasma within a plasma expansion volume 756 of a plasma chamber 758. The electron optical system 770 with its nested accelerating grids for beam extraction is positioned adjacent to the plasma chamber 758 and, together with the plasma chamber 758 and the plasma source 754, within an electrostatic shield 752.

[0155] In an exemplary embodiment, the process of electron beam formation includes the following steps: plasma generation, plasma expansion, electron extraction, and acceleration. An initial hydrogen plasma is generated inside an expansion volume 756 of a plasma chamber 758 by an arc plasma generator 754. The plasma generator 754 creates a hydrodynamic flow of plasma, and the plasma covers the surface of a first grid electrode or plasma grid electrode 772 (see FIG. 33) of an electron optical system 770. While plasma generation and plasma expansion are relatively easy to achieve using modern technology, simulation of electron extraction from the plasma and its acceleration can be achieved using a computer simulation such as that shown in FIG. 32.

[0156] The electron current is extracted and accelerated in an electron optical system 770 designed to form an electron beam with the lowest possible emittance, i.e., extract an elementary beam with minimum RMS angular divergence from a single cell aperture. Each elementary acceleration cell of the grid electrode contributes a small current to the overall beam.

[0157] As shown in FIG. 33 , the electron-optical system 770 includes a plasma grid electrode 772, a suppression grid electrode 774, and a grounded grid electrode 776. Each of the grid electrodes 772, 774, and 776 has an array of individual apertures or cells 782, 792, and 794, respectively. The plasma grid 772 is in direct contact with the plasma in the extended volume 756 of the plasma chamber 758. It carries a high potential, which is the system's accelerating voltage, and forms a uniquely curved plasma emitter meniscus, providing initial focusing of the beamlets within the extraction region. Each plasma emitter aperture 782 is formed from a first counterbore 783 extending from the plasma side 778 of the plasma grid 772 and a second counterbore 785 extending from the beam side 779 of the plasma grid 772, leaving an annular protrusion 787 with an inner chamfer angle P at 60 degrees, electrostatically aligned with the beam axis B for beam focusing. The suppression grid 774 serves the purpose of suppressing backflow of ions from the secondary plasma generated from the ambient gas immediately after the last (grounded) grid 776. Each aperture 792 in the suppression grid 774 contains a 0-30 degree countersink that reduces the defocusing power of the electrostatic lens and facilitates beam formation.

[0158] A grounded grid 776 is required to provide a potential reference point for the beam and serves as the anode of the acceleration cell.

[0159] The electron beam is transported in an external axial magnetic field formed by the coils (see, e.g., 762, 764, 766) of magnetic system 760. Magnetic system 760 should include at least two coils, and can optionally include more coils.

[0160] If the beam needs to be injected into a region with its own magnetic field, it is necessary to generate an axial magnetic field surrounding the beam emitter. Due to generalized momentum conservation, particles of the beam can only enter regions with a non-zero axial magnetic field at the cathode (given that the particle captures an amount of magnetic flux inside a circle the size of the particle's radial coordinate measured relative to the beam symmetry axis).

[0161] If the plasma generator is located in a region with a non-zero magnetic field, the plasma flow may tend to follow the field lines of the external magnetic field, depending on the magnitude of the external magnetic field. It may also be necessary to install a strong coil over the anode location of the arc plasma generator 754 in order to cover the surface of the first (plasma) electrode of the electron optical system with a relatively uniform plasma flow.

[0162] In an exemplary embodiment, as depicted in Figures 34A and 34B, the beam includes masking a portion of the plasma emitter grid 772 to produce a hollow beam, which will mitigate beam space charge effects and generally improve beam dynamics. As shown in Figure 34A, a mask 784, e.g., in a hexagonal shape, is positioned centrally on the plasma side 778 of the plasma grid 772 over an aperture array 780 having a plurality of apertures 782. The mask 784 facilitates the formation of a hollow or annular shaped beam.

[0163] For a more uniform hollow or annular shaped beam, the plasma emitter 772 can include a second mask 786 that has the same shape as the first mask 784 and forms the same inner and outer mask profiles on the emitter grid 772.

[0164] As shown in Figures 35 and 36, when injecting a beam axially into the vessel 100 of a plasma containment system (e.g., a mirror device), there can be challenges transporting the beam through the volume of the divertor 300, 302 if there is no drift tube (see, e.g., grounded drift tube 755 as shown in Figure 36) and the magnetic field is lower than necessary. In this case, it is possible to rely on plasma-assisted transport. The plasma present in the divertor volume compensates for the space charge and beam current, but it results in a significant reduction of effects that would normally prevent the beam from propagating through open spaces such as the divertor volume.

[0165] In an alternative exemplary embodiment, the beam may be created using a LaB6 cathode instead of a plasma cathode.

