Systems and methods for forming and maintaining high-energy high-temperature FRC plasmas via spheromak merging and neutral beam injection

Abstract

A high performance field reversed configuration (FRC) system includes a central confinement chamber, two diverter chambers coupled to the chamber, and two diametrically opposed spheromak injectors coupled to the diverter chambers. A magnetic system includes a quasi-dc coil positioned axially along the FRC system components.

Description

Technical Field

[0001] The embodiments described herein generally relate to magnetic plasma confinement systems, and more particularly, to systems and methods for promoting the formation and maintenance of high-energy, high-temperature field-reverse configuration (FRC) plasmas with excellent stability and particle, energy, and flux confinement. Background Technology

[0002] Field-reverse configurations (FRCs) belong to a category of magnetically confined plasma topologies known as compact toroidal (CT) topologies. They primarily exhibit a poloidal magnetic field and possess a self-generated toroidal field of zero or small magnitude (see M. Tuszewski's Nucl. Fusion 28, 2033 (1988)). The appeal of this configuration lies in its simple geometry, facilitating the construction and maintenance of naturally unconstrained divertors for energy extraction and ash removal, and its very high β (the ratio of the average plasma pressure to the average magnetic field pressure within the FRC) (i.e., high power density). This high β property is advantageous for economical operation and for the use of advanced, neutron-free fuels such as D-He3 and p-B11.

[0003] The conventional approach to forming a FRC uses field-reverse angular pinch (Ɵ-pinch) technology to generate a hot, high-density plasma (AL Hoffman and JT Slough, Nucl. Fusion 33, 27 (1993)). A variation of this is the translation-capture method, in which the plasma generated in the angular pinch “source” is more or less immediately ejected from one end into the confinement chamber. The translated plasma puff is then captured between two strong mirrors at the end of the chamber (see, for example, H. Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191 (1995)). Once in the confinement chamber, various heating and current-driven methods can be applied, such as beam injection (neutral or neutral), rotating magnetic fields, RF, or ohmic heating. This separation of the source and confinement functions provides key engineering advantages for potential future fusion reactors. FRCs have proven to be extremely robust, adaptable to dynamic formation, translation, and violent capture events. Furthermore, they exhibit a tendency to present preferred plasma states (see, for example, HY Guo, AL Hoffman, KE Miller, and LCSteinhauer, Phys. Rev. Lett. 92, 245001 (2004)). Significant progress has been made in the development of other FRC formation methods over the past decade: incorporating spherical marks with anti-helical properties (see, for example, Y. Ono, M. Inomoto, Y. Ueda, T. Matsuyama, and T. Okazaki, Nucl. Fusion 39, 2001 (1999)) and driving currents with rotating magnetic fields (RMF) (see, for example, IR Jones, Phys. Plasmas 6, 1950 (1999)), which also provides additional stability.

[0004] Collision-merging techniques, proposed long ago (see, for example, DR Wells, Phys. Fluids 9, 1010 (1966)), have been significantly further developed: two separate angular clamps at opposite ends of a confinement chamber simultaneously generate two plasma blobs and accelerate them toward each other at high speed; they then collide and merge at the center of the confinement chamber to form a combined FRC. Conventional collision-merging methods have been shown to produce stable, long-lived, high-flux, high-temperature FRCs in the construction and successful operation of one of the largest FRC experiments to date (see, for example, M. Binderbauer et al., Phys. Rev. Lett. 105, 045003 (2010)). Recently, major progress has been made in the use of collision-merging techniques in beam-driven FRC experiments, which utilize high-power neutral beam (NB) injection (NBI) and effective edge bias to generate relatively high-temperature FRCs over extended periods (typical plasma parameters: T0). e ~250 eV, T i ~1 keV、 <n e > ~2-3×10 13 cm -3 B e ~1 kG, plasma lifetime ~30 ms). (See, for example, Gota, H. et al., Nucl. Fusion 57, 116021 (2017); Gota, H. et al., Nucl. Fusion 59, 112009 (2019); and Gota, H. et al., Bull. Am. Phys. Soc. 64, UP10.00123 (2019)). In this experiment, the target plasma of NBI was generated by colliding and merging two FRC plasmas using the field reverse angular pinch (FRTP) dynamic formation technique (Binderbauer, Phys. Rev. Lett. 105), where the trapped magnetic flux of the merged FRC was initially ~5 mWb based on a rigid rotor model and had an external magnetic field of ~1 kG in the confined section. By injecting a high-power NBI of >13 MW (increased to ~21 MW by adjusting the beam energy during the shot) into the target plasma, the injected fast particles are trapped and travel inside and outside the interface with large orbits to primarily heat electrons and for current-driven confinement, where fast ions are almost classically confined. This high-power NBI has not been achieved in any other CT experiment and is a very important demonstration of the effectiveness of the beam-driven FRC concept and its technical readiness. (Gota, Nucl. Fusion 59; Gota, Bull. Am. Phys. Soc. 64).

[0005] Improved systems, apparatus, and methods are desired for generating high-flux target FRC plasma and axial refueling. Summary of the Invention

[0006] This document provides example embodiments of systems, apparatus, and methods for generating high-flux targeted FRC plasma and axially refeeding FRC plasma. To generate optimal initial high-flux targeted FRC plasma, a mesoscale spherical mark injector (also known as a CT injector) is relatively coupled to the end of a centrally located plasma confinement chamber. The spherical mark injector injects spherical marks toward the midplane of the confinement chamber, where the spherical marks merge within the confinement chamber and form the FRC plasma. The anti-helical merging of two spherical marks tends to produce an FRC plasma with increased trapping magnetic flux. Multiple neutral beam injectors are also coupled to the confinement chamber to drive and hold the FRC plasma.

[0007] In an example embodiment, the neutral beam injector can be adjusted from an initial power level to an increased power level.

[0008] In a further example embodiment, the ball mark injector is capable of injecting multi-pulse ball marks into the FRC plasma along the geometric axis of the confinement chamber to achieve efficient refeeding and reflow.

[0009] Other systems, apparatuses, methods, features, and advantages of the subject matter described herein will be apparent to those skilled in the art upon viewing the following figures and detailed description. It is intended that all such additional systems, methods, features, and advantages are included within the scope of this description, the subject matter described herein, and protected by the appended claims. Features of the exemplary embodiments should in no way be construed as limiting the appended claims, where no explicit statement of those features is made in the claims. Attached Figure Description

[0010] The accompanying drawings, which are included as a part of this specification, illustrate the exemplary embodiments and, together with the general description given above and the detailed description of the exemplary embodiments given below, serve to explain and teach the principles of the invention.

[0011] Figure 1 The illustration shows particle confinement in this FRC system under the high-performance FRC regime (HPF) compared to the conventional FRC regime (CR), and compared to other conventional FRC experiments.

[0012] Figure 2 The diagram illustrates the components of this FRC system and the magnetic topology of the FRCs that can be generated in this FRC system.

[0013] Figure 3A The diagram illustrates the basic layout of this FRC system as viewed from above, which includes a preferred arrangement of a central confinement container, a formation section, a divertor, a neutral beam, electrodes, a plasma gun, a mirror plug, and a pellet injector.

[0014] Figure 3B The illustration shows the central constraint container of the neutral bundle, as viewed from above, and arranged at an angle orthogonal to the principal axis of symmetry in the central constraint container.

[0015] Figure 3C The illustration shows the central constraint container as viewed from above, and illustrates the neutral beam of particles injected into the central constraint container at an angle less than orthogonal to the principal axis of symmetry in the central constraint container.

[0016] Figure 3D and Figure 3E Top and perspective views of a basic layout of an alternative embodiment of the FRC system are shown, respectively. The basic layout includes a central confinement container, a forming section, internal and external divertors, a neutral beam arranged at an angle less than orthogonal to the principal axis of symmetry in the central confinement container, electrodes, a plasma gun, and a mirror plug, in a preferred arrangement.

[0017] Figure 4 The diagram illustrates the components of a pulsed power system used to form a segment.

[0018] Figure 5 The illustration shows an isometric view of a single pulsed power forming skid.

[0019] Figure 6 The illustration shows an isometric view of the forming tube assembly.

[0020] Figure 7 The illustration shows a partial cross-sectional isometric view of the neutral beam system and key components.

[0021] Figure 8 An isometric view of the neutral bundle arrangement in the constraint chamber is shown.

[0022] Figure 9 The illustration shows a partial cross-sectional isometric view of a preferred arrangement of Ti and Li intake systems.

[0023] Figure 10 The illustration shows a partial cross-sectional isometric view of a plasma gun installed in a divertor chamber. The associated magnetic mirror plug and divertor electrode assembly are also shown.

[0024] Figure 11 The illustration shows a preferred arrangement of the annular bias electrode at the axial end of the constraint chamber.

[0025] Figure 12The diagram illustrates the evolution of the repulsive flux radius in the FRC system, obtained from a series of external diamagnetic coils and a magnetic probe embedded within the central metal confinement chamber at the two field reversal angles towards the pinch-forming section. Time is measured from the moment the synchronous field in the forming source reverses, and distance z is given relative to the axial midplane of the machine.

[0026] Figure 13A , Figure 13B , Figure 13C and Figure 13D The figure illustrates representative non-HPF, non-sustained discharge data from this FRC system. The data shown as a function of time are (…). Figure 13A The repulsive flux radius at the mid-plane, ( Figure 13B The six chords of the line integral density from the mid-plane CO2 interferometer Figure 13C Abel inversion density radial distribution from CO2 interferometer data, and ( Figure 13D The total plasma temperature comes from pressure equilibrium.

[0027] Figure 14 The diagram illustrates the... Figure 13A , Figure 13B , Figure 13C and Figure 13D The axial distribution of the repulsive flux of the same discharge in this FRC system at a selected time is shown.

[0028] Figure 15 The illustration shows an isometric view of a saddle-shaped coil installed outside the constraint chamber.

[0029] Figure 16A , Figure 16B , Figure 16C and Figure 16D The figure illustrates the correlation between FRC lifetime and the pulse length of the injected neutral beam. As shown, longer beam pulses result in FRCs with longer lifetimes.

[0030] Figure 17A , Figure 17B , Figure 17C and Figure 17D The diagram illustrates the individual and combined effects of different components of the FRC system on FRC performance and HPF mechanism acquisition.

[0031] Figure 18A , Figure 18B , Figure 18C and Figure 18D The figure shows representative HPF and non-sustained discharge data from this FRC system. The data shown as a function of time are (…). Figure 18A The repulsive flux radius at the mid-plane, ( Figure 18B The six chords of the line integral density from the mid-plane CO2 interferometer, Figure 18C Abel inversion density radial distribution from CO2 interferometer data, and ( Figure 18D The total plasma temperature comes from pressure equilibrium.

[0032] Figure 19 The diagram illustrates the electron temperature (T). e The flux constraint of the function. It represents the graphical representation of the newly established superior scaling mechanism of HPF discharge.

[0033] Figure 20 The figure illustrates the FRC lifetime corresponding to the pulse lengths of neutral beams injected at non-angle and angle.

[0034] Figure 21A , Figure 21B , Figure 21C , Figure 21D and Figure 21E The illustration shows the lifetime of FRC plasma parameters, including the pulse length of an angled injected neutral beam and the plasma radius, plasma density, plasma temperature, and magnetic flux corresponding to the pulse length of the angled injected neutral beam.

[0035] Figure 22A and Figure 22B The diagram illustrates the basic layout of the compact ring (CT) injector.

[0036] Figure 23A and Figure 23B The illustration shows a central constraint container, to which a CT injector is mounted.

[0037] Figure 24A and Figure 24B The illustration shows the basic layout of an alternative embodiment of a CT injector with a drift tube coupled thereto.

[0038] Figure 25 The illustration shows a cross-sectional isometric view of the neutral beam system and key components for adjustable energy beam output.

[0039] Figure 26 This is a schematic diagram of a neutral beam system with adjustable energy beam output.

[0040] Figure 27 This is a schematic diagram of the axial position control mechanism of FRC plasma within a confinement container (CV).

[0041] Figure 28 This is a flowchart of a general sliding mode control scheme.

[0042] Figure 29 This is a composite diagram of an example of sliding mode axial position control simulation.

[0043] Figure 30 This is a composite diagram of an example of sliding mode axial position control simulation.

[0044] Figure 31A and Figure 31B This is a schematic diagram depicting an example embodiment of an FRC constraint system with opposing ball mark injectors.

[0045] Figure 32A , Figure 32B , Figure 32C and Figure 32D The diagram illustrates the steps in the formation process of FRC via the merging of anti-spiral spherical marks.

[0046] Figure 33 This is a schematic diagram depicting an example embodiment of a ball mark injector.

