Plasma control system

Abstract

A double null, DN, plasma control system for a tokamak comprising a first poloidal field coil 20 configured to be positioned proximate to a first divertor 111 of the tokamak and a magnetic flux monito

Description

Technical Field The present disclosure relates to tokamaks. More particularly, the present disclosure relates to double null, DN, plasma control systems for tokamaks. Background Tokamaks are toroidal devices, provided for confining fusion fuels in a plasma approximately symmetrically about an axis in a topological torus. The toroid-shaped plasma carries a current around the tokamak in the toroidal direction. In this context, the toroidal direction is that around the torus and the poloidal direction is that perpendicular to the toroidal direction on the torus surface and to the radial direction. The poloidal plane is a two-dimensional slice through the tokamak, which includes the central axis of symmetry of the tokamak. The poloidal field is the component of the magnetic field in the poloidal plane. The plasma cross-sectional shape and position are typically controlled by circular poloidal field coils (which carry toroidal current), whose axis coincides with the central axis of symmetry of the tokamak. Unlike a mathematical ring torus and solid torus, the toroid-shaped plasma cross section need not be circular. In some scenarios, the plasma boundary may be defined by an X-point-a location where the poloidal magnetic field is zero. In turn, the X-point defines a topological boundary: on one side of the X-point, the poloidal magnetic field lines close on themselves within the vacuum vessel of the tokamak and the plasma is confined (this may be referred to as the core plasma); on the other sides of the X-point, the magnetic field lines do not close on themselves before intersecting a wall, and therefore the plasma is not confined - rather, the plasma is diverted. The region of open field lines may be referred to as scrape-off-layer (SOL). The poloidal field line that lies on this boundary may be referred to as the separatrix. Typical configurations utilise one X-point, most commonly at the top or the bottom of the plasma, in a configuration called single null. An alternative is to use a double null (DN) configuration, in which there are two X-points typically located at the top and bottom of the plasma and two separatrices (a main separatrix and a secondary separatrix). One of the fundamental components of a tokamak fusion reactor is the divertor. The divertor typically sits adjacent to the X-point, so at the bottom or top of the reactor in a single null configuration (or at the top and bottom in a DN configuration). The role of the divertor is to provide a route for plasma exhaust (for example, heat and exhaust electrons, fuel ions, He ions, and other plasma impurity ions) produced by the fusion reaction to leave the reactor. The target surfaces or plates of the divertor are subjected to incredible heat and particle fluxes and therefore the design of the divertor and control of the plasma in this region is key in order to prolong the life of this component; this is particularly the case as the flux of heavy ions may be a determining factor in the effective life of the divertor. While a single null configuration tokamak is relatively simpler to engineer and simpler to control, a DN configuration and DN plasma topology is attractive in tokamak power plant or fusion reactor design due to the ability to reduce exhaust heat and exhaust particle loads by spreading the loads over two divertors. As a DN plasma has two X-points rather than one, located at the top and bottom of the plasma, a DN configuration incorporates two divertors. DN configurations, although typically more complex, may provide the benefit that inner divertor targets (positioned at smaller major radii of the tokamak and therefore providing a relatively smaller plasma-wetted area) are topologically separated from the plasma outboard side (through which the majority of the heat and particle flux is expected to flow); this benefit would be maximised if the DN configuration were perfectly ‘balanced’ - that is, if the two nulls (X-points) were to be positioned on exactly the same flux surface (that is, if the two nulls lie on a contour of constant poloidal magnetic flux). In practice, however, power sharing between the four divertor targets (two legs or plates per divertor) is largely determined by how close the plasma is to a perfectly balanced DN and by the length-scale over which exhaust fluxes decay outside the plasma boundary. The work of Brunner et al (“The dependence of divertor power sharing on magnetic flux balance in near double-null configurations on Alcator C-Mod”, 2018 Nucl. Fusion 58 076010), for instance, examines the effect of magnetic flux balance on the power sharing among four divertor legs in near-DN plasmas. A power plant (fusion reactor) plasma will typically be elongated (i.e., have a large ratio of height to width when viewed cross-sectionally in the poloidal plane) in order to improve confinement, stability, and the self-generation of current. In turn, however, this makes the plasma vertically unstable. To produce the elongation, poloidal field coils above and below the plasma must carry currents parallel to the plasma current, to attract the plasma and therefore stretch the plasma vertically. Such coils are used to produce an equilibrium plasma shape and may therefore be referred to as equilibrium poloidal field coils. However, small perturbations to the plasma’s vertical position are amplified as the plasma is attracted more strongly towards the poloidal field coils towards which the plasma moves. Without any other physical mechanism, vertical plasma instability accelerates at a rate equal to the destabilising force (which is very large for the large currents involved) divided by the plasma mass (which is very small), and is therefore too fast to sense and perform feedback control (on the order of microseconds). However, eddy currents induced in ‘passive’ conducting structures that may be provided around the moving plasma may act (by Lenz’s law) to slow the plasma down - but not to completely stabilise the plasma. Such passive stabilisation techniques bring the timescale of the unstable vertical plasma movements up to a value in which it is feasible for one to sense and apply a feedback control mechanism for stabilisation. It is advantageous for tokamaks to additionally include active feedback control systems to provide plasma stability. Generally, such active feedback control systems include poloidal field coils, which may carry equal and opposite currents at roughly vertically symmetric locations above and below the midplane of the plasma and may therefore be referred to as vertical control coils. This arrangement produces a horizontal field