[0166] Advantages of exemplary embodiments of electron beams over conventional electron beams include long pulses, high beam currents, and a non-degrading plasma emitter. The exemplary embodiments overcome the problem of cathode degradation by using a plasma cathode instead of a solid material cathode. The plasma emitter is represented by a system of grid electrodes, with each elementary cell of the grid forming a single elementary beam. The plasma emitter allows for nearly unlimited beam extraction cycles, in contrast to solid cathodes, which have a limited number of cycles and degrade after a certain number of pulses. Furthermore, the plasma cathode can withstand much longer pulse durations, up to about 1 second, with passive cooling, and even longer pulse durations with special measures taken for active cooling of the grid electrode.

[0167] Space charge effects in high perveance electron beams can be controlled by the design of a magnetic system that generates an external magnetic field along the beamline, allowing the embodiments provided herein to adjust the beam envelope and transport the beam to where it is needed, depending on conditions including the presence of any additional external magnetic fields, such as the magnetic fields of a plasma confinement device.

[0168] Exemplary embodiments provided herein are described in US Provisional Patent Application No. 63 / 111,446, which is incorporated herein by reference.

[0169] According to an embodiment of the present disclosure, a method for generating and sustaining a field-reversed configuration (FRC) plasma includes forming an FRC around a plasma in a confinement chamber, injecting an electron beam axially into the FRC plasma from an electron beam source, and injecting a plurality of neutral beams into the FRC plasma at an angle toward a midplane of the confinement chamber.

[0170] According to a further embodiment of the present disclosure, an electron beam source includes an arc plasma source, an electron optical system having a system of accelerating grids, and a beamline including a magnetic system configured to provide electron beam formation, transport, and injection into the FRC plasma.

[0171] According to a further embodiment of the present disclosure, an electron beam source includes a beam emitter configured to provide an annular beam.

[0172] According to a further embodiment of the present disclosure, a beam emitter includes a multi-aperture emitter grid and a mask covering the apertures in a central region of the emitter grid.

[0173] According to a further embodiment of the present disclosure, a beam emitter includes a multi-aperture emitter grid and first and second masks covering apertures in a central region of the emitter grid and in outer regions in a spaced apart relationship to the central region.

[0174] According to a further embodiment of the present disclosure, the second mask has an inner profile shape that matches the outer profile shape of the first mask.

[0175] According to a further embodiment of the present disclosure, the magnetic system includes a plasma generator coil, a plasma emitter coil, a lens coil, and a beam transport coil.

[0176] According to a further embodiment of the present disclosure, injecting the electron beam axially includes generating a plasma, expanding the plasma, extracting electrons from the plasma, and accelerating the extracted electrons.

[0177] According to a further embodiment of the present disclosure, the method further includes adjusting beam energies of the plurality of neutral beams between a first beam energy and a second beam energy, the second beam energy being different from the first beam energy.

[0178] According to a further embodiment of the present disclosure, the second beam energy is higher than the first beam energy.

[0179] According to a further embodiment of the present disclosure, the multiple Neutral Beams are switched between a first beam energy and a second beam energy for the duration of the implant shot.

[0180] According to a further embodiment of the present disclosure, the method further includes controlling beam energy of the plurality of neutral beams by a feedback signal received from an active feedback plasma control system.

[0181] According to a further embodiment of the present disclosure, the method further includes controlling beam energy of the plurality of neutral beams by a feedback signal received from an active feedback plasma control system.

[0182] According to a further embodiment of the present disclosure, controlling the beam energy of the multiple neutral beams includes adjusting the beam energy of the multiple neutral beams, adjusting a radial beam power deposition profile, and adjusting a pressure gradient value.

[0183] According to a further embodiment of the present disclosure, the method further includes generating a magnetic field within the confinement chamber using a quasi-DC coil extending around the confinement chamber, and a mirror magnetic field within the opposing end of the confinement chamber using a quasi-DC mirror coil extending around the opposing end of the confinement chamber.

[0184] According to a further embodiment of the present disclosure, forming the FRC includes forming the formed FRC in opposing first and second forming sections coupled to the containment chamber, and accelerating the formed FRC from the first and second forming sections toward a central through-plane of the containment chamber, wherein the two formed FRCs merge to form the FRC.

[0185] According to a further embodiment of the present disclosure, the method further includes directing a magnetic flux surface of the FRC into the first and second inner diverters.