[0047] It should be noted that the drawings are not necessarily drawn to scale, and throughout the drawings, elements with similar structures or functions are often indicated by similar reference numerals for illustrative purposes. It should also be noted that the drawings are intended only to facilitate the description of the various embodiments described herein. The drawings do not necessarily depict every aspect of the teachings disclosed herein and do not limit the scope of the claims. Detailed Implementation

[0048] Before describing this subject matter in detail, it will be understood that this disclosure is not limited to the specific embodiments described, as these are of course subject to variation. It will also be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting, as the scope of this disclosure will be limited only by the appended claims.

[0049] Representative examples of the embodiments described herein will now be described in more detail with reference to the accompanying drawings. These examples utilize many of these additional features and teachings, both individually and in combination. This detailed description is intended only to teach those skilled in the art further details for practicing the preferred aspects of this teaching and is not intended to limit the scope of the invention. Therefore, in the broadest sense, the combination of features and steps disclosed in the following detailed description may not be necessary for practicing the invention, but rather is only taught to specifically describe representative examples of this teaching.

[0050] Furthermore, the various features of the representative examples and dependent claims may be combined in a manner not specifically and explicitly enumerated to provide additional useful embodiments of this teaching. Additionally, it is expressly stated that all features disclosed in the specification and / or claims are intended to be disclosed individually and independently of each other, for the purposes of the original disclosure and for the purpose of limiting the claimed subject matter independently of the composition of features in the embodiments and / or claims. It is also expressly stated that, for the purposes of the original disclosure and for the purpose of limiting the claimed subject matter, all indications of value ranges or entity groups disclose every possible intermediate value or intermediate entity.

[0051] The embodiments provided herein relate to systems and methods for promoting the formation and maintenance of FRCs with excellent stability and particle, energy, and flux confinement. Some of these embodiments relate to systems and methods for promoting the formation and maintenance of FRCs with increased system energy and improved maintenance using neutral beam injectors with tunable beam energy capabilities. Some of these embodiments also relate to systems and methods for promoting the stability of FRC plasmas in both radial and axial directions, and for controlling the axial position of the FRC plasma along the axis of symmetry of the FRC plasma confinement chamber, independent of the FRC plasma equilibrium.

[0052] Before moving on to systems and methods for generating and sustaining high-flux target FRC plasmas using a pair of mesoscale spherical mark injectors (or magnetized coaxial plasma guns (MCPGs)) and for axial refeeding of FRC plasmas, this paper provides a discussion of systems and methods for forming and sustaining high-performance FRCs with superior stability and excellent particle, energy, and flux confinement compared to conventional FRCs. Such high-performance FRCs provide pathways to a wide range of applications, including compact neutron sources (for medical isotope production, nuclear waste management, materials research, neutron radiography, and tomography), compact photon sources (for chemical production and processing), mass separation and enrichment systems, and reactor cores for light nuclear fusion to generate future energy.

[0053] Various auxiliary systems and operating modes have been explored to evaluate the existence of superior constraint mechanisms in FRC. These efforts have led to groundbreaking findings and the development of a high-performance FRC paradigm described in this paper. Based on this new paradigm, this system and method combine a number of novel ideas and means to significantly improve FRC constraints (such as...). Figure 1 (As illustrated in the diagram) and provides stability control without adverse side effects. This will be discussed in more detail below. Figure 1The following describes FRC system 10 (see: FRC System 10) operating according to the High Performance FRC mechanism (HPF) for forming and maintaining FRC, in contrast to operating according to the conventional mechanism CR for forming and maintaining FRC, and in contrast to particle confinement according to the conventional mechanisms for forming and maintaining FRC used in other experiments. Figure 2 And particle constraints in Figure 3). This disclosure will outline and detail the innovative components of the FRC system 10 and method, as well as their collective effects.

[0054] FRC System Vacuum system Figure 2 Figure 3 illustrates a schematic diagram of the FRC system 10. The FRC system 10 includes: a central confinement container 100 surrounded by two opposing diameter reverse field angle-pinch forming sections 200; and two divertor chambers 300 extending beyond the forming sections 200, these divertor chambers being used to control neutral density and impurity contamination. The FRC system 10 is configured to accommodate ultra-high vacuum and... -8 The typical base pressure of the Törg is used for operation. This vacuum pressure requires the use of double pumping mating flanges between mating parts, metal O-rings, high-purity inner walls, and meticulous initial surface finishing of all parts before assembly (such as physical and chemical cleaning, followed by 24 hours of vacuum baking at 250°C and hydrogen glow discharge cleaning).

[0055] The reverse field angular pinch forming section 200 is a standard field reverse angular pinch (FRTP), although it has an advanced pulsed power forming system discussed in detail below (see Figures 4 to 6 Each forming section 200 is made of standard opaque industrial-grade quartz tubing, characterized by a 2 mm ultrapure quartz liner. The confinement chamber 100 is made of stainless steel to allow for multiple radial and tangential ports; it also serves as a flux conserver on the timescales of the experiments described below and confines rapid magnetic transients. A vacuum is generated and maintained within the FRC system 10 using a suite of dry vortex low-vacuum pumps, turbomolecular pumps, and cryogenic pumps.

[0056] Magnetic system Figure 2 The magnetic system 400 is illustrated in Figure 3. Among other features, Figure 2 The diagram illustrates the FRC flux and density contours (as a function of radial and axial coordinates) related to the FRC 450 that can be generated by FRC system 10. These contours were obtained through 2-D resistive Hall-MHD numerical simulations using code developed to simulate the system and methods corresponding to FRC system 10, and agree well with measured experimental data. Figure 2 As seen in the diagram, the FRC 450 consists of a closed loop of force lines at the interior 453 of the FRC 450 (inside the interface 451) and a ring of annular edge layers 456 on the open force lines 452 just outside the interface 451. The edge layers 456 coalesce into jets 454 that extend beyond the length of the FRC, thus providing a natural divertor.

[0057] The main magnetic system 410 includes a series of quasi-DC coils 412, 414, and 416 located at specific axial positions along the components of the FRC system 10 (i.e., along the constraint chamber 100, forming section 200, and divertor 300). The quasi-DC coils 412, 414, and 416 are fed by a quasi-DC switching power supply and generate a fundamental magnetic bias field of approximately 0.1 T in the constraint chamber 100, forming section 200, and divertor 300. In addition to the quasi-DC coils 412, 414, and 416, the main magnetic system 410 also includes a quasi-DC mirror coil 420 (fed by a switching power supply) located between any end of the constraint chamber 100 and an adjacent forming section 200. The quasi-DC mirror coil 420 provides a magnetic mirror ratio of up to 5 and can be independently excited for balancing forming control. Additionally, mirror plugs 440 are positioned between each of the forming sections 200 and the divertor 300. The mirror plug 440 includes 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 a switching power supply), which generate an additional guiding field to focus the magnetic flux surface 455 toward a small-diameter channel 442 passing through the mirror plug coil 444. The mirror plug coil 444, wrapped around the small-diameter channel 442 and fed by an LC pulsed power circuit, generates a strong magnetic mirror field up to 4 T. The purpose of this entire coil arrangement is to tightly bundle and guide the magnetic flux surface 455 and the end-flowing plasma jet 454 into the remote chamber 310 of the divertor 300. Finally, a set of saddle-shaped coil "antennas" 460 (see...) Figure 15 Located outside the confinement chamber 100, two antennas are positioned on each side of the midplane and fed by a DC power supply. The saddle-shaped coil antennas 460 can be configured to provide a quasi-static magnetic dipole or quadrupole field of approximately 0.01 T for controlling rotational instability and / or electronic current control. Depending on the direction of the applied current, the saddle-shaped coil antennas 460 can flexibly provide a magnetic field that is symmetrical or antisymmetrical about the midplane of the machine.

[0058] Pulse power forming system The pulsed power forming system 210 operates based on a modified angular pinch principle. There are two systems, each supplying power to one of the forming sections 200. Figures 4 to 6The diagram illustrates the main building blocks and arrangement of the forming system 210. The forming system 210 comprises a modular pulsed power arrangement consisting of individual units (=skids) 220, each of which excites a subset of coils 232 surrounding a strip assembly 230 (=strip) wrapped around the forming quartz tube 240. Each skid 220 consists of a capacitor 221, an inductor 223, a fast high-current switch 225, and associated triggers 222 and dump circuitry 224. In total, each forming system 210 stores capacitive energy between 350 and 400 kJ, providing up to 35 GW of power to form and accelerate the FRC. Coordinated operation of these components is achieved via current-process-level triggers and control systems 222 and 224, which allow for synchronized timing between forming systems 210 on each forming section 200 and minimize switching bounce to tens of nanoseconds. The advantage of this modular design is its flexible operation: FRC can be formed in situ and then accelerated and injected (=static formation) or formed and accelerated simultaneously (=dynamic formation).

[0059] Neutral beam injector A neutral atom beam 600 was deployed on the FRC system 10 to provide heating and current drive, as well as the pressure to develop fast particles. Figure 3A , Figure 3B and Figure 8 As shown, the beamlines of the neutral atom beam injector systems 610 and 640 are positioned around the central confinement chamber 100 and inject fast particles tangentially to the FRC plasma with collision parameters (and perpendicular to the principal axis of symmetry in the central confinement chamber 100 or at an angle orthogonal to the principal axis of symmetry), such that the target capture region is well located at the interface 451 (see...). Figure 2 Within the system. Each injector system 610 and 640 is capable of injecting up to 1 MW of neutral beam power into FRC plasmas with particle energies between 20 and 40 keV. Systems 610 and 640 are based on a positive ion porous extraction source and utilize geometric focusing, inertial cooling of the ion extraction grid, and differential pumping. Aside from using different plasma sources, the main difference between systems 610 and 640 lies in their physical design to accommodate their respective mounting locations, thus enabling side and top injection capabilities. Typical components of these neutral beam injectors are located within... Figure 7 The side injector system 610 is illustrated in detail. For example... Figure 7As shown, each individual neutral beam system 610 includes an RF plasma source 612 located at the input end (this is replaced by an arc source in system 640), and a magnetic shield 614 covers this end. An ion source and an acceleration grid 616 are coupled to the plasma source 612, and a gate valve 620 is positioned between the ion source and the acceleration grid 616 and the neutralizer 622. A deflection magnet 624 and an ion dump 628 are located between the neutralizer 622 and the aiming device 630 at the outlet end. The cooling system includes two cryogenic refrigerators 634, two cryogenic plates 636, and an LN2 shield 638. This flexible design allows operation over a wide range of FRC parameters.

[0060] An alternative configuration for the neutral atom beam injector 600 is one that injects fast particles tangentially to the FRC plasma but at an angle A less than 90° relative to the principal axis of symmetry in the central confinement container 100. These types of orientations of the beam injector 615 are... Figure 3C As shown in the diagram. Additionally, the beam injectors 615 can be oriented such that beam injectors 615 on either side of the midplane of the central confinement container 100 inject their particles toward the midplane. Ultimately, the axial position of these beam systems 600 can be selected to be closer to the midplane. These alternative injection embodiments facilitate a more central feeding option, thereby providing better beam coupling and higher capture efficiency of the 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 over the axial elongation and other characteristics of the FRC 450. For example, injecting the beam at a shallow angle A relative to the container's principal axis of symmetry will produce an FRC plasma with a longer axial extension and a lower temperature, while selecting a more perpendicular angle A will result in a plasma with a shorter but hotter axial extension. In this way, the injection angle A and position of the beam injectors 615 can be optimized for different purposes. Furthermore, this angled and positioned beam injector 615 allows for the injection of higher-energy beams (which are generally more advantageous for depositing greater power with smaller beams) into a lower magnetic field compared to the magnetic field required to trap such beams in other ways. This is due to the fact that the azimuth component of the energy determines the fast ion orbital scale (which gradually becomes smaller with decreasing injection angle relative to the principal axis of symmetry of the container at constant beam energy). Moreover, angled injection toward the midplane, with the axial beam position close to the midplane, improves beam-plasma coupling, even during the injection period when the FRC plasma shrinks or otherwise axially contracts.

[0061] Go to Figure 3D and Figure 3EAnother alternative configuration of the FRC system 10, in addition to the angled beam injector 615, includes an internal divertor 302. The internal divertor 302 is located between the formation section 200 and the confinement chamber 100 and is constructed and operates substantially similarly to the external divertor 300. This includes the fact that the internal divertor 302, which rapidly switches magnetic coils, is effectively inactive during the formation process, allowing the formed FRCs to pass through the internal divertor 302 as they translate toward the mid-plane of the confinement chamber 100. Once the formed FRCs have passed through the internal divertor 302 and entered the confinement chamber 100, the internal divertor is activated to operate substantially similarly to the external divertor and isolate the confinement chamber 100 from the formation section 200.