that exerts a vertical force on the plasma. Known vertical control coils are typically resistive rather than superconducting due to AC losses in superconducting coils, and are powered by fast, high voltage amplifiers. Example vertical control coils include fast plasma position control coils. Current passive and active stabilisation systems and techniques are unavoidably imperfect given that plasma position tends to fluctuate around stable configurations. For example, with a DN configuration, the plasma may intermittently adopt either an upper or a lower single null. Adoption of a single null intermittently allows heat and particles to travel from the plasma outboard to inner divertor targets along magnetic field lines. It is not currently known whether vertical plasma stabilisation using conventional vertical control coils and passive conducting structures is capable of providing adequate precision so as to keep inner divertor targets sufficiently insulated from outboard plasma; this depends upon unknown heat and particle flux decay lengths and any vertical control system performance, and accordingly may vary between implementations. The above uncertainty represents a significant risk associated with the architecture-defining decision - whether to implement DN configuration - for a power-producing tokamak. Approaches to control of plasma shape and position on existing tokamaks includes use of conventional poloidal field coils (rather than vertical control coils), which may include real-time estimation and feedback control of the X-point locations. Such approaches, however, are not able to resolve the problem of balancing DN heat fluxes, since vertical plasma fluctuations occur faster than a controller using conventional poloidal field coils may react. It is desirable to provide techniques capable of maintaining plasma balance in DN configurations for prolonged periods of time. Summary of the Disclosure The disclosure is defined in the independent claims. Further features are set out in the dependent claims. According to an aspect of the present disclosure, there is provided a double null, DN, plasma control system for a tokamak (for example, a tokamak utilised as a fusion reactor). The skilled reader will appreciate that the techniques and arrangements herein are equally suited for other toroidal machines for which vertical position and flux control on the same time scale is advantageous, such as other magnetic confinement fusion configurations, including stellarators, toroidal Z-pinch, and reversed field pinches in a toroidal configuration. The DN plasma control system comprises a (first) poloidal field coil configured to be positioned proximate to a first divertor of the tokamak. This is in contrast to conventional tokamak design, where vertical coils are not typically positioned with regard to divertor placement. Equivalently, when the tokamak is in operation, the poloidal field coil may be configured to be positioned proximate to a first X-point of a magnetic field generated by the tokamak. The first divertor (and indeed any divertors that are present) may be arranged in any configuration suitable for operation of the tokamak, including in a conventional configuration, a Super-X configuration (see the work of Valanju et al, “Super X divertors for solving heat and neutron flux problems of fusion devices”, 2010 Fusion Engineering and Design 85 46-52), or in a snowflake configuration (see the work of Ryutov, “Geometrical properties of a “snowflake” divertor”, 2007 Phys. Plasmas 14 064502)). The DN plasma control system comprises a magnetic flux monitoring system configured to obtain (for instance, through estimation (including through inference) or through direct monitoring) magnetic flux values of a first X-point and a second X-point of a magnetic field generated by the tokamak. Additionally or alternatively, the magnetic flux monitoring system may be configured to obtain (again via estimation or through direct monitoring) positions (e.g., geometric coordinates) of the X-points within the plasma. As discussed above, the X-point is the point in space at which the poloidal field has zero magnitude and which defines the boundary between core plasma and confined plasma. Advantageously, the poloidal field coil may be positioned such that the X-point is located between the poloidal field coil and core plasma. The DN plasma control system comprises a (sub-) control system configured to receive the obtained magnetic flux values of the first X-point and the second X-point (and / or the obtained positions thereof). The control system is also configured to control a difference in magnetic flux between the first X-point and the second X-point using the poloidal field coil (i.e., the poloidal field coil positioned proximate to the first divertor of the tokamak). Through implementation of poloidal field coils - similar in character to conventional vertical control coils - near to an X-point (or X-points) of a DN tokamak, the techniques herein implement feedback control using the difference in magnetic flux between the two X-points, where the feedback is actuated using at least one poloidal field coil located in or around the tokamak divertor (or divertors or elements thereof). The control may be performed simultaneously with conventional control of any vertical instability (e.g., using conventional vertical coils), acting on the same timescale or faster, and - accordingly - the two methods for plasma shape and position control may share the same means used for control, such as a same multi-input multi-output (MIMO) controller. For example, techniques herein may sense the magnetic fluxes at the X-points and feed these values into a MIMO controller, which may be designed to both vertically stabilise the plasma and to directly control the flux difference between the X-points using a combination of conventional vertical control coils and the new coils near the X-points. The techniques herein result in a reduction in the amplitude of fast fluctuations to the separation of the field lines on which the X-points lie (or, equivalently, the amplitude of fast fluctuations of a quantity referred to as dr-sep - see below for a full explanation). In turn, the techniques herein allow for smaller fluctuations in the distribution of heat and particle loads to upper and lower divertors of a tokamak. By improving distribution between divertors, the techniques herein allow for reduction in heat and particle loads to the inner divertor targets. Additionally, the techniques herein mitigate the risk of large fluctuations to the separation of the field lines on which the X-points lie causing the plasma to exit the so-called H-mode (again, see below for a full explanation) and undergoing catastrophic disruption. For the avoidance of doubt, “slow” plasma shape control using poloidal field coils may still