[0186] According to a further embodiment of the present disclosure, a system for generating and sustaining a field-reversed configuration (FRC) plasma includes a confinement chamber, first and second diverters coupled to first and second formation sections, first and second axial plasma guns operably coupled to the first and second diverters, the first and second formation sections, and the confinement chamber, a plurality of neutral atom beam injectors coupled to the confinement chamber and oriented to inject neutral atom beams toward a midplane of the confinement chamber at an angle less than perpendicular to a longitudinal axis of the confinement chamber, a plurality of quasi-DC coils positioned around the confinement chamber, the first and second formation sections, and the first and second diverters, and a plurality of quasi-DC coils positioned between the confinement chamber and the first and second formation sections. the magnetic system including first and second sets of quasi-DC mirror coils positioned between the first and second formation sections and the first and second diverters; a gettering system coupled to the confinement chamber and the first and second diverters; one or more bias electrodes for electrically biasing the open flux surface of the generated FRC, the one or more bias electrodes being positioned within one or more of the confinement chamber, the first and second formation sections, and the first and second diverters; two or more saddle coils coupled to the confinement chamber; and one or more electron beams axially coupled to one or more of the first and second diverters.

[0187] According to a further embodiment of the present disclosure, a system for generating and sustaining a Field Reversed Configuration (FRC) plasma includes a confinement chamber, first and second diverters coupled to the first and second forming sections, and one or more of a plurality of plasma guns, one or more bias electrodes, and first and second mirror plugs, wherein the plurality of plasma guns include first and second axial plasma guns operably coupled to the first and second diverters, the first and second forming sections, and the confinement chamber, the one or more bias electrodes being positioned within one or more of the confinement chamber, the first and second forming sections, and the first and second diverters, and the first and second mirror plugs being positioned between the first and second forming sections and the first and second diverters. the bias electrodes and one or more of the first and second mirror plugs; a gettering system coupled to the confinement chamber and the first and second diverters; a plurality of neutral atom beam injectors coupled to the confinement chamber and oriented perpendicular to the axis of the confinement chamber; a magnetic system including a plurality of quasi-DC coils positioned around the confinement chamber, the first and second formation sections, and the first and second diverters; a set of first and second quasi-DC mirror coils positioned between the confinement chamber and the first and second formation sections; and one or more electron beams axially coupled to one or more of the first and second diverters, wherein the system is configured to generate and maintain an FRC without damping while the neutral beam is injected into the plasma.

[0188] According to a further embodiment of the present disclosure, an electron beam comprises an arc plasma source, an electron optical system comprising a system of acceleration grids, and a beamline including a magnetic system configured to provide electron beam formation, transport, and injection into a plasma confinement device of interest.

[0189] However, the exemplary embodiments provided herein are intended merely as illustrative examples and are not limiting in any way.

[0190] All features, elements, components, functions, and steps described with respect to any embodiment provided herein are intended to be freely combinable and substituted with those from any other embodiment. If a feature, element, component, function, or step is described with respect to only one embodiment, it should be understood that that feature, element, component, function, or step can be used with all other embodiments described herein unless expressly stated otherwise. Therefore, this paragraph always serves as a precursor and written support for the introduction of claims, which combine features, elements, components, functions, and steps from different embodiments or substitute features, elements, components, functions, and steps from one embodiment for another, even if the following description does not explicitly state that such combinations or substitutions are possible in specific cases. Explicitly listing all possible combinations and substitutions would be an undue burden, especially considering that, upon reading this specification, any and all such combination and substitution possibilities would be readily recognized by those skilled in the art.

[0191] In many instances, entities are described herein as being coupled to other entities. The terms "coupled" and "connected" (or any of their forms) are used interchangeably herein and should be understood to be inclusive, in both cases, of the direct coupling of two entities (without any non-negligible (e.g., parasitic) intervening entities) and the indirect coupling of two entities (with one or more non-negligible intervening entities). When entities are shown as being directly coupled together or described as being coupled together without description of any intervening entities, it should be understood that those entities can also be indirectly coupled together, unless the context clearly dictates otherwise.

[0192] While the embodiments are susceptible to various modifications and alternative forms, specific examples thereof have been shown in the drawings and described in detail herein. It should be understood, however, that these embodiments are not limited to the particular forms disclosed; on the contrary, these embodiments are intended to cover all modifications, equivalents, and alternatives falling within the spirit of the disclosure. Furthermore, negative limitations may be recited or added to the claims that define the scope of the claimed invention by any feature, function, step, or element of the embodiments, but also by any feature, function, step, or element not falling within its scope.< / n> < / n>

Claims

1. 1. A method for generating and sustaining a field-reversed configuration (FRC) plasma, the method comprising: forming an FRC around the plasma in a confinement chamber; injecting an electron beam axially into the FRC plasma from an electron beam source; maintaining the FRC plasma at a constant or near-constant value by injecting a beam of fast neutral atoms from a neutral beam injector into the FRC plasma at an angle toward the midplane of the confinement chamber; Including, The electron beam source comprises: an arc plasma source; an electron optical system comprising a system of accelerating grids; a beamline including a magnetic system configured to provide electron beam formation, transport, and injection into the FRC plasma; The method comprises:

2. The method of claim 1 , wherein the electron beam source further comprises a beam emitter configured to provide an annular beam.