[0062] Particle injector To provide a means of injecting new particles and better controlling the FRC particle stock, a 12-cylinder pellet injector 700 was utilized on the FRC system 10 (see, for example, I. Vinyar et al., “Pellet Injectors Developed at PELIN for JET, TAE, and HL-2A,” Proceedings of the 26th Symposium on Fusion Science and Technology, 09 / 27–10 / 01 (2010)). Figure 3 illustrates the layout of the pellet injector 700 on the FRC system 10. Cylindrical pellets (D ~ 1 mm, L ~ 1–2 mm) were injected into the FRC at velocities ranging from 150 to 250 km / s. Each individual pellet contained approximately 5 × 10⁻⁶ particles. 19 One hydrogen atom, which is comparable to the number of FRC particles.

[0063] Inhalation system It is well known that neutral gas halos are a serious problem in all confinement systems. The charge exchange and recovery (release of cold impurity material from the walls) processes have a devastating impact on energy and particle confinement. Furthermore, any significant density of neutral gas at or near the edge will lead to the rapid loss of injected large orbital (high-energy) particles or at least a severely shortened lifetime (large orbits are defined as particles with orbits on the scale of the FRC topology or at least orbital radii much larger than the characteristic magnetic field gradient length scale), a fact detrimental to all high-energy plasma applications, including fusion heated via auxiliary beams.

[0064] Surface finishing is a means of controlling or reducing the adverse effects of neutral gases and impurities in the confinement system. For this purpose, the FRC system 10 presented herein employs titanium and lithium deposition systems 810 and 820, which coat the plasma-facing surfaces of the confinement chamber (or container) 100 and divertors 300 and 302 with films of Ti and / or Li (tens of micrometers thick). The coating is achieved via vapor deposition. Solid Li and / or Ti are evaporated and / or sublimated and sprayed onto nearby surfaces to form the coating. The source is a nuclear furnace with a guide nozzle (in the case of Li) 822 or a heated solid ball 812 with a guide shield (in the case of Ti). Li evaporator systems typically operate in continuous mode, while Ti sublimators mostly operate intermittently between plasma operations. These systems operate at temperatures above 600°C to achieve rapid deposition rates. Multiple strategically positioned evaporator / sublimator systems are necessary to achieve good wall coverage. Figure 9 The preferred arrangement of getter deposition systems 810 and 820 in FRC system 10 is described in detail. The coating serves as an getter surface and effectively pumps hydrogen-like atomic and molecular substances (H and D). The coating also reduces other typical impurities (such as carbon and oxygen) to negligible levels.

[0065] Mirror plug As stated above, the FRC system 10 adopts the following... Figure 2And the grouped mirror coils 420, 430, and 444 shown in Figure 3. The first group of mirror coils 420 is located at the two axial ends of the confinement chamber 100 and is independently excited by the DC confinement, forming, and divertor coils 412, 414, and 416 of the main magnetic system 410. The first group of mirror coils 420 primarily helps to manipulate and axially contain the FRC 450 during merging and provides balanced forming control during holding. The first group of mirror coils 420 generates a magnetic field (approximately 0.4 to 0.5 T) that is nominally larger than the central confinement field generated by the central confinement coil 412. The second group of mirror coils 430, comprising 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 switching power supply. 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 contraction section 442, form a mirror plug 440, which provides a narrow, low-gas conduction path with a very high magnetic field (between 2 and 4 T and a rise time of about 10 to 20 ms). The most compact pulsed mirror coil 444 has a compact radial dimension, a 20 cm aperture, and a similar length compared to the meter-plus-scale orifice and pancake-shaped design of the confined coils 412, 414, and 416. The mirror plug 440 serves multiple purposes: (1) the coils 432, 434, 436, and 444 tightly confine the magnetic flux surface 452 and the end-flowing plasma jet 454 and guide it into the remote divertor chamber 300. This ensures that the emitted particles properly reach the divertor 300 and that there is a continuous flux surface 455 of the divertor 300 traced from the open field force line 452 region of the central FRC 450. (2) The physical contraction section 442 in the FRC system 10 provides an obstruction to the flow of neutral gas from the plasma gun 350 placed in the divertor 300, through which the coils 432, 434, 436 and 444 allow the magnetic flux surface 452 and the plasma jet 454 to pass. Similarly, the contraction section 442 prevents the backflow of gas from the formation section 200 to the divertor 300, thereby reducing the number of neutral particles that must be introduced into the entire FRC system 10 when the FRC is started. (3) The strong axial mirror generated by the coils 432, 434, 436 and 444 reduces axial particle loss and thus reduces parallel particle diffusion along the open field force line.

[0066] exist Figure 3D and Figure 3E In the alternative configuration shown, a set of low-profile necking coils 421 are positioned between the internal divertor 302 and the forming section 200.

[0067] Axial plasma gun The plasma flow from the gun 350, installed in the divertor chamber 310 of the divertor 300, is designed to improve stability and neutral beam performance. The gun 350 is mounted on an axis inside the chamber 310 of the divertor 300 (as shown in Figure 3 and...). Figure 10 (As illustrated in the diagram), and generates plasma flowing along the open flux line 452 in the divertor 300 and toward the center of the confinement chamber 100. The gun 350 operates under high-density gas discharge in a gasket-stacked channel and is designed to generate a fully ionized plasma of several thousand amperes within 5 to 10 ms. The gun 350 includes pulsed magnetic coils that match the output plasma flow to the desired size of plasma in the confinement chamber 100. The technical parameters of the gun 350 are characterized by a channel having an outer diameter of 5 to 13 cm and an inner diameter of up to about 10 cm, and providing a discharge current of 10 to 15 kA at 400–600 V with an internal magnetic field between 0.5 and 2.3 T.

[0068] The gun plasma flow can penetrate the magnetic field of the lens plug 440 and flow into the forming section 200 and the confinement chamber 100. As the distance between the gun 350 and the plug 440 decreases, and by making the plug 440 wider and shorter, the efficiency of plasma transfer through the lens plug 440 increases. Under suitable conditions, the gun 350 can deliver approximately 10-1 ions and electrons respectively at high ion and electron temperatures of approximately 150 to 300 eV and approximately 40 to 50 eV. 22 Each proton passes through a 2 to 4 T mirror plug 440. Gun 350 provides significant refeeding of the FRC edge layer 456 and improved overall FRC particle confinement.

[0069] To further increase the plasma density, a gas box can be used to inject additional gas into the plasma stream from gun 350. This technique allows the injected plasma density to be increased several times over. In FRC system 10, the gas box mounted on the divertor 300 side of mirror plug 440 improves the refeeding of FRC edge layer 456, the formation of FRC 450, and plasma line-tying.

[0070] Given all the adjustment parameters discussed above, and considering that operation with only one gun or with two guns is possible, it is readily apparent that a wide range of operating modes can be obtained.

[0071] bias electrode The electrical bias of the open flux surface can provide radial potentials, which cause azimuth angle E×B movement. This provides a control mechanism similar to turning a knob to control the rotation of the open field force line plasma and the actual FRC core 450 via velocity shear. To achieve this control, the FRC system 10 employs various electrodes strategically placed in various parts of the machine. Figure 3 depicts the bias electrodes positioned at preferred locations within the FRC system 10.

[0072] In principle, there are four types of electrodes: (1) point electrodes 905 in the confinement chamber 100, which contact specific open field force lines 452 in the edge of the FRC 450 to provide local charging; (2) annular electrodes 900 between the confinement chamber 100 and the forming section 200 to charge the far-edge flux layer 456 in an azimuth-symmetrical manner; (3) stacked concentric electrodes 910 in the divertor 300 to charge multiple concentric flux layers 455 (thereby the selection of layers is controllable by adjusting the divertor magnetic field by adjusting the coil 416 to terminate the desired flux layer 456 on the appropriate electrode 910); and finally, (4) the anode 920 of the plasma gun 350 itself (see Figure 10 (Its internal open flux surface 455 is near the interface of the FRC 450.) Figure 10 and Figure 11 Some typical designs for some of these electrodes are shown.

[0073] In all cases, these electrodes are driven by a pulsed or DC power supply at voltages up to approximately 800 V. Depending on the electrode size and the flux surface it intersects with, currents in the range of kiloamperes can be drawn.

[0074] Non-continuous operation of FRC system - regular mechanism Standard plasma formation on the FRC system 10 follows a well-developed reverse field angular pinch technique. A typical process for starting the FRC begins by driving quasi-DC coils 412, 414, 416, 420, 432, 434, and 436 to steady-state operation. Then, the RFTP pulsed power circuit of the pulsed power forming system 210 drives the pulsed fast reverse magnetic field coil 232 to generate a temporary reverse bias of approximately −0.05 T in the formation section 200. At this time, a predetermined amount of neutral gas is injected at 9–20 psi into the two formation volumes defined by the quartz chambers 240 of the (north and south) formation sections 200 via a set of azimuth-oriented puff-vales located at the outer ends of the formation sections 200. Next, a small RF (~hundreds of kilohertz) field is generated from a set of antennas on the surface of the quartz tubes 240 to generate pre-ionization within the neutral gas column in the form of localized seed ionization regions. This is followed by theta-ringing modulation applied to the current driving the pulsed fast reverse magnetic field coil 232, resulting in more comprehensive pre-ionization of the gas column. Finally, the main pulsed power group of the pulsed power forming system 210 is excited to drive the pulsed fast reverse magnetic field coil 232, thereby generating a forward bias field up to 0.4 T. This step can be sequential, such that a forward bias field is generated uniformly along the length of the forming tube 240 (static forming), or such that a continuous creeping field modulation is achieved along the axis of the forming tube 240 (dynamic forming).

[0075] Throughout this formation process, the actual field reversal in the plasma occurs rapidly within approximately 5 μs. The multi-gigawatt pulsed power delivered to the forming plasma readily generates a thermal FRC, which is then emitted from the formation section 200 via the application of a time-sequential modulation (magnetic creep) of the forward magnetic field or a temporary increase in current in the last coil of coil group 232 near the axial outer end of the formation tube 210 (forming an axial magnetic field gradient pointing axially towards the confinement chamber 100). The two (north and south) formed and accelerated FRCs then extend into the larger-diameter confinement chamber 100, where a quasi-DC coil 412 generates a forward bias field to control radial expansion and provide a balancing external magnetic flux.

[0076] Once the north and south-forming FRCs reach the vicinity of the midplane of confinement chamber 100, these FRCs collide. During the collision, the axial kinetic energy of the north and south-forming FRCs is largely thermalized as the FRCs eventually merge into a single FRC 450. A large set of plasma diagnostics is available in confinement chamber 100 to investigate the equilibrium of the FRC 450s. Typical operating conditions in FRC system 10 produce composite FRCs with an interface radius of approximately 0.4 m and an axial extension of approximately 3 m. Further characteristics include an external magnetic field of approximately 0.1 T and approximately 5 × 10⁻⁶ T / m². 19 m -3 The plasma density and total plasma temperature are as high as 1 keV. Without any sustaining (i.e., without heating and / or current driving via neutral beam injection or other auxiliary means), the lifetime of these FRCs is limited to about 1 ms, i.e., the inherent characteristic configuration decay time.

[0077] Experimental data from non-continuous operation—conventional mechanism Figure 12 It shows the radius r of the interface. s Repulsive flux radius r ΔΦ The typical time evolution is illustrated to show the dynamics of the angular pinch-and-merge process in FRC450. Two separate plasma blobs (north and south) are generated simultaneously and then move at supersonic speeds of v. Z The plasma clumps accelerate out of the corresponding formation segment 200 at approximately 250 km / s and collide near the midplane at z = 0. During the collision, the plasma clumps are axially compressed, followed by rapid radial and axial expansion, before finally merging to form FRC 450. The radial and axial dynamics of the merged FRC 450 are both demonstrated by detailed density distribution measurements and tomographic imaging based on a radiometer.

[0078] Representative non-sustained discharge data from FRC System 10 Figure 13A , Figure 13B , Figure 13C and Figure 13D The FRC is shown as a function of time. It begins at t = 0. The repulsive flux radius at the axial midplane of the machine is... Figure 13A As shown in the figure. This data was obtained from an array of magnetic probes located directly inside the stainless steel wall of the confinement chamber, which measure the axial magnetic field. The steel wall acts as a good flux retainer on this discharge timescale.

[0079] Figure 13B The line integral density is shown, derived from a 6-string CO2 / He-Ne interferometer located at z = 0. Abel inversion produces, taking into account the vertical (y) FRC shift as measured by radiometric thermal tomography. Figure 13CThe density contour lines. After some axial and radial oscillations during the first 0.1 ms, the FRC stabilizes with a hollow density distribution. This distribution is fairly flat, with a fairly large density along the axis, as is required for typical 2-D FRC equilibrium.

[0080] Figure 13D The total plasma temperature is shown, which originates from pressure equilibrium and is in perfect agreement with Thomson scattering and spectroscopic measurements.

[0081] Analysis of the entire repulsive flux array indicates that the shape of the FRC interface (approximated by the axial distribution of the repulsive flux) gradually evolves from a racetrack shape to an ellipse. Figure 14 The evolution shown corresponds to a gradual magnetic reconnection from two to a single FRC. In fact, a rough estimate suggests that approximately 10% of the magnetic flux of the two initial FRCs reconnects during the collision at this particular moment.