be employed (either by means of a separate feedback loop, or a unified controller). In this way, the average value of any vertical control coil current may be maintained around zero. As the vertical control coils are typically resistive, any DC component to their supplied current means energy is wasted as heat. By maintaining the current around zero, there is no (or reduced) need to provide coil cooling. The techniques herein allow for control of the difference in flux between two X-points on the same timescale as control of the vertical plasma position; poloidal coils positioned in the divertor region actuate plasma control on the basis of the difference in flux. Any or all poloidal field coils may be vertical control coils. For example, existing vertical control coils may be updated with components suitable to provide the desired functionality of the poloidal field coils (namely, control of the difference in magnetic flux between X-points). The repurposed vertical control coil may be a fast control coil (or, equivalently, a fast-response coil), which typically (but not always) possesses resistive qualities and is positioned inside the vessel. For example, existing vertical control coils may be modified (and repositioned as necessary) for use for any or all poloidal field coils by connecting a fast response power supply (and other necessary connections thereof) to the control system. The DN plasma control system may comprise multiple poloidal field coils. For instance, the DN plasma control system may comprise multiple poloidal field coils positioned proximate to the first divertor, and / or may comprise multiple poloidal field coils positioned proximate to a second divertor of the tokamak. In providing distinct poloidal field coils at distinct divertors, the ability to vertically stabilise plasma (and X-points thereof) is improved. The first poloidal field coil may be positioned substantially vertically above the upper X-point of a DN plasma (or where the X-point would be if the tokamak were active if currently inactive) on an axis or line parallel to the central rotational axis of the tokamak and substantially passing through the upper X-point. Similarly, any second poloidal field coil may be positioned substantially vertically below the lower X-point of a DN plasma. That is, the first poloidal field coil and second poloidal field coil may be positioned on a line that is substantially parallel to a central axis of the tokamak (and substantially passing through the X-points - or where those X-points would be if the tokamak were active). In this arrangement, the poloidal field coils are arranged at substantially 12 O’clock and 6 O’clock and efficiently provide X-point vertical stabilisation; by contrast, conventional vertical control coils are typically positioned around substantially 2 O’clock and 4 O’clock. Both the first poloidal field coil and the second poloidal field coil may be configured to be used by the control system for controlling the difference in magnetic flux between the first X-point and the second X-point. As above, any or all poloidal field coils may be fast response coils. The control system may additionally use one or more (further) vertical control coils to control the difference in magnetic flux between the first X-point and the second X-point (that is, in addition to poloidal field coils positioned proximate to divertors). Such vertical control coils may be positioned in conventional arrangements within the tokamak (within or on the exterior of the vessel). Any poloidal field coil may be integrated into a divertor coil of the tokamak. For instance, any poloidal field coil may be integrated into existing divertor coil winding. In this manner, the functionality of the poloidal field coil becomes inherent in the divertor itself, allowing for very rapid control of vertical stabilisation and minimisation of the space occupied by the DN plasma control system. The magnetic flux monitoring system may comprise one or more magnetic sensors, where each magnetic sensor may be located proximate to an X-point within the tokamak (or proximate to where the X-point would be if the tokamak were active) and configured to directly sense magnetic flux values. Additionally or alternatively, magnetic flux values may be determined using real-time reconstruction of the magnetic field shape within the tokamak (for instance, using EFIT or LEMUR modelling techniques); such techniques may involve interpolation or extrapolation of field or flux values in or around the X-point(s), and are particularly suited for tokamaks when active as direct measurements within plasmas are difficult to obtain. Additionally or alternatively, the magnetic flux monitoring system may model the magnetic flux values of the first X-point and second X-point based on measurements of plasma properties, such as heat flux or data acquired using optical techniques. The control system may implement a first linear controller for controlling plasma vertical position (e.g., using any vertical control coils) and a second linear controller for controlling X-point flux difference (e.g., using any poloidal field coils). Equivalently, the first linear controller may be configured for controlling X-point vertical position of the plasma. Additionally or alternatively, the control system may implement a multi-input multi-output, MIMO, algorithm (which may be linear or may be non-linear) for controlling X-point vertical position and X-point flux difference. The control system may be configured to control the first X-point and the second X-point to be located on substantially a same magnetic flux surface. In some instances, however, it is desirable to seek a very slight offset between flux values at distinct X-points due to asymmetries in how plasma exhaust heat flux flows. According to a further aspect of the present disclosure, there is provided a tokamak comprising a DN plasma control system as described above. According to a further aspect of the present disclosure, there is provided a method of DN plasma control for a tokamak, wherein a first poloidal field coil is positioned proximate to a first divertor of the tokamak. The method comprises a step of obtaining, using a magnetic flux monitoring system, magnetic flux values of a first X-point and a second X-point of a magnetic field generated by the tokamak. The method comprises a step of receiving, by a control system, the obtained magnetic flux values of the first X-point and the second X-point. The method comprises a step of controlling, by the control system, a difference in magnetic flux between the first X-point and the second X-point using the first poloidal field coil. According to a further aspect of the present disclosure, there is provided a computer program or computer program product comprising instructions, which, when executed a DN plasma control