3. 3. The method of claim 2, wherein the beam emitter includes a multi-aperture emitter grid and a mask covering an aperture in a central region of the emitter grid.

4. 3. The method of claim 2, wherein the beam emitter includes a multi-aperture emitter grid and first and second masks covering apertures in a central region of the emitter grid and in outer regions in a spaced-apart relationship to the central region.

5. The method of claim 4 , wherein the second mask has an inner profile shape that matches an outer profile shape of the first mask.

6. The magnetic system comprises: a plasma generator coil; A plasma emitter coil; Beam transport coil and The method of claim 1 , comprising:

7. Injecting the electron beam axially comprises: generating a plasma; expanding the plasma; and extracting electrons from the plasma; accelerating the extracted electrons; The method of claim 1 , comprising:

8. The step of injecting a beam of fast neutral atoms comprises: adjusting beam energies of the plurality of Neutral Beams between a first beam energy and a second beam energy, the second beam energy being different from the first beam energy; or adjusting beam energies of the plurality of Neutral Beams between a first beam energy and a second beam energy, the second beam energy being different from the first beam energy and higher than the first beam energy; or adjusting beam energies of the plurality of Neutral Beams between a first beam energy and a second beam energy, the second beam energy being different from the first beam energy, and the plurality of Neutral Beams switching between the first beam energy and the second beam energy for the duration of an implant shot; The method according to any one of claims 1 to 4, comprising one of:

9. generating a magnetic field within the chamber using a quasi-DC coil extending around the chamber; or generating a magnetic field within the chamber using a quasi-DC coil extending around the chamber and generating a mirror magnetic field within the opposing end of the chamber using a quasi-DC mirror coil extending around the opposing end of the chamber. The method of any one of claims 1 to 4, further comprising one of:

10. The step of forming the FRC plasma includes: forming first and second forming FRC plasmas in first and second forming sections coupled to opposite ends of the confinement chamber; accelerating the forming FRC plasma toward a mid-plane of the chamber to form the FRC; The method according to any one of claims 1 to 4, comprising:

11. The method of claim 7 , further comprising the step of directing a magnetic flux surface of the FRC into a diverter coupled to an end of the forming section.

12. A system for generating and sustaining a field-reversed configuration (FRC) plasma according to the method of any one of claims 1 to 11, said system comprising: a containment chamber; and first and second diverters coupled to the first and second forming sections; first and second axial plasma guns operably coupled to the first and second diverters, the first and second formation sections, and the containment chamber; a plurality of neutral atom beam injectors coupled to the confinement chamber, the plurality of neutral atom beam injectors oriented to inject neutral atom beams toward a midplane of the confinement chamber at an angle less than perpendicular to a longitudinal axis of the confinement chamber; a magnetic system comprising: a plurality of quasi-DC coils positioned around the confinement chamber, the first and second forming sections, and the first and second diverters; first and second sets of quasi-DC mirror coils positioned between the confinement chamber and the first and second forming sections; and first and second mirror plugs positioned between the first and second forming sections and the first and second diverters; a gettering system coupled to the confinement chamber and the first and second diverters; one or more bias electrodes for electrically biasing open flux surfaces of the generated FRC, the one or more bias electrodes being positioned within one or more of the containment chamber, the first and second formation sections, and the first and second diverters; two or more saddle coils coupled to the containment chamber; one or more electron beams axially coupled to one or more of the first and second divertors; A system comprising:

13. A system for generating and sustaining a field-reversed configuration (FRC) plasma according to the method of any one of claims 1 to 11, said system comprising: a containment chamber; and first and second diverters coupled to the first and second forming sections; one or more of a plurality of plasma guns, one or more bias electrodes, and first and second mirror plugs, the plurality of plasma guns including first and second axial plasma guns operably coupled to the first and second diverters, the first and second forming sections, and the confinement chamber, the one or more bias electrodes being positioned within one or more of the confinement chamber, the first and second forming sections, and the first and second diverters, and the first and second mirror plugs being positioned between the first and second forming sections and the first and second diverters; a gettering system coupled to the confinement chamber and the first and second diverters; a plurality of neutral atom beam injectors coupled to the confinement chamber and oriented perpendicular to the axis of the confinement chamber; a magnetic system including a plurality of quasi-DC coils positioned around the confinement chamber, the first and second formation sections, and the first and second divertors, and a set of first and second quasi-DC mirror coils positioned between the confinement chamber and the first and second formation sections; one or more electron beams axially coupled to one or more of the first and second divertors; Equipped with The system is configured to generate an FRC and maintain the FRC while the neutral beam is injected into the plasma.

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