[0082] The FRC length steadily decreased from 3 m to approximately 1 m during the FRC's lifespan. Figure 14 The contraction visible in the figure indicates that most of the convective energy loss is dominated by the FRC confinement. Because the plasma pressure inside the interface decreases faster than the external magnetic pressure, the magnetic field line tension in the end region axially compresses the FRC, thus restoring axial and radial balance. (See Figure 13 and...) Figure 14 The discharge discussed in the paper, when the FRC equilibrium declines, the FRC magnetic flux, particle stock, and thermal energy (approximately 10 mWb, 7 × 10 mWb, and 7 × 10 mWb, respectively) are... 19 The number of particles and 7 kJ decreased by approximately an order of magnitude within the first millisecond.

[0083] Continuous Operation—HPF Mechanism Figures 12 to 14 The example in the example is the characteristic of a decaying FRC without any maintenance. However, several techniques have been deployed on FRC system 10 to further improve the FRC constraint (core and edge layers) to an HPF mechanism and sustain this configuration.

[0084] Neutral bundle First, fast (H) neutral particles are injected perpendicularly to B in a beam from eight neutral beam injectors 600. zInjection. Beams of fast neutral particles formed from north and south in the FRC are injected at the moment they merge into a single FRC 450 in confinement chamber 100. The fast ions, primarily generated by charge exchange, have electron-inductively coupled accelerator orbits (with principal radii on the scale of the FRC topology or at least much larger than the characteristic magnetic field gradient length scale) that are added to the FRC 450. After a partial discharge (0.5 to 0.8 ms after ingress), a sufficiently large fast ion population significantly improves the stability and confinement properties of the inner FRC (see, for example...). MW Binderbauer and N. Rostoker, Plasma Phys. 56, Part 3, 451 (1996) Furthermore, from a maintenance perspective, the beam from the neutral beam injector 600 is also the primary means of driving the current and heating the FRC plasma.

[0085] In the plasma mechanism of FRC system 10, fast ions are primarily slowed down by plasma electrons. During the early portion of the discharge, the typical orbital slowing time for fast ions is 0.3–0.5 ms, resulting in significant FRC heating, primarily of the electrons. Fast ions exhibit large radial offset outside the interface due to the inherently low internal FRC magnetic field (averaging approximately 0.03 T for an external axial field of 0.1 T). If the neutral gas density is too high outside the interface, fast ions will be susceptible to charge exchange losses. Therefore, wall-driven gas delivery and other techniques deployed on FRC system 10 (such as the plasma gun 350 and mirror plug 440, which are particularly helpful for gas control) tend to minimize edge neutral particles and achieve the desired accumulation of fast ion current.

[0086] Particle injection When a significant fast ion population (with higher electron temperature and longer FRC lifetime) has accumulated within the FRC 450, frozen H or D pellets are injected from the pellet injector 700 into the FRC 450 to maintain the FRC particle stock in the FRC 450. The expected ablation timescale is sufficiently short to provide a significant FRC particle source. This rate can also be increased by increasing the surface area of ​​the injector and by breaking individual pellets into smaller fragments while in the cylinder or injection tube of the pellet injector 700 and before entering the confinement chamber 100. This can be achieved by increasing the friction between the pellets 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 excitation sequence and rate of the 12 cylinders (injection tubes) and the fragmentation, it is possible to tune the pellet injection system 700 to provide exactly the desired particle stock maintenance level. This, in turn, helps maintain the internal dynamic pressure in the FRC 450, as well as the FRC 450's continued operation and lifespan.

[0087] Once the ablated atoms encounter significant plasma in FRC 450, they become completely ionized. The resulting cold plasma components are then impact-heated by the inherent FRC plasma. The energy necessary to maintain the desired FRC temperature is ultimately supplied by the beam injector 600. In this sense, the spherical injector 700, together with the neutral beam injector 600, forms a system that maintains steady state and sustains FRC 450.

[0088] CT injector As an alternative to the pellet injector, a compact ring (CT) injector is provided, primarily for feeding field-reverse configuration (FRC) plasma. The CT injector 720 includes a magnetized coaxial plasma gun (MCPG), such as... Figure 22A and Figure 22B As shown, the magnetized coaxial plasma gun includes: a coaxial cylindrical inner electrode 722 and an outer electrode 724; a bias coil 726 positioned inside the inner electrode; and an electrical break 728 at the end of the CT injector 720 opposite to the discharge. Gas is injected through a gas injection port 730 into the space between the inner electrode 722 and the outer electrode 724, and a spherical marker plasma is thereby generated by discharge and ejected from the gun by the Lorentz force. Figure 23A and Figure 23B As shown, a pair of CT injectors 720 are coupled to the confinement container 100 near and on opposite sides of the midplane of the container 100 to inject CT into the central FRC plasma within the confinement container 100. Similar to the neutral beam injector 615, the discharge ends of the CT injectors 720 are guided toward the midplane of the confinement container 100 at an angle to the longitudinal axis of the confinement container 100.

[0089] In alternative embodiments, such as Figure 24A and Figure 24B As shown, the CT injector 720 includes a drift tube 740, which comprises an elongated cylindrical tube coupled to a discharge end of the CT injector 720. As depicted, the drift tube 740 includes drift tube coils 742 positioned around the tube and spaced apart along the tube's axial direction. A plurality of diagnostic ports 744 are depicted along the length of the tube.

[0090] The advantages of the CT injector 720 are: (1) controllability and adjustability of the particle stock of CT injected each time; (2) deposition of hot plasma (instead of frozen spherules); (3) the ability of the system to operate in repeat-rate mode to allow for continuous feeding; and (4) the ability of the system to recover some magnetic flux because the injected CT carries an 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 exiting the electrode 722. As depicted, a bias coil 726 is mounted inside the inner electrode 722.

[0091] In recent experiments, supersonic CT translational velocities reaching ~100 km / s were achieved. Other typical plasma parameters are as follows: electron density ~5 × 10⁻⁶. 21 m -3 The electron temperature is ~30-50 eV, and the particle stock is ~0.5–1.0 × 10⁻⁶ eV. 19 The high dynamic pressure of the CT allows the injected plasma to penetrate deeply into the FRC and deposit particles inside the interface. In recent experiments, FRC particle feeding has resulted in the successful delivery of ~10-20% of the FRC particle stock via the CT injector, demonstrating that feeding can be easily implemented without disrupting the FRC plasma.

[0092] Saddle coil To achieve steady-state current driving and maintain the required ion current, it is desirable to prevent or significantly reduce electron spin-up caused by electron-ion friction (caused by momentum transfer between colliding ions and electrons). The FRC system 10 utilizes an innovative technique to provide electron breakup via an externally applied static magnetic dipole or quadrupole field. This is achieved through… Figure 15 This is achieved using the external saddle-shaped coil 460 depicted in the diagram. A radial magnetic field applied laterally from the saddle-shaped coil 460 induces an axial electric field in the rotating FRC plasma. The resulting axial electron current interacts with the radial magnetic field to generate an azimuth-breaking force on the electrons, F. θ =-σV eθ ‹∣B r | 2For typical conditions in FRC System 10, the magnetic dipole (or quadrupole) field required to be applied within the plasma is only about 0.001 T to provide sufficient electron breakup. The corresponding external field of about 0.015 T is small enough not to cause significant fast particle loss or otherwise negatively affect confinement. In fact, the applied magnetic dipole (or quadrupole) field helps suppress instabilities. Combined with tangential neutral beam injection and axial plasma injection, the saddle coil 460 provides an additional level of control regarding current retention and stability.

[0093] Mirror plug The design of the pulsed coil 444 within the mirror plug 440 allows for the local generation of a high magnetic field (2 to 4 T) with a moderate (approximately 100 kJ) capacitance energy. To form the typical magnetic field for the current operation of the FRC system 10, all field lines within the forming volume pass through the contraction 442 at the mirror plug 440, as if... Figure 2 As indicated by the magnetic field lines, no plasma wall contact occurs. Furthermore, the mirror plug 440, connected in series with the quasi-DC divertor magnet 416, can be adjusted to guide the field lines to the divertor electrode 910, or to spread the field lines in a cusp configuration (not shown). The latter improves stability and suppresses parallel electron thermal conduction.

[0094] The mirror plug 440 itself also contributes to neutral gas control. The mirror plug 440 allows for better utilization of the deuterium gas introduced into the quartz tube during FRC formation, as the gas backflow into the divertor 300 is significantly reduced by the small gas conduction (a mere 500 L / s) through these plugs. Most of the residual introduced gas inside the formation tube 210 is rapidly ionized. Furthermore, the high-density plasma flowing through the mirror plug 440 provides efficient neutral ionization, thus providing an effective gas barrier. As a result, most of the neutral particles recovered from the FRC edge layer 456 in the divertor 300 do not return to the confinement chamber 100. Additionally, most of the neutral particles associated with the operation of the plasma gun 350 (discussed below) will be confined to the divertor 300.

[0095] Finally, the mirror plug 440 tends to improve the confinement of the FRC edge layer. Using a mirror ratio (plug / confinement magnetic field) in the range of 20 to 40, and utilizing a length of 15 m between the north and south mirror plugs 440, the edge layer particle confinement time τ... ∥ It was increased by an order of magnitude. Improvement τ ∥ It can easily increase the confinement of FRC particles.

[0096] Assume that the radial diffusion (D) particle loss from the interface volume 453 is equal to the axial loss (τ) from the edge layer 456. ∥ If the equilibrium is achieved, then (2πr) is obtained. sL s )(Dn s / δ) = (2πr s L s δ)(n s / τ ∥ Therefore, the interface density gradient length can be rewritten as δ = (Dτ) ∥ ) 1 / 2 Here, r s L s and n s These are the interface radius, interface length, and interface density, respectively. The FRC particle confinement time is τ. N = [πr s 2 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 / 4. Physically, improving τ ∥ This leads to an increase in δ (reducing the interface density gradient and drift parameter), and thus a reduction in FRC particle loss. The overall improvement in FRC particle constraint is generally slightly less than the quadratic, because n s With τ ∥ Increase.

[0097] τ ∥ Significant improvements in this area also require that the edge layer 456 remain very stable (i.e., without the n=1 groove, fire belt, or other MHD instabilities typical of open systems). The use of the plasma gun 350 provides this preferred edge stability. In this sense, the mirror plug 440 and the plasma gun 350 form an effective edge control system.

[0098] plasma gun The plasma gun 350 improves the stability of the FRC emission jet 454 through coiling. Gun plasma from the plasma gun 350 is generated without azimuth angular momentum, which proves useful in controlling FRC rotational instability. Therefore, the gun 350 is an effective means of controlling FRC stability without requiring older quadrupole stabilization techniques. Consequently, the plasma gun 350 makes it possible to utilize the beneficial effects of fast particles or access advanced hybrid dynamics FRC mechanisms as outlined in this disclosure. Thus, the plasma gun 350 enables the FRC system 10 to operate with saddle coil currents that are just sufficient for electron breakup but below thresholds that would cause FRC instability and / or result in significant fast particle diffusion.

[0099] As discussed above Mirror plug As mentioned in the text, if τ can be significantly improved ∥ The supplied gun plasma will then be related to the edge layer particle loss rate (~10). 22 The lifetime of the plasma generated by the gun in FRC system 10 is in the millisecond range ( / s). In fact, considering a plasma with n... e ~ 10 13 cm -3 The plasma, with a density of approximately 200 eV and an ion temperature of approximately 200 eV, is confined between end-pivots 440. The trapping length L and mirror ratio R are approximately 15 m and 20, respectively. The mean free path of the ions due to Coulomb collisions is λ. ii ~ 6×10 3 cm, and because λ ii Since lnR / R < L, the ions are confined within the gas dynamic mechanism. The plasma confinement time in this mechanism is τ. gd ~ RL / 2V s ~ 2 ms, where V s This is the ion sound velocity. For comparison, the classical ion confinement time for these plasma parameters would be τ. c ~ 0.5τ ii (lnR + (lnR) 0.5 ~0.7 ms. In principle, anomalous transverse diffusion can shorten the plasma confinement time. However, in FRC system 10, if we assume Bohmian diffusion rate, the estimated transverse confinement time for gun plasma is τ⊥ > τ gd ~2 ms. Therefore, the gun will provide significant refeeding of the FRC edge layer 456 and improved overall FRC particle confinement.