system (or components thereof), causes the DN plasma control system to execute a method of DN plasma control for a tokamak as described above. According to a further aspect of the present disclosure, there is provided a (non-transitory) computer readable medium having stored thereon a computer program comprising instructions, which, when executed a DN plasma control system (or components thereof), causes the DN plasma control system to execute a method of DN plasma control for a tokamak as described above. The disclosure may be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations thereof. The disclosure may be implemented as a computer program or a computer program product, i.e., a computer program tangibly embodied in a non-transitory information carrier, e.g., in a machine-readable storage device or in a propagated signal, for execution by, or to control the operation of, one or more hardware modules. A computer program may be in the form of a stand-alone program, a computer program portion, or more than one computer program, and may be written in any form of programming language, including compiled or interpreted languages, and it may be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a data processing environment. A computer program may be deployed to be executed on one module or on multiple modules at one site or distributed across multiple sites and interconnected by a communication network. Method steps of the disclosure may be performed by one or more programmable processors executing a computer program to perform functions of the disclosure by operating on input data and generating output. Apparatus of the disclosure may be implemented as programmed hardware or as special purpose logic circuitry, including e.g., an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit). Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for executing instructions coupled to one or more memory devices for storing instructions and data. The disclosure is described in terms of particular embodiments. Other embodiments are within the scope of the following claims. For example, the steps of the disclosure may be performed in a different order and still achieve desirable results. Elements of the disclosure have been described using such terms as “processor” and “input device” The skilled person will appreciate that such functional terms and their equivalents may refer to parts of the system that are spatially separate but combine to serve the function defined. Equally, the same physical parts of the system may provide two or more of the functions defined. For example, separately defined means may be implemented using the same memory and / or processor as appropriate. Brief Description of the Drawings Reference is made, by way of example only, to the accompanying drawings in which: FIGURE 1 is a poloidal cross-section schematic of a tokamak in DN configuration with conventional means of vertical plasma stabilisation; FIGURE 2 is a poloidal cross-section schematic of a tokamak in DN configuration with a DN plasma control system according to embodiments; FIGURE 3 is a block diagram of a DN plasma control scheme; FIGURE 4 is a comparative time evolution of plasma simulations, with and without active feedback provided by poloidal field coils according to embodiments; FIGURE 5 is a general method of DN plasma control for a tokamak according to embodiments; and FIGURE 6 is a block diagram of computational means for implementation of methods according to embodiments. Detailed Description FIGURE 1 is an example poloidal cross-section schematic excerpt for a tokamak in DN configuration (note that the tokamak is axisymmetic around a vertical axis, not shown). Vertical control coils including vertical control coil 15 and vertical control coil 16 produce magnetic fields that confine, shape, and control the plasma, forming upper X-point 14 and lower X-point 13 at which the poloidal magnetic field is zero. As above, in a single null configuration, the separatrix is the boundary between closed and open magnetic field lines of the plasma, separating the toroidally confined region from the region where field lines connect to material surfaces, and which exists on both the high-field side (HFS) and low-field side (LFS) of the tokamak. In the case of the DN configuration, two separatrices may be distinguished: the main (or primary) separatrix and the secondary separatrix. Only the main separatrix truly separates the regions of closed and open field lines; for the secondary separatrix, one moves from open field lines to open field lines. A Scrape-Off Layer (SOL) is a plasma region characterised by open field lines (commencing or ending at some material surface). In the DN configuration, the SOL may be divided into two topologically distinct regions: an inner SOL, which is the plasma immediately outside of the main separatrix; and an outer SOL, which is the plasma outside the secondary separatrix. Heat and particles are transported from the core plasma through the main separatrix into the inner SOL. The SOL is likely to be very narrow with respect to the machine dimension (on the order of millimetres) in reactor-size tokamaks because energy is transported much faster parallel to magnetic field lines than it is across magnetic field lines. The heat and particles in the SOL, when transported past the X-point(s) (as indicated with arrows), are managed by the divertor. The example tokamak includes a lower divertor with inner lower divertor plate 111 and outer lower divertor plate 112, and includes an upper divertor with inner upper divertor plate 121 and outer upper divertor plate 122. Parallel heat and particle flux for the inner SOL are directed towards inner and outer divertor plates, whereas outer SOL heat and particle flux are directed to outer divertor plates only. When the separatrices coincide, the parallel heat and particle flux is separated between both inner divertor plates 111, 121 and both outer divertor plates 112, 122. Each divertor may, in effect, be considered as a collection of subsystems, including a subsystem for establishing (and maintaining) separatrix position and magnetic field flux in the region past the X-points: a poloidal field coil (or plurality thereof) may be used to control separatrix and magnetic field. The divertor is also responsible for gas introduction (e.g., deuterium, radiating impurities), and for pumping. The divertor plates 111, 112, 121, 122 (also referred to as divertor targets) are the solid surfaces that are positioned so as to intersect the separatrices / SOL: the points where this happens are called the Strike Points. The divertors may also be equipped with diagnostic capabilities. As the SOL is narrow, the divertor heat loads tend to be concentrated on a very small surface area, and therefore the power density is very high. This is especially