[0100] Furthermore, the gun plasma flow can be turned on within approximately 150 to 200 microseconds, which allows for use during FRC startup, translation, and merging into confinement chamber 100. If turned on near t ~ 0 (FRC main bank start-up), the gun plasma helps maintain the currently dynamically forming and merging FRC 450. The combined particle stock from FRC formation and from the gun is sufficient for neutral beam trapping, plasma heating, and long-term maintenance. If turned on within t in the range of -1 to 0 ms, the gun plasma can either fill the quartz tube 210 with plasma or ionize the gas filled into the quartz tube, thus allowing FRC formation with reduced or even potentially zero gas filling. The latter may require a sufficiently cold forming plasma to allow for rapid diffusion of the reverse bias magnetic field. If turned on within t < -2 ms, the plasma flow can be used for several 10 13 cm -3 The target plasma density fills the formation of the formation section 200 and the confinement chamber 100, and the confinement region is approximately 1 to 3 m. 3 The field force line volume is sufficient to allow the FRC to accumulate in the neutral beam before it arrives. The formed FRC can then be formed and translated into the resulting confined container plasma. In this way, the plasma gun 350 enables a wide variety of operating conditions and parameter mechanisms.

[0101] Electrical bias Control of the radial electric field distribution in the edge layer 456 benefits FRC stability and confinement in various ways. With the innovative biasing components deployed in FRC system 10, it is possible to apply various intentional potential distributions to a set of open flux surfaces throughout the machine from a region completely outside the central confinement region in confinement chamber 100. In this way, radial electric fields can be generated precisely outside FRC 450 across edge layer 456. These radial electric fields then modify the azimuth rotation of edge layer 456 and achieve its confinement via E×B velocity shear. Thus, any differential rotation between edge layer 456 and FRC core 453 can be sheared into the interior of the FRC plasma. As a result, controlling edge layer 456 directly affects FRC core 453. Furthermore, since the free energy in plasma rotation can also be a cause of instability, this technique provides a direct means of controlling the initiation and growth of instability. In FRC system 10, appropriate edge biasing provides effective control over open field force line transport and rotation, as well as FRC core rotation. The positions and shapes of the various provided electrodes 900, 905, 910, and 920 allow for control of different sets of flux surfaces 455 at different and independent potentials. In this way, a wide variety of different electric field configurations and intensities can be achieved, each of which has a different characteristic effect on plasma performance.

[0102] The key advantage of all these innovative biasing techniques lies in the fact that the core and edge plasma performance can be influenced entirely from outside the FRC plasma, i.e., without requiring any physical components to come into contact with the central hot plasma (contact would have a significant impact on energy, flux, and particle loss). This has a major beneficial impact on the performance of the HPF concept and all its potential applications.

[0103] Experimental Data – HPF Operation Fast particles injected via beam from a neutral beam gun 600 play an important role in realizing the HPF mechanism. Figure 16A , Figure 16B , Figure 16C and Figure 16D This fact is illustrated. The figure depicts a set of curves showing how FRC lifetime relates to the length of the beam pulse. All other operating conditions were kept constant for all discharges included in this study. The data are averages derived from many emissions and therefore represent typical performance. It is clear that a longer beam duration results in a longer FRC lifetime. Looking at this evidence, along with other diagnostics during this study, it demonstrates that the beam increases stability and reduces losses. The correlation between beam pulse length and FRC lifetime is not perfect, as beam trapping becomes inefficient below a certain plasma size; that is, not all injected beams are intercepted and trapped when the FRC 450 shrinks in physical size. The shrinkage of the FRC is primarily due to the fact that, for a given experimental setup, the net energy loss from the FRC plasma during discharge (approximately ~4 MW throughout the discharge) is slightly greater than the total power fed into the FRC via the neutral beam (~2.5 MW). Positioning the beam closer to the midplane of container 100 tends to reduce these losses and extend the FRC lifetime.

[0104] Figure 17A , Figure 17B , Figure 17C and Figure 17D The diagram illustrates the impact of different components on achieving the HPF mechanism. It shows a series of typical curves depicting the lifetime of the FRC 450 as a function of time. In all cases, a constant, moderate beam power (approximately 2.5 MW) is injected for the entire duration of each discharge. Each curve represents a different combination of components. For example, operating the FRC system 10 without any mirror plug 440, plasma gun 350, or getter from the getter system 800 results in a rapid onset of rotational instability and a loss of FRC topology. Adding only the mirror plug 440 delays the onset of instability and increases constraint. The combination of the mirror plug 440 and plasma gun 350 further reduces instability and increases the FRC lifetime. Finally, adding getter (in this case, Ti) in addition to the gun 350 and plug 440 produces the best results—the resulting FRC exhibits no instability and the longest lifetime. It is clear from this experimental demonstration that the complete combination of components produces the best effect and provides optimal target conditions for the beam.

[0105] like Figure 1 As shown, the newly discovered HPF mechanism exhibits significantly improved transport performance. Figure 1 The diagram illustrates the change in particle confinement time in FRC system 10 between the conventional and HPF mechanisms. As can be seen, it has been improved by more than 5 times in the HPF mechanism. Furthermore, Figure 1 The particle confinement time in FRC System 10 is detailed relative to that in existing conventional FRC experiments. Regarding these other machines, the HPF mechanism in FRC System 10 has improved confinement by between 5 and nearly 20 times. Last and foremost, the nature of confinement scaling in FRC System 10 under the HPF mechanism is significantly different from all existing measurements. Prior to the establishment of the HPF mechanism in FRC System 10, in existing FRC experiments, various empirical scaling laws were derived from data to predict confinement time. Most of these scaling laws depended on the ratio R... 2 / ρ i Where R is the radius of the magnetic field zero point (null) (a loose measurement on the physical scale of the machine), and ρ i It is the Larmor radius of the ion evaluated in an externally applied field (a loose measurement of the applied magnetic field). From Figure 1 It is clear that in conventional FRC, long confinement is only possible with large machine sizes and / or high magnetic fields. Operating an FRC system using a conventional FRC mechanism tends to follow scaling laws such as... Figure 1 As indicated in [the document]. However, the HPF mechanism is extremely superior and shows that much better confinement can be obtained without large machine sizes or high magnetic fields. More importantly, from [the document]... Figure 1 It is also clear that, compared to the CR mechanism, the HPF mechanism results in improved confinement time and reduced plasma size. Similar trends are observed for flux and energy confinement time, as described below, increasing by more than 3-8 times in FRC System 10. Therefore, the breakthrough in the HPF mechanism enables the maintenance and preservation of FRC equilibrium in FRC System 10 and future higher-energy machines using moderate beam power, lower magnetic fields, and smaller size. These improvements are accompanied by lower operating and construction costs and reduced engineering complexity.

[0106] For further comparison, Figure 18A , Figure 18B , Figure 18C and Figure 18D Data as a function of time are shown for representative HPF mechanism discharges from FRC system 10. Figure 18A The flux exclusion radius at the mid-plane is depicted. For these longer timescales, the conductive steel wall is no longer such a good flux conserver, and the magnetic probe inside the wall is enhanced with a probe outside the wall to properly account for the diffusion of magnetic flux through the steel. Compared to typical performance in conventional mechanism CR, such as Figure 13A , Figure 13B , Figure 13C and Figure 13D As shown, the HPF mechanism operating mode exhibits a lifespan that is more than 400% longer.

[0107] Figure 18B The figure shows a representative chord of the line integral density trace, where Figure 18C The image shows its Abel inverted complement and density contour lines. For example... Figure 13A , Figure 13B , Figure 13C and Figure 13D As shown, compared to the conventional FRC mechanism CR, the plasma penetration pulse is more static, indicating very stable operation. Figure 18D As shown, the peak density is also slightly lower in HPF emission—a result of the hotter overall plasma temperature (up to twice as high).

[0108] for Figure 18A , Figure 18B , Figure 18C and Figure 18D The corresponding discharge illustrated in the figure has energy, particle, and flux confinement times of 0.5 ms, 1 ms, and 1 ms, respectively. At the reference time of 1 ms before entering the discharge, the stored plasma energy is 2 kJ with a loss of approximately 4 MW, making this target highly suitable for neutral beam maintenance.

[0109] Figure 19 This paper summarizes all the advantages of the HPF mechanism presented in the form of a newly established experimental HPF flux-constrained scaling. For example... Figure 19 As can be seen, based on measurements taken before and after t = 0.5 ms (i.e., t ≤ 0.5 ms and t > 0.5 ms), for a given interface radius (r) s Flux constraints (and similarly, particle and energy constraints) are roughly related to electron temperature ( T e It is proportional to the square of ). T e This strong scaling, with its positive power (rather than a negative power), is the complete opposite of that exhibited by conventional tokamak devices, where confinement is typically inversely proportional to a power of the electron temperature. This scaling is a direct result of the HPF states and the large orbital (i.e., orbitals on the FRC topological scale and / or at least on the characteristic magnetic field gradient length scale) ion population. Fundamentally, this new scaling largely favors high operating temperatures and enables reactors with relatively modest sizes.

[0110] Leveraging the advantages of the HPF mechanism, neutral beam-driven FRC maintenance or steady-state can be achieved. This means that global plasma parameters (such as plasma thermal energy, total particle number, plasma radius and length, and magnetic flux) are maintained at reasonable levels without substantial decay. For comparison, Figure 20 Plot A shows data as a function of time for a representative HPF mechanism discharge from FRC system 10, and Plot B shows data as a function of time for a projected representative HPF mechanism discharge from FRC system 10, where the duration of the neutral beam pulse through FRC 450 is maintained without decay. For Plot A, a neutral beam with a total power in the range of approximately 2.5–2.9 MW is injected into FRC 450 with an active beam pulse length of approximately 6 ms. The plasma diamagnetic lifetime depicted in Plot A is approximately 5.2 ms. More recent data show that a plasma diamagnetic lifetime of approximately 7.2 ms can be obtained with an active beam pulse length of approximately 7 ms.

[0111] As mentioned above Figure 16A , Figure 16B , Figure 16C and Figure 16D As noted, the correlation between beam pulse length and FRC lifetime is not perfect because beam trapping becomes inefficient below a certain plasma size; that is, not all injected beams are intercepted and trapped when the FRC 450 shrinks in physical size. The shrinkage or decay of the FRC is primarily due to the fact that, for a given experimental setup, the net energy loss from the FRC plasma during discharge (approximately -4 MW midway through the discharge) is slightly greater than the total power fed into the FRC via the neutral beam (-2.5 MW). (See also: [link to relevant information]). Figure 3C As noted, angled beam injection from the neutral beam gun 600 toward the midplane improves beam-plasma coupling, even when the FRC plasma contracts or otherwise axially contracts during the injection period. Additionally, appropriate pellet feeding will maintain the required plasma density.

[0112] Curve B shows the results of a simulated run using an active beam pulse length of approximately 6 ms and a total beam power slightly greater than approximately 10 MW from the neutral beam injector 600, where the neutral beam is to inject H (or D) neutral particles with a particle energy of approximately 15 keV. The equivalent current injected by each of the beams is approximately 110 A. For Curve B, the beam injection angle relative to the device axis is approximately 20°, and the target radius is 0.19 m. The injection angle can be varied within the range of 15°–25°. The beam will be injected in a co-current direction at the azimuth angle. The net lateral force and net axial force from the neutral beam momentum injection should be minimized. As in the case of Curve A, fast (H) neutral particles are injected from the neutral beam injector 600 at the moment when they form FRCs from the north and south and merge into a single FRC 450 in the confinement chamber 100.

[0113] The simulations that form the basis of plot B use a multidimensional Hall-MHD solver for background plasma and equilibrium, a fully dynamic Monte Carlo solver for high-energy beam components and all scattering processes, and a large number of coupled transport equations for all plasma matter to model the interactive loss processes. The transport components are empirically calibrated and extensively benchmarked against experimental databases.

[0114] As shown in curve B, the steady-state diamagnetic lifetime of the FRC 450 will be the length of the beam pulse. However, it is important to note that the key correlation curve B shows that the plasma or FRC begins to decay when the beam is turned off, not before. The decay will be similar to that observed in un-beam-assisted discharges (which may extend beyond the beam-off time by about 1 ms) and is simply a reflection of the characteristic decay time of the plasma driven by intrinsic loss processes.

[0115] Go to Figure 21A , Figure 21B , Figure 21C , Figure 21D and Figure 21E The experimental results illustrated in these figures indicate the achievement of FRC sustainment or steady state driven by an angled neutral beam, meaning that global plasma parameters (such as plasma radius, plasma density, plasma temperature, and magnetic flux) can be positioned at constant levels without decay related to the NB pulse duration. For example, such plasma parameters remain essentially constant over ~5+ ms. This plasma performance (including sustainment characteristics) is strongly correlated with the NB pulse duration, with diamagnetic persistence even a few milliseconds after NB termination due to the accumulation of fast ions. As illustrated, the plasma performance is limited only by pulse length constraints, which are caused by the limited stored energy in the associated power sources of many critical systems (such as the NB injector and other system components).

[0116] Neutral beam tunable beam energy As mentioned above Figure 3A , Figure 3B , Figure 3C , Figure 3D , Figure 3E and Figure 8 As indicated, the neutral atom beam 600 is deployed on the FRC system 10 to provide heating and current drive, as well as to generate fast particle pressure. The beamlines, including the neutral atom beam injector system 600, are positioned around the central confinement chamber 100, and as... Figure 3C , Figure 3D and Figure 3E The method shown is preferably angled to inject neutral particles toward the midplane of the confinement chamber 100.