problematic at the inner divertor plates 111, 121, which are those positioned at a smaller radius and therefore are of a smaller surface area. The amount of heat the divertor is able to handle is a design-driving parameter for tokamak power-plants and important in determining the overall size (and therefore cost). The X-point closest to the plasma core (the primary X-point) defines the main separatrix, which separates hot, confined core plasma from cooler diverted plasma. In this example (at least at the instance in time depicted), lower X-point 13 is the primary X-point. The other X-point (upper X-point 14) defines a secondary separatrix. Substantially all heat and particles between the primary and secondary separatrices are conducted to the primary divertor (the one corresponding to the primary X-point); in this instance, the lower divertor is the primary divertor. Substantially only heat and particles transported past the secondary separatrix can reach the secondary divertor (the upper divertor in this example). The distance between primary and secondary separatrices at the outboard midplane is referred to as the quantity dr-sep. It is highly advantageous to keep dr-sep as small as feasible (that is, maintain the primary and secondary separatrices close to each other during tokamak operation, or - equivalently - maintain the primary and secondary X-points on the same field line). When dr-sep = 0, the field arrangement may be referred to as a connected DN. In a connected DN configuration, the primary divertor is the divertor receiving the majority of the heat and particle flux and may be considered as the two outer divertor plates 112, 122, whereas the secondary divertor may be considered as the two inner divertor plates 111, 121. A disconnected configuration will have either upper divertor or lower divertor as the primary divertor. With a connected DN, there is substantially equal net heat and particle loads to the upper and lower divertors. A connected DN provides optimal insulation of the inner divertors from the outboard (i.e., further from the symmetry axis) SOL. The majority of the heat and particles are expected to be exhausted through the outboard side of the core plasma. By having a connected DN, the outboard SOL is topologically distinct from the inboard - there are no field lines that may carry heat and particles directly from the outboard SOL to the inboard targets. In addition, a connected DN enables access to improved core plasma confinement by lowering the threshold for power crossing the separatrix to access the high-confinement mode (or H-mode - the mode at which energy confinement time approximately doubles in magnitude). It is therefore advantageous to obtain a dr-sep value smaller than the width of the SOL to mitigate heat loads. It is also advantageous to obtain a small dr-sep value to ensure H-mode initiation. The threshold in dr-sep for H-mode access may depend upon quantities such as the ion gyroradius, ion banana orbit width, and the SOL width. These quantities depend upon device parameters such as size and magnetic field strength, but the expected threshold in dr-sep for both heat load mitigation and H-mode access is likely to be on the order of millimetres for a tokamak reactor. Of course, it is also advantageous to maintain the small dr-sep value, such that undesirable heat loads are continually mitigated and the H-mode is continually accessed. The advantages of a DN configuration with respect to heat load mitigation and H-mode access may only be achieved if the plasma may be controlled such that the plasma stays in a connected, balanced DN configuration. The extent to which a DN configuration is connected is, according to current wisdom, directly related to the vertical position of the plasma. If the plasma moves upwards, the upper X-point becomes the primary X-point and the heat load and the particle load to the upper divertor increases (and vice versa). The vertical instability of the plasma means that, even with a vertical stabilisation feedback loop turned on, the plasma vertical position may fluctuate due to the presence of noise and disturbances in the system. Maintaining a connected DN is therefore reliant on achieving a high-performance vertical control system, as the only way to minimise fluctuations is to minimise vertical position fluctuations. FIGURE 2 is an example poloidal cross-section schematic excerpt for a tokamak in DN configuration, implementing poloidal field coils in accordance with an embodiment. The DN configuration largely corresponds to that depicted in FIGURE 1. The depicted tokamak arrangement additionally includes a DN plasma control system comprising a first poloidal field coil 20. The first poloidal field coil 20 is positioned proximate to the lower divertor (comprising plates 111, 112). The first poloidal field coil 20 therefore may be positioned proximate to the equilibrium poloidal field coils used to shape the plasma and, in turn, produce the X-point. The first poloidal field coil 20 is used to control (or at least contribute to the control of) the magnetic fluxes provided at lower X-point 13 and upper X-point 14. This example arrangement further includes a second poloidal field coil 21, positioned proximate to the upper divertor and used to control magnetic fluxes at lower and upper X-points 13, 14. First poloidal field coil 20 and second poloidal field coil 21 are arranged substantially on the same vertical axis, which is parallel to central axis of the tokamak (not shown) and which passes through the vicinity of both lower and upper X-points 13, 14. The example DN plasma control system includes lower flux loop 22 and upper flux loop 23, which together correspond to (at least part of) a magnetic flux monitoring system. Both flux loops are loops of wire through which the plasma’s magnetic field passes. As the field varies inside the loop, the loop generates a voltage by Faraday's law of induction, driving a current. The current is measured and induced voltage calculated, for instance using an integrator circuit (not shown). From these values, magnetic field and magnetic flux may be determined using known techniques. Of course, alternative magnetic sensors may be used in the place of upper and lower flux loops 22, 23, such as a Mirnov coils. The example DN plasma control system includes a control system (not shown), which obtains the magnetic flux values for each X-point 13, 14. The control system performs signal control so as to increase or decrease the current supplied to one or both of first and second poloidal field coils 20, 21 in a manner that is expected to shape the plasma and reduce the dr-sep value and connect the X-points 13, 14. FIGURE 3 is a simplified block diagram of a control scheme for implementation by a control system according to an embodiment. Dashed lines indicate a known scheme of vertical stability and control, for example using vertical coil 15 and vertical coil 16. Reference signals are input into a controller component, which instructs the tokamak (or relevant components thereof) to adjust the current and / or voltage of vertical coils 15, 16. Reference signals may be, for example, a reference vertical position of the plasma, which may be zero or non-zero. Using known techniques (such as LEMUR; see the work of Anand et al, “Real-time plasma equilibrium reconstruction and shape control for the MAST Upgrade tokamak”, 2024 Nucl. Fusion 64 086051), the tokamak estimates the vertical position of the X-points 13, 14 . For example, flux loops 22, 23 may be configured to measure the plasma velocity, which may be integrated to obtain position measurements. The system may extrapolate the expected positions of the X-points at the time at which a next iteration of control may take place. The vertical position (and the velocity) may be fed as an input into the controller (in addition to the previously used reference signal) and the control scheme may repeat in an iterative manner. The control system of the present embodiment implements feedback control on the difference in magnetic flux between the two X-points 13, 14, where actuation of the plasma (and thus the X-points) is provided using poloidal field coils 20, 21 located in the divertor regions. The control system may be implemented using a proportional-integral-derivative controller (PID controller). In some examples, a first PID controller may be configured to continuously modulate the coarse vertical position of the plasma with control of vertical coils 15, 16 and a second PID controller may be configured to modulate the fine vertical position of the X-points 13, 14 with control of poloidal field coils 20, 21. Poloidal field coils 20, 21 provide the flux difference resulting from the vertical shift of the plasma current. More complex, non-linear multi-input multi-output (MIMO) control processes may of course be implemented. Mathworks’ Matlab Control System Toolbox, which provides algorithms and apps for systematically analysing, designing, and tuning control systems, is well-suited for use for modelling the control process (The MathWorks, Inc. (2024). Control System Toolbox (R2022b). Accessed: August 08, 2024. Available: https: / / www.mathworks.com). Mathworks’ Matlab Simulink environment, which is used for modelling and analyzing multidomain dynamical systems, is similarly well-suited for use for modelling the control process (The MathWorks, Inc. (2024). Accessed: August 08, 2024. Available: FIGURE 4 provides a set of simulation results, demonstrating the efficacy of a DN plasma control system according to an embodiment. The modelling is based on the FGE linear time independent (LTI) deformable plasma model; the reader is directed to the work of Carpanese, F. (2021) Development of free-boundary equilibrium and transport solvers for simulation and real-time interpretation of tokamak experiments (Thesis no. 7914) [PhD Thesis, EPFL] for further information. Simulink is used to model independent PID controllers for control of vertical position (extracted directly), actuated with conventional vertical coils, and for control of the difference in flux sensor measurements, actuated with poloidal field coils positioned proximate to tokamak divertors. The FGE output includes the linearised changes in dr-sep, vertical position, and coil voltages and currents. The simulations consider a tokamak with geometry corresponding to the Mega Ampere Spherical Tokamak Upgrade (MAST-U) and with an imposed 100mm displacement in plasma vertical position (imposed at t=50ms). FIGURE 4 shows time evolution of dr-sep both without and with a DN control system according to an embodiment. The conventional vertical controller is the same in both cases. A DN plasma control system according to an embodiment provides a plasma with a reduced dr-sep value; the primary and secondary X-points are on the substantially same field isoline. With the DN plasma control system, the connected DN is achieved rapidly after plasma displacement, thereby providing equal net heat and particle loads to the upper and lower divertors and providing optimal insulation of the inner divertors from the outboard SOL. FIGURE 5 illustrate a general method of DN plasma control for a tokamak, where the tokamak includes a first poloidal field coil positioned proximate to a first divertor of the tokamak as described above. The method may be implemented using computing means. At step 51, the computing means obtains, from a magnetic flux monitoring system, magnetic flux values of a first X-point and a second X-point of a magnetic field generated by the tokamak. At step 52, the computing means receives, from a control system, the obtained magnetic flux values of the first X-point and the second X-point. At step 53, the computing means controls, using the control system, a difference in magnetic flux between the first X-point and the second X-point using the first poloidal field coil. FIGURE 6 is a block diagram of an implementation of a DN plasma control system 600, suitable for executing methods DN plasma control for a tokamak according to embodiments. The example DN plasma control system 600 comprises a control system 610 within which a set of instructions, for causing the control system 610 to perform the method (or steps thereof) discussed herein, may be executed. The control system 610 may also be referred to as a computer or computing system. In particular, the methods described herein may be implemented by a processor or controller circuitry 611 of the control system 610. The control system 610 shall be taken to include any number or collection of machines, e.g., computing device(s), that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methods discussed herein. That is, hardware and / or software may be provided in a single computing device, or distributed across a plurality of computing devices in the computing system. In some implementations, one or more elements of the computing system may be connected (e.g., networked) to other machines, for example in a Local Area Network (LAN), an intranet, an extranet, or the Internet. One or more elements of the computing system may operate in the capacity of a server or a client machine in a clientserver network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. One or more elements of the computing system may be a personal computer (PC), a tablet computer, a set-top box (STB), a Personal Digital Assistant (PDA), a cellular telephone, a web appliance, a server, a network router, switch or bridge, or any machine capable of executing a set of instructions (sequential or otherwise) that specify actions to be taken by that machine. The control system 610 may include controller circuitry 611 and a memory 613 (e.g., read-only