[0117] To further improve FRC sustaining and demonstrate FRC ramp-up to higher plasma temperatures and increased system energies, this FRC system 10 includes a neutral beam injector (NBI) system 600 with increased power and extended pulse length, for example, for illustrative purposes only, with a power of approximately 20+ MW and a pulse length up to 30 ms. The NBI system 600 includes multiple positive ion-based injectors 615 characterized by a flexible, modular design (see...). Figure 3D and Figure 3E A subset of the NBI injectors 615 (e.g., four (4) of the eight (8) NBI injectors 615) has the ability to tune the beam energy from an initial lower beam energy to an increased beam energy during emission, for example from about 15 keV to about 40 keV at a constant beam current. This capability of the NBI injectors 615 is desirable in order to achieve more efficient heating and thus pressurization of the plasma core 450. In particular, this capability enables highly desired performance improvements at peak energy operating levels compared to lower energy levels: for example, (i) up to 2x times higher heating power; (ii) charge exchange losses reduced to close to 4 / 5; and (iii) heating efficiency increased to up to two times. In addition, the continuously variable beam energy that can be generated by the NBI injectors 615 enables optimal matching of the orbital parameters of the injected and then captured fast ions with respect to the instantaneous magnetobaric distribution during the ramp-up process. Finally, the rapid ramp rate, allowing for a ramp duration of 0.1–10 ms, along with the rapid (around 1 ms or less) tunability 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 modulating beam energy and power.

[0118] Sufficient heating power is required to heat and pressurize the FRC 450, thereby maintaining and ramping up to both high plasma temperatures and increased system energy. Assuming a sufficiently low loss rate, the ramp rate is largely a function of how much power the NBI injector 615 can deposit in the FRC core 450 at any given time. Therefore, a high main neutral beam power through the injection port is always desirable.

[0119] Furthermore, the effective heating rate induced by the NBI injector 615 is a complex interplay between the characteristics of the injected beam and the subsequent, persistent instantaneous distributions of the following: the temperature of all matter, electron and ion density, neutral particle concentration, and the magnetic field across the FRC core 450. Of these, the magnetic field distribution is intentionally altered on a sub-millisecond timescale by the control system during ramp-up, while the dynamic pressure-related distribution evolves via intrinsic alterations arising from self-organizing processes and turbulence within the plasma, as well as the energy deposited through the injection process. The tunability of the beam provides a means for optimally adapting to these varying conditions.

[0120] For example, the charge exchange cross section (i.e., the probability of fast ions capturing electrons to form neutral atoms) is a strong function of beam energy. For the range of 15–40 keV, the main charge exchange rate as a function of beam energy decreases significantly. Therefore, at any given field level, the energy retention in the plasma is highest when particles are injected at the highest energy compatible with that field level (among other things, this requires the energy of the injected particles to cause the orbital radius of the trapped ions to fit within the inner walls of the confinement system).

[0121] Another example of the impact of distribution on overall heating efficiency relates to the location where power is deposited. Higher beam energies generally result in relatively higher energy deposition in the periphery of the FRC compared to the core. Increasing the magnetic field while maintaining the same beam energy will result in tighter trapped ion orbitals and consequently, higher power coupling to the FRC core plasma. These facts, in turn, have a strong impact on energy retention—for example, energy deposited in the periphery is transported out of the system much more easily along the open field force line structure, while energy deposited in the core is lost relatively more slowly due to the lower cross-field transport time. Therefore, close coordination between the magnetic field ramping and the appropriate increase in beam energy is desirable.

[0122] The beam system 600 is designed for rapid voltage ramping in the 0.1–10 ms range. This offers the potential to increase ion and electron temperatures by a factor of 2 and 10, respectively, on a shorter timescale than typical macroscopic instability growth times. Consequently, plasma stability, operational reliability, and reproducibility are fundamentally increased.

[0123] The variable voltage rise time of 0.05 to 1 ms provides a sufficiently fast response time, allowing the beam to be utilized as part of an active feedback system. In this way, beam modulation can be used to control macroscopic and microscopic stability. For example, by temporarily altering the radial power deposition distribution by changing the beam energy (and thus the radial energy deposition mode), the pressure gradient can be affected, which can counteract the initiation of unstable plasma modes. Figure 3D and Figure 3E The FRC system 10 shown utilizes this capability, along with rapid magnetic feedback, to control internal tilt, rotation rate, drift wave development, and other operational scenarios.

[0124] Figure 25 An illustration depicts the NBI injector 615 of this FRC system 10. In an example embodiment, the NBI injector 615 is shown to include: an arc driver 650; a plasma chamber 651; an ion optics system 652 including a group of triodes or tetrodes comprising an extraction grid and an acceleration grid; a gimbal 653; a neutralizer 654 including an arc evaporator 655 (such as, for example, a Ti arc evaporator); a cryogenic pump 656 having a surface structure (such as, for example, a ribbed surface structure) configured to increase cryopumping; a deflecting magnet 656 for removing unneutralized ions; and a collimating aperture 658 including an insertable calorimeter 659 for intermittent beam characterization, diagnostics, and recalibration.

[0125] More specifically and refer to Figure 26 As shown in the figure, the tunable beam system is preferably implemented based on a transistor-type ion optical system (IOS) 660. The concept is an acceleration-deceleration scheme. Figure 26 As illustrated in the figure, the first grid G1 is set to a voltage V1, the second grid G2 is set to a voltage V2, and the last grid G3 is set to a voltage V3. The extracted ions are first accelerated to an energy E1=e*(V1-V2) while passing across the gap between G1 and G2, where e is the charge of the ion. They are then decelerated in the gap between G2 and G3, such that E2=E1+e*(V2-V3). These voltages are typically adjusted such that V1>V2<V3. Based on the corresponding respective power supplies PS1, PS2 and PS3, the grid voltages can be adjusted incrementally during the pulse to change the output of the emitted ions 662. For example, to start 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 will first be accelerated to 40 keV, and then exit the IOS with an energy of 15 keV. Later in the pulse, the power supplies can be switched to provide V1=40 kV, V2=-1 kV, V3=0 V. Thus, there is substantially no beam deceleration in the second gap, resulting in an output beam energy of approximately 40 keV. The power supplies are each individually controllable and provide appropriate voltage modulation. The initial beam ions are extracted from many standard arc-based or RF-based plasma sources PS. After exiting the IOS 660, the beam ions 662 pass across a neutralizer 664, where fast ions are converted into neutral atoms via charge exchange with electrons from the cold neutral gas present in the neutralizer 664. Appropriate cryogenic pumping prevents neutral gas from flowing out through the downstream orifice of the neutralizer 664. At the end of the neutralizer, there are also provided: an appropriate bending magnet 666 that provides removal of unneutralized fast ions 663; and an associated ion dump 668 for absorbing the fast ions and their energy. The resulting atomic beam 670 then passes through an appropriate aperture 6720 to reduce beam divergence and provide a well-collimated neutral atom flow toward the reactor core.

[0126] In an alternative variant, the IOS is based on a tetrode design. In this case, the IOS consists of four grids, which have the same acceleration-deceleration principle as explained for the triode case. A person skilled in the art will readily recognize the similarity between the system components and the operating principle. The introduction of the fourth grid provides further possibilities for fine tuning and overall greater operational flexibility.

[0127] The exemplary embodiments provided herein have been described in U.S. Provisional Patent Application Serial No. 62 / 414,574, which is incorporated herein by reference.

[0128] Plasma stability and axial position control Conventional solutions to FRC instability typically provide axial stability at the expense of radial instability, or radial stability at the expense of axial instability, but not stability in both directions simultaneously. For first-order solutions, axial instability is sacrificed, where the equilibrium of transverse or radial stability of the plasma position has the desired axisymmetric properties. In light of the foregoing, the embodiments presented herein relate to systems and methods for promoting stability of the FRC plasma in both radial and axial directions, as well as axial stability properties independent of the FRC plasma equilibrium, for controlling the axial position of the FRC plasma along the axis of symmetry of the FRC plasma confinement chamber. However, the axial position instability is actively controlled using a set of external axisymmetric coils that control the axial position of the FRC plasma. By acting on a voltage applied to a set of external coils concentric with the plasma and using nonlinear control techniques, these systems and methods provide feedback control of the FRC plasma axial position with stability properties independent of the plasma equilibrium.

[0129] The embodiments presented herein utilize the axial instability of the FRC to enhance radial stability while stabilizing or controlling axial instability. In this way, stability can be achieved in both the axial and radial directions. The control method is designed to modify the external or balancing magnetic field to stabilize the FRC plasma radially or laterally at the expense of axial instability, and then act on the radial field coil current to rapidly restore the FRC plasma position toward the mid-plane while minimizing overshooting and / or oscillations around the mid-plane of the confinement chamber. The advantage of this solution is that it reduces the complexity of the actuators required for control. Compared to conventional solutions with multiple degrees of freedom, the method of the embodiments presented herein reduces the complexity to a control problem along the rotational axis of the FRC plasma, which has only one degree of freedom.

[0130] The combination of waveforms in the coil current, feed, and neutral beam power that leads to axially unstable plasma defines the plasma control scenario that sets the plasma in an axially unstable state. This scenario can be pre-programmed using prior knowledge from simulation or experiment, or by feedback controlled to maintain an axially unstable equilibrium. During discharge, the plasma position should be controlled independently of the stability properties of the equilibrium; for example, the control scheme should work for both axially stable and axially unstable plasmas up to a limit. The most axially unstable plasma that can be controlled has a growth time comparable to the skin time of the container.

[0131] Now we turn to systems and methods for promoting the stability of FRC plasma in both radial and axial directions, and for controlling the axial position of FRC plasma along the axis of symmetry of the FRC plasma confinement chamber. Figure 27 A simplified scheme is shown to illustrate an example embodiment of the axial position control mechanism 510. The FRC plasma 520, shown rotating within the confinement chamber 100, has a plasma current 522 and an axial displacement direction 524. An equilibrium field (not shown) is generated within the chamber 100 by symmetrical current components, such as, for example, a quasi-DC coil 412 (see...). Figure 2 , Figure 3A , Figure 3D and Figure 3E The equilibrium field does not produce a net force along the axial displacement direction 524, but can be tuned to produce a transversely / radially or axially stable plasma. For the purposes of the embodiments presented herein, the equilibrium field is tuned to produce a transversely / radially stable FRC plasma 520. As noted above, this results in axial instability, and thus axial displacement of the FRC plasma 520 along the axial displacement direction 524. As the FRC plasma 520 moves axially, it induces antisymmetric currents 514 and 516 (i.e., in opposite directions on each side of the midplane of the confinement chamber 100 in the walls of the confinement chamber 100). The FRC plasma 520 will induce this type of current component both in the container and in the external coil. These antisymmetric current components 514 and 516 generate a radial field that interacts with the circumferential plasma current 522 to produce a force opposite to the movement of the FRC plasma 520, and this force results in slowing down the axial displacement of the plasma. Due to the resistivity of the confinement chamber 100, these currents 514 and 516 gradually dissipate over time.

[0132] Radial field coils 530 and 531, disposed on each side of the midplane around the confinement chamber 100, provide additional radial field components due to currents 532 and 534 induced in the coils 530 and 531 in opposite directions. The radial field coils 530 and 531 may comprise a set of axisymmetric coils, which may be positioned inside or outside the containment vessel 100. The radial coils 530 and 531 are shown as resembling a quasi-DC coil 412 (see...). Figure 2 , Figure 3A , Figure 3D and Figure 3E The coils 530 and 531 are positioned outside the receiving container 100. Each of these coils, or the group of coils, may carry a different current than the coils on opposite sides of the mid-plane, but these currents are anti-symmetrical about the mid-plane of the receiving container 100 and generate currents along the mid-plane with... B z ≠ 0、 B r = 0 magnetic field structure. Radial field coils 530 and 531 generate complementary radial field components, which interact with the circumferential plasma current 522 to generate axial force. The axial force then causes the plasma to move away from the mid-plane of the confinement chamber 100.

[0133] Control mechanism 510 includes a control system configured to act on the radial field coil current to rapidly restore the plasma position toward the mid-plane while minimizing overshoot and / or oscillations around the machine's mid-plane. The control system includes a processor operatively coupled to radial field coils 530 and 531, quasi-DC coil 412, their respective power supplies, and other components (such as, for example, magnetic sensors) to provide plasma position, plasma velocity, and effective 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 comprising non-transitory computer-readable media. It may include processor-based or microprocessor-based systems, including systems using microcontrollers, reduced instruction set computers (RISCs), application-specific integrated circuits (ASICs), logic circuits, and any other circuitry or processor capable of performing the functions described herein. The above is merely illustrative and is therefore not intended to limit the definition and / or meaning of the terms "processor" or "computer" in any way.