memory (ROM), flash memory, dynamic random access memory (DRAM) such as synchronous DRAM (SDRAM) or Rambus DRAM (RDRAM), etc.). The memory 613 may comprise a static memory (e.g., flash memory, static random access memory (SRAM), etc.), and / or a secondary memory (e.g., a data storage device), which communicate with each other via a bus (not shown). Memory 613 may be used to store or buffer magnetic flux data 670 until required for DN plasma control (e.g., until a PID controller component is ready to process the data). Controller circuitry 611 represents one or more general-purpose processors such as a microprocessor, central processing unit, accelerated processing units, or the like. More particularly, the controller circuitry 611 may comprise a complex instruction set computing (CISC) microprocessor, reduced instruction set computing (RISC) microprocessor, very long instruction word (VLIW) microprocessor, processor implementing other instruction sets, or processors implementing a combination of instruction sets. Controller circuitry 611 may also include one or more special-purpose processing devices such as an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), network processor, or the like. One or more processors of the controller circuitry may have a multicore design. Controller circuitry 611 is configured to execute the processing logic for performing the operations and steps discussed herein. The control system 610 may further include a network interface circuitry 615. The control system 610 may be communicatively coupled to an input device 620 and / or an output device 630, via input / output circuitry 616. In some implementations, the input device 620 and / or the output device 630 may be elements of the control system 610. The input device 620 may include an alphanumeric input device (e.g., a keyboard or touchscreen), a cursor control device (e.g., a mouse or touchscreen), an audio device such as a microphone, and / or a haptic input device. The output device 630 may include an audio device such as a speaker, a video display unit (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)), and / or a haptic output device. In some implementations, the input device 620 and the output device 630 may be provided as a single device, or as separate devices. In some implementations, the control system 610 may comprise dedicated signal processing circuitry 614. Signal processing circuitry 614 may be configured to process or pre-process magnetic flux data 670, such as magnetic flux values corresponding to any X-point, or current / voltage data 660 for control of poloidal field coil 640. In some implementations, signal processing circuitry 614 may be combined with controller circuitry 611. The DN plasma control system 600 further comprises a poloidal field coil 640 and a magnetic flux monitoring system 650. The poloidal field coil 640 and the flux monitoring system 650 may be provided as a single device. Poloidal field coil 640 may be configured to output current / voltage data 660, which may be accessed by control system 610. Magnetic flux monitoring system 650 may be configured to output magnetic flux data 670, which may be accessed by control system 610 . Magnetic flux data 670 may be obtained from an internal data source (e.g., from memory 613) or from an external data source, such as magnetic flux monitoring system 650 or an external database. Of course, while the above described implementation of a DN plasma control system 600 is incorporates digital electronics, the skilled reader will appreciate that a DN plasma control system may be readily implemented using analogue electronics. The various methods described above may be implemented by a computer program. The computer program may include computer code (e.g., instructions) arranged to instruct a computer to perform the functions of one or more of the various methods described above. For example, the steps of the methods described in relation to FIGURE 5 may be performed by the computer code. The steps of the methods described above may be performed in any suitable order. The computer program and / or the code for performing such methods may be provided to an apparatus, such as a computer, on one or more computer readable media or, more generally, a computer program product. The computer readable media may be transitory or non-transitory. The one or more computer readable media could be, for example, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, or a propagation medium for data transmission, for example for downloading the code over the Internet. Alternatively, the one or more computer readable media could take the form of one or more physical computer readable media such as semiconductor or solid state memory, magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), a rigid magnetic disc, and an optical disk, such as a CD-ROM, CD-R / W or DVD. The instructions may also reside, completely or at least partially, within the memory 613 and / or within the controller circuitry 611 during execution thereof by the control system 610, the memory 613 and the controller circuitry 611 also constituting computer-readable storage media. In an implementation, the modules, components and other features described herein may be implemented as discrete components or integrated in the functionality of hardware components such as ASICS, FPGAs, DSPs or similar devices. A “hardware component” is a tangible (e.g., non-transitory) physical component (e.g., a set of one or more processors) capable of performing certain operations and may be configured or arranged in a certain physical manner. A hardware component may include dedicated circuitry or logic that is permanently configured to perform certain operations. A hardware component may comprise a special-purpose processor, such as an FPGA or an ASIC. A hardware component may also include programmable logic or circuitry that is temporarily configured by software to perform certain operations. In addition, the modules and components may be implemented as firmware or functional circuitry within hardware devices. Further, the modules and components may be implemented in any combination of hardware devices and software components, or only in software (e.g., code stored or otherwise embodied in a machine-readable medium or in a transmission medium). Unless specifically stated otherwise, as apparent from the following discussion, it is appreciated that throughout the description, discussions utilising terms such as “receiving”, “determining”, “comparing ”, “enabling”, “maintaining”, “identifying”, “obtaining”, “accessing”, or the like, refer to the actions and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the computer system's registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices. While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the disclosure.

Claims

1. A double null, DN, plasma control system for a tokamak, the DN plasma control system comprising:a first poloidal field coil configured to be positioned proximate to a first divertor of the tokamak;a magnetic flux monitoring system configured to obtain magnetic flux values of a first X-point and a second X-point of a magnetic field generated by the tokamak; anda control system configured to receive the obtained magnetic flux values of the first X-point and the second X-point, and to control a difference in magnetic flux between the first X-point and the second X-point using the first poloidal field coil.

2. The DN plasma control system of claim 1, wherein the first poloidal field coil is a vertical control coil.

3. The DN plasma control system of claim 2, wherein the vertical control coil is modified for use as the first poloidal field coil by connecting a fast response power supply and connections to the control system.

4. The DN plasma control system of any of claims 1 to 3, further comprising a second poloidal field coil configured to be positioned proximate to a second divertor of the tokamak.

5. The DN plasma control system of claim 4, wherein the second poloidal field coil is a vertical control coil.

6. The DN plasma control system of claim 5, wherein the vertical control coil is modified for use as the second poloidal field coil by connecting a fast response power supply and connections to the control system.

7. The DN plasma control system of any of claims 4 to 6, wherein the first poloidal field coil and the second poloidal field coil are positioned on a line that is substantially parallel to a central axis of the tokamak.

8. The DN plasma control system of any of claims 4 to 7, wherein the first poloidal field coil and the second poloidal field coil are configured to be used by the control system for controlling the difference in magnetic flux between the first X-point and the second X-point.

9. The DN plasma control system of claim 8, wherein the control system uses one or more vertical control coils to control the difference in magnetic flux between the first X-point and the second X-point.

10. The DN plasma control system of any preceding claim, wherein at least one poloidal field coil is integrated into a divertor coil of the tokamak.

11. The DN plasma control system of any preceding claim, wherein the magnetic flux monitoring system comprises one or more magnetic sensors, each of said magnetic sensors being located proximate to an X-point within the tokamak.

12. The DN plasma control system of any preceding claim, wherein the magnetic flux monitoring system utilises real-time reconstruction of the magnetic field shape within the tokamak.

13. The DN plasma control system of any preceding claim, wherein the magnetic flux monitoring system models the magnetic flux values of the first X-point and second X-point based on measurements of plasma properties.

14. The DN plasma control system of any preceding claim, wherein the control system implements a first linear controller for controlling plasma vertical position and a second linear controller for controlling X-point flux difference.

15. The DN plasma control system of any of claims 1 to 13, wherein the control system implements a multi-input multi-output, MIMO, algorithm for controlling plasma vertical position and X-point flux difference.

16. The DN plasma control system of any preceding claim, wherein the control system is configured to control the first X-point and the second X-point to be located on substantially a same magnetic flux surface.

17. A tokamak comprising the DN plasma control system of any preceding claim.

18. A method of DN plasma control for a tokamak, wherein a first poloidal field coil is positioned proximate to a first divertor of the tokamak, the method comprising:obtaining, using a magnetic flux monitoring system, magnetic flux values of a first X-point and a second X-point of a magnetic field generated by the tokamak;receiving, by a control system, the obtained magnetic flux values of the first X-point and the second X-point; andcontrolling, by the control system, a difference in magnetic flux between the first X-point and the second X-point using the first poloidal field coil.

19. A computer program comprising instructions to cause the DN plasma control system of any of claims 1 to 17 to perform the method of claim 18.

20. A computer readable medium having stored thereon the computer program of claim 19.

Images