[0134] The functionality of a processor can be implemented using software routines, hardware components, or a combination thereof. Hardware components can be implemented using various technologies, including integrated circuits or discrete electronic components. A processor unit typically includes a read / write memory storage device and usually also includes hardware and / or software for writing to and / or reading from the memory storage device.

[0135] A processor may include a computing device, an input device, a display unit, and an interface (e.g., for accessing the Internet). A computer or processor may include a microprocessor. The microprocessor may be connected to a communication bus. A computer or processor may also include memory. Memory may include random access memory (RAM) and read-only memory (ROM). A 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 devices for loading computer programs or other instructions into the computer or processor.

[0136] A processor executes a set of instructions stored in one or more storage elements to process input data. Storage elements may also store data or other information as desired or required. Storage elements may take the form of information sources or physical memory elements within the processing machine.

[0137] The problem of controlling the position of axially stable or unstable FRC configurations using a branch of nonlinear control theory known as sliding mode control is addressed using a radial field coil actuator. A linear function of the system state (sliding surface) is used as an error signal with the desired asymptotically stable (sliding) performance. The sliding surface is designed using Liapunov theory to exhibit asymptotic stability over a wide range of FRC dynamic parameters. The proposed control scheme can then be applied to both axially stable and unstable plasmas without requiring retuning of the parameters used in the sliding surface. This property is advantageous because, as mentioned earlier, the equilibrium may need to transition between axially stable and axially unstable equilibrium at different stages of FRC discharge.

[0138] Figure 28 The configuration of control scheme 500 is shown. A low-pass filter limits the switching frequency within the desired control bandwidth. A digital control loop is assumed to be required for sampling and signal transmission with a sampling delay. The error signal (sliding surface) is a linear combination of coil current, plasma position, and plasma velocity. The plasma position and velocity are obtained from external magnetic measurements. The current in the effective coil system can be measured using standard methods.

[0139] Position control is achieved using coil current and plasma position. Plasma velocity is required to improve performance, but this is optional. The nonlinear function of the error signal (relay control law) produces discrete voltage levels for each pair of power supplies connected to the mid-plane symmetrical coil. The mid-plane symmetrical coil is fed relay voltages of equal strength but opposite sign. This generates a radial field component to recover the plasma position toward the mid-plane.

[0140] To demonstrate the feasibility of the control scheme, a rigid plasma model is used to simulate plasma dynamics. This model utilizes magnet geometry. When considering only the plasma and container, the plasma current distribution corresponds to an axially unstable equilibrium with a growth time of 2 ms. The power supply is assumed to operate at discrete voltage levels (typically in the 800 V range (step)).

[0141] Figure 29 Several plasma control simulations are shown, highlighting the relationship between the voltage applied to the coils and the plasma position settling time, along with the peak coil current and ramp rate required to bring a plasma axially displaced by 20 cm back to the mid-plane. These sliding mode axial position control simulation examples were performed at 0.3 T using four pairs of external trimming coils. Four cases are shown, corresponding to power supplies with discrete voltage levels at 200 V (solid square), 400 V (solid circle), 800 V (solid triangle), and 1600 V (hollow square). For all four cases, the control bandwidth was 16 kHz and the sampling frequency was 32 kHz. The plasma position (top view), the current in the outermost coil pair (middle), and the coil current ramp rate (bottom view) are shown. The plasma displacement is allowed to become unstable until it reaches 20 cm. At this point, feedback control is applied.

[0142] Simulation results indicate: 1. To bring the plasma back to the mid-plane within 5 ms (solid square trace), a coil ramp rate of 0.5 MA / s is sufficient, and a 200 V power supply is required.

[0143] 2. To bring the plasma back to the mid-plane within 2.3 ms (solid circular trace), a coil ramp rate of 1 MA / s is sufficient, requiring a power supply of 400 V.

[0144] 3. To bring the plasma back to the mid-plane within 1.3 ms (solid triangular trace), a coil ramp rate of 2 MA / s is sufficient, requiring an 800 V power supply.

[0145] 4. To bring the plasma back to the mid-plane within 1.0 ms (hollow square trace), a coil ramp rate of 4 MA / s is sufficient, requiring a power supply of 1600 V.

[0146] For the third case studied above (the ramp rate case of 2 MA / s), the peak current of all trimming coils is... Figure 30 The position of the trimming coil is also shown as a function of the trimming coil position. A sliding mode axial position control simulation example was performed at 0.3 T using four pairs of external trimming coils with a power supply having three levels (+800V, 0, -800V), a control bandwidth of 16 kHz, and a sampling rate of 32 kHz. A coil ramp rate of 2 MA / s was required to bring the plasma back to the mid-plane within 1.3 ms. The peak current required in all coil pairs was less than 1.5 kA. The actual switching frequency required (approximately 2 kHz) was much lower than the control system bandwidth.

[0147] The control system can also implement a target surface that is only a function of coil current and plasma velocity, not plasma position. In this case, the axial position control loop provides only axial dynamic stabilization, not control. This means the plasma is in a metastable state and will drift slowly along its axis. An additional feedback loop is then used to provide position control, which controls the plasma gap between the plasma interface and the container, thus performing both plasma shape and position control simultaneously.

[0148] Another plasma confinement device that uses a similar control system is the tokamak. To maintain plasma confinement, the plasma current in the tokamak must be kept between a lower limit and an upper limit that are approximately proportional to the plasma density and the toroidal field, respectively. To operate at high plasma densities, the plasma current must be increased. Simultaneously, the poloidal field must be kept as low as possible, thus requiring a safety factor q greater than q=2. This is achieved by elongating the plasma along the machine axis, allowing for a large plasma current (and therefore a high plasma density) without increasing the boundary magnetic field beyond its safety limits. These elongated plasmas are unstable along the machine axis (referred to as the vertical direction in tokamak terminology) and also require plasma stabilization mechanisms. Vertical plasma position control in a tokamak also uses a set of radial field coils for recovery, making it very similar to the position control problem in the RFC. However, the reasons for needing stabilization differ between tokamaks and RFCs. In tokamaks, vertical plasma instability is a penalty for operating with large plasma currents, which requires plasma elongation to operate with high toroidal fields. In the case of FRC, plasma instability is the penalty for achieving transverse stability. Tokamak devices have a circumferential field that stabilizes this configuration, therefore they do not require transverse stability.

[0149] This disclosure relates to systems and methods for promoting the generation and maintenance of high-flux target FRC plasmas and for axial refeeding of FRC plasmas. In an example embodiment, the process includes forming a high-flux FRC (up to 30 mWb) by merging two spherical marks having opposite helicalities. Merging experiments have been carried out on various devices to study magnetic reconnection by merging two spherical mark-type plasma rings together by contacting and reconnecting them along a circumferential line of symmetry. A spherical mark is a spherical or toroidal plasma in which there is no force current ( j × B = 0) The equilibrium configuration is determined by the presence of a current (flux) aperture at the main axis. Two toroidal ball marks (carrying equicyclic currents with the same or opposite toroidal fields) are forced to merge through a controlled external coil current; these are referred to as co-spiral or anti-spiral merging, respectively. As described by Yamada, M. et al. in Phys. Rev. Lett. 65, 721 (1990), anti-spiral merging produces antiparallel magnetic field reconnection at the reconnection site, where magnetic reconnection is expected to occur very efficiently (Bhattacharjee, A., Phys. Fluids 26, 3332 (1983)). Experimental results also indicate that anti-spiral merging does indeed achieve faster reconnection globally than co-spiral merging, and then forms a high-flux FRC structure (consisting only of a poloidal field) after eliminating the reverse-pointing toroidal field of the ball marks due to merging.

[0150] In an example embodiment, the process includes: 1. Using MCPG to generate high magnetic flux target FRC plasma via anti-spiral spherical mark merging (MCPG) φ p ~25-30 mWb); 2. By forming a target plasma with sufficient magnetic flux and injecting a high-energy neutral beam, the FRC plasma is amplified, stabilized, and powered towards the fusion reactor plasma conditions, thus further converting the energy of the beam into thermal energy; 3. Form additional multi-pulse spherical markers and inject them into the FRC plasma for particle refeeding and recirculation, in order to maintain and enhance the confinement properties of the FRC plasma and achieve a high-flux and dense FRC mechanism.

[0151] Go to Figure 31A and Figure 31B An example embodiment of the FRC confinement system is depicted as having a confinement chamber 100 and a pair of divertors 302 coupled to the confinement chamber 100 at each end. To generate an optimal initial high-flux target FRC plasma 453, a pair of mesoscale ball mark injectors 250 (or magnetized coaxial plasma guns (MCPGs)) are coupled relatively to the centrally located ends of the confinement chamber 100. The ball mark injectors 250 inject high-flux (>20 mWb) ball mark plasma toward the midplane of the confinement chamber 100, where the ball marks merge within the confinement chamber 100 and form an FRC plasma. The anti-helical merging of the two ball marks tends to produce a high-flux target FRC plasma with an increased trapping flux. φ p (~25-30 mWb). Multiple neutral beam injectors 615 are also coupled to the confinement chamber 100 at an angle toward the midplane of the confinement chamber 100 to drive and maintain the FRC plasma 453. In an example embodiment, the neutral beam injectors 615 are adjustable from an initial power level to an increased power level. In a further example embodiment, the ball mark injector 250 is capable of injecting multi-pulse ball marks into the FRC plasma along the geometric axis of the confinement chamber to achieve efficient refeeding and recirculation.

[0152] Previous studies on spherical mark merging (see Figures 32A-32D This demonstrated the feasibility and potential of compact toroidal fusion plasmas. During the 2004–2008 activities of the MRX experiment at the Princeton Plasma Physics Laboratory, anti-helical merging was applied to the study of the formation, stability, and maintenance of flattened FRCs. It was demonstrated that the central ohmic heating solenoid used in tokamak devices could be utilized to amplify the toroidal current in the FRC, allowing it to be maintained for a longer time than resistive decay (Gerhardt, SP et al., Phys. Plasmas 15, 032503 (2008)). Additionally, shaping field coils were used to control the boundary shape and elongation of the FRC. This allowed for the study of the effects of these shaping fields on stability. Experimentally, it was demonstrated that the n=1 tilt mode (n: toroidal modulus) can be stabilized in flattened FRCs (Gerhardt, SP et al., Phys. Rev. Lett. 99, 245003 (2007)). Moreover, n The growth rate of ≥ 2 modes slows down with favorable formation. These results represent a significant advance in understanding open-boundary FRC physics. In addition to these stability and maintenance results, significant ionic heating was observed in the anti-helical merging experiments. The co-helical merging of two spherical marks produces less heat, but the β-spherical mark plasma is sufficiently high (β ~ 0.2–0.3). This generates ionic temperatures with non-negligible Ti. i > 25 eV, T e 10 eV, n e >10 14 cm -3 The ability of the combined plasma to study the stability characteristics of high-β plasmas with variable circumferential field components allows for the investigation of these plasmas.

[0153] In example embodiments, such as Figure 33 The ball mark injector 250, as depicted, is a relatively compact ball mark injector having an outer electrode 254, an inner electrode 255 with a W coating, an outer bias coil 252 positioned around the outer electrode 254, a core bias coil 253 positioned within the inner electrode 255, a gas injector 256, and an HV power supply 258. The ball mark injector 250 generates sufficient magnetic flux by utilizing and upgrading the recently developed core bias coil system 253 (see Edo, T. et al., Jrnl of Plasma and Fusion Res. 13, 3405062 (2018)). In recent preliminary tests, an air-core bias coil with a DC power supply produced a magnetic flux of ~1.67 µWb / Amp for the formed ball mark, while an MCPG with an iron core (cast iron; permeability µ ~250) bias coil system could produce approximately 100 times higher magnetic flux (i.e., ~0.16 mWb / Amp). By keeping the current density constant, the size of the ball mark injector can be appropriately increased proportionally to produce much higher magnetic flux (>30 mWb) without causing the undesirable effects typically associated with electrode discharge. In a further example embodiment, the iron core is formed using pure iron (99.9% Fe; µ >200000), which tends to achieve even higher magnetic flux with a reasonable bias current.

[0154] Figure 3D and Figure 3E A CT-integrated FRC plasma conferencing system 10 is described, comprising a confinement chamber 100, a first pair of internal divertors 302 coupled to opposite ends of the confinement chamber 100, an opposing CT formation and injection system 200 coupled to the internal divertors 302 at the first end, and a second pair of external divertors 300 coupled to the second end of the CT formation and injection system 300. To achieve ball-mark merging, such as... Figure 31A As shown, Figure 3D and Figure 3E The CT formation / injection section 200 and external divertor 300 shown are removed and replaced with a ball-mark injector 250 coupled to the internal divertor, as shown. Figure 31A and Figure 31B As illustrated in the diagram, the ball-shaped mark injector 250 is positioned precisely inside the concentric electrodes 310 of the divertor, which are used for FRC 453 stability control via edge bias. The edge bias system generates a radial electric field along the open field lines, thus affecting the FRC interface (scraped layer region) through... E r × B z An azimuth current is generated, which, in conjunction with NBI, stabilizes the global MHD mode. The ball mark injector 250 is operated and controlled independently to generate various ball mark plasmas and initial FRCs, allowing for variations in the initial plasma density and trapped flux to find the optimal target FRC for efficient neutral beam injection. During the ball mark formation, translation, and merging processes, a relatively low balancing and mirror field (Bi) is applied in the confined section via balancing and mirror coils 412 and 420. e ~1 kG, mirror ratio of ~2), so that FRC plasma 453 can be properly formed, after which those fields should be gradually increased (B e Up to 3 kG (with a mirror ratio of ~3-3.5) is used to confine and sustain FRC plasma 453. A neutral beam is also injected through discharge from injector 615 into confinement chamber 100, and the beam energy can be increased from the initial power level to elevated power levels, for example, ~15 keV to 40 keV, along with B... e The corresponding ramp is then used. Furthermore, the magnet and neutral beam injector systems can be actively controlled to ensure the real-time stabilization and maintenance of the FRC plasma.

[0155] To adequately refill the confinement chamber 100 with particles and to recirculate the already formed FRC, a separately controlled power supply 258 powers the ball-mark injector 250. When a relatively oriented CT injector with multi-pulse capability is mounted near the mid-plane of the confinement chamber, the CT injector radially injects the ball-mark-like plasma cluster into the FRC; in other words, the injected CT must penetrate the transverse magnetic field (…). Bz ~1 kG This prevents the ion from breaking apart or generating strong magnetic / density perturbations. Furthermore, radial CT injection near the midplane somewhat affects fast ion confinement, and the system tends to be non-scalable to high-field fusion devices. Therefore, from several scientific perspectives, CT injection along the geometric axis from the ball-mark injector 250 (i.e., "axial" CT injection) is significantly more advantageous than radial CT injection.

[0156] Alternatively, in the example embodiment, Figure 2 , Figure 3A , Figure 3D and Figure 3E The system configuration depicted (which includes two opposing diameter reverse field angle pinch-forming sections 200) can be modified to include opposing diameter ball mark injectors 250 coupled to an external divertor 300 for refeeding the FRC plasma contained within the containment chamber.

[0157] According to embodiments of this disclosure, a method for generating and maintaining a magnetic field having a field-reversed configuration (FRC) includes: merging first and second spherical Mark plasmas in a confinement chamber and forming an FRC around the merged plasma; and maintaining the FRC at a constant value or approximately a 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.

[0158] According to a further embodiment of this disclosure, the method further includes: injecting ball-mark plasma from opposing first and second ball-mark injectors toward the mid-plane of the chamber and merging these ball-mark plasmas to form an FRC.

[0159] According to a further embodiment of this disclosure, the method further includes: performing anti-spiral ball-mark merging on the ball-mark plasma injected from the first and second ball-mark injectors into the confinement chamber.

[0160] According to a further embodiment of this disclosure, the first and second ball mark injectors include a magnetized coaxial plasma gun (MCPG).

[0161] According to a further embodiment of this disclosure, the first and second ball mark injectors include a core bias coil system.

[0162] According to a further embodiment of this disclosure, the core of the core bias coil system comprises cast iron with a permeability of about 250.

[0163] According to a further embodiment of this disclosure, the core of the core bias coil system is about 99.9% Fe, and its permeability is equal to or greater than about 200,000.

[0164] According to a further embodiment of this disclosure, the method further includes: independently controlling the first and second ball-shaped injectors.

[0165] According to a further embodiment of this disclosure, the ball-mark plasma ejected from the first ball-mark injector is different from the ball-mark plasma ejected from the second ball-mark injector.

[0166] According to a further embodiment of this disclosure, the method further includes: refeeding the FRC plasma along the geometric axis of the confinement chamber with one or more ball-mark plasmas from one or more of the first and second ball-mark injectors.

[0167] According to a further embodiment of this disclosure, the method further includes: multi-pulse injection of one or more ball-mark plasmas from one or more of the first and second ball-mark injectors into the FRC plasma.

[0168] According to a further embodiment of this disclosure, the method further includes: forming a multi-pulse spherical mark and injecting it into an FRC plasma.

[0169] According to a further embodiment of this disclosure, the method further includes: tuning the beam energy of the plurality of neutral beams between a first beam energy and a second beam energy, wherein the second beam energy is different from the first beam energy; or tuning the beam energy of the plurality of neutral beams between a first beam energy and a second beam energy, wherein the second beam energy is different from the first beam energy, and wherein the second beam energy is higher than the first beam energy; or tuning the beam energy of the plurality of neutral beams between a first beam energy and a second beam energy, wherein the second beam energy is different from the first beam energy, and wherein the plurality of neutral beams switch between the first beam energy and the second beam energy during the duration of the injection emission.

[0170] According to a further embodiment of this disclosure, the method further includes: generating a magnetic field in the room using a quasi-DC coil extending around the room.

[0171] According to a further embodiment of this disclosure, the method further includes: guiding the magnetic flux surface of the FRC into a divertor coupled to the end of the confinement chamber.

[0172] According to a further embodiment of this disclosure, the method further includes: generating a magnetic field within the divertor using a quasi-DC coil wound around the forming section and extending from the divertor.

[0173] According to a further embodiment of this disclosure, the method further includes: generating a mirror magnetic field within the opposite ends of the chamber using a quasi-DC mirror coil extending around the opposite ends of the chamber.

[0174] According to a further embodiment of this disclosure, the method further includes: generating one of a magnetic dipole field and a magnetic quadrupole field in the room using a saddle coil coupled to the room.

[0175] According to a further embodiment of this disclosure, the method further includes: using an intake system to adjust the inner surfaces of the chamber and the divertor.

[0176] According to a further embodiment of this disclosure, the intake system includes one of a titanium deposition system and a lithium deposition system.

[0177] According to a further embodiment of this disclosure, the method further includes: controlling the radial electric field distribution in the edge layer of the FRC plasma.

[0178] According to a further embodiment of this disclosure, a potential distribution is applied to a set of open flux surfaces of the FRC using a bias electrode.

[0179] According to a further embodiment of the present disclosure, the method further includes one of the following: injecting sphere-mark plasma having a magnetic flux greater than 20 mWb from the first and second sphere-mark injectors, or injecting sphere-mark plasma having a magnetic flux greater than about 25-30 mWb from the first and second sphere-mark injectors.

[0180] According to a further embodiment of this disclosure, a system for generating and maintaining a magnetic field having a field-reversed configuration (FRC) includes: a confinement chamber; first and second divertors coupled to the confinement chamber; first and second diameter-opposite ballmark injectors coupled to the first and second divertors for generating a ballmark plasma and translating the ballmark plasma toward the mid-plane of the confinement chamber; a plurality of neutral atom beam injectors coupled to the confinement chamber and oriented to inject neutral atom beams toward the mid-plane of the confinement chamber at an angle less than orthogonal to the longitudinal axis of the confinement chamber; a magnetic system including a plurality of quasi-DC coils positioned around the confinement chamber and the first and second divertors; a first set and a second set of quasi-DC mirror coils positioned between the confinement chamber and first and second forming sections; first and second mirror plugs positioned between the confinement chamber and the first and second divertors; a getter system coupled to the confinement chamber and the first and second divertors; 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 the confinement chamber and one or more of the first and second divertors; and two or more saddle coils coupled to the confinement chamber.

[0181] According to a further embodiment of this disclosure, a system for generating and maintaining a magnetic field having a field-reversed configuration (FRC) includes: a confinement chamber; first and second divertors coupled to the confinement chamber; first and second diameter-opposite ball-mark injectors coupled to the first and second divertors; a plurality of bias electrodes and one or more of first and second mirror plugs, wherein the one or more bias electrodes are positioned within the confinement chamber and one or more of the first and second divertors, and wherein the first and second mirror plugs are positioned between the confinement chamber and the first and second divertors; an intake system coupled to the confinement chamber and the first and second divertors; a plurality of neutral atom beam injectors coupled to the confinement chamber and oriented at an angle toward the midplane of the confinement chamber; and a magnetic system including a plurality of quasi-DC coils positioned around the confinement chamber and the first and second divertors, and a first set and a second set of quasi-DC mirror coils positioned between the confinement chamber and the first and second forming sections, wherein the system is configured to generate and maintain the FRC without decay when a neutral beam is injected into the plasma.

[0182] According to a further embodiment of this disclosure, the first and second ball mark injectors are configured to inject ball mark plasma toward the midplane of the chamber to merge and form FRC plasma.

[0183] According to a further embodiment of this disclosure, the first and second spherical mark injectors are configured to form and inject first and second spherical mark plasmas with anti-helical properties into a confinement chamber.

[0184] According to a further embodiment of this disclosure, the first and second ball mark injectors include a magnetized coaxial plasma gun (MCPG).

[0185] According to a further embodiment of this disclosure, the first and second ball mark injectors include a core bias coil system.

[0186] According to a further embodiment of this disclosure, the core of the core bias coil system is cast iron with a permeability of about 250.

[0187] According to a further embodiment of this disclosure, the core of the core bias coil system is about 99.9% Fe, and its permeability is equal to or greater than about 200,000.

[0188] According to a further embodiment of this disclosure, the first and second ball-shaped injectors are individually controllable.

[0189] According to a further embodiment of this disclosure, the first and second ball mark injectors are configured to inject more than one ball mark plasma into the confinement chamber in multiple pulses.

[0190] According to a further embodiment of this disclosure, the plurality of neutral beams are adjustable between a first beam energy and a second beam energy, wherein the second beam energy is different from the first beam energy, and wherein the beam energy of the plurality of neutral beams is switchable between the first beam energy and the second beam energy during the duration of the injection emission.

[0191] According to a further embodiment of the present disclosure, the bias electrode includes one or more of the following: one or more point electrodes positioned in the confinement chamber to contact open field lines; a set of annular electrodes between the confinement chamber and the first and second divertors; and a plurality of concentrically stacked electrodes positioned in the first and second divertors to charge a plurality of concentric flux layers.

[0192] According to a further embodiment of this disclosure, the system further includes: first and second diameter-opposite reverse field angle clamping forming sections, which are inserted between the first and second divertors and the confinement chamber.

[0193] According to a further embodiment of this disclosure, the system further includes: third and fourth divertors inserted between the first and second diameter-opposite reverse field angle compression forming sections and the confinement chamber.

[0194] However, the exemplary embodiments provided herein are intended merely as illustrative examples and are not intended to be limiting in any way.

[0195] All features, elements, components, functions, and steps described with respect to any embodiments provided herein are intended to be freely combined and can be 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 such feature, element, component, function, or step can be used with every other embodiment described herein unless expressly stated otherwise. This paragraph therefore serves at all times as the basis for reference and written support for claims that combine features, elements, components, functions, and steps from different embodiments, or features, elements, components, functions, and steps from one embodiment substituted with those from another embodiment, even if the following description does not expressly state in a particular context that such combinations or substitutions are possible. Explicitly recounting every possible combination and substitution would be cumbersome, especially considering that those skilled in the art will readily recognize the permissibility of each and every such combination and substitution upon reading this description.

[0196] In many instances, entities are described herein as coupled to other entities. It should be understood that the terms "coupled" and "connected" (or any form thereof) are used interchangeably herein, and in both cases, direct coupling between two entities (without any non-negligible (e.g., parasitic) intervening entities) and indirect coupling between two entities (with one or more non-negligible intervening entities) are common. Where entities are shown as directly coupled together, or described as coupled together without any intervening entities described, it should be understood that those entities may also be indirectly coupled together, unless the context clearly specifies otherwise.

[0197] While various modifications and alternative forms may be made to the embodiments, specific examples have been shown in the accompanying drawings and described in detail herein. However, it should be understood that these embodiments are not limited to the specific forms disclosed, but rather, they will cover all modifications, equivalents, and alternatives falling within the spirit of this disclosure. Furthermore, any feature, function, step, or element of the embodiments, as well as any negative limitations defining the scope by features, functions, steps, or elements not within the inventive step of the claims, may be recited in or added to the claims.< / n> < / n>

Claims

1. A method for generating and maintaining a magnetic field having a field reversal configuration (FRC), the method comprising the steps of: First and second spherical mark plasmas are axially injected from the opposing first and second spherical mark injectors toward the midplane of the confinement chamber; The first and second spherical Mark plasmas are merged in the confinement chamber and orbit the merged plasma to form an FRC. as well as The FRC is maintained at a 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.

2. The method according to claim 1, wherein, The first and second ball-shaped mark injectors comprise either a magnetized coaxial plasma gun (MCPG) or a core bias coil system.

3. The method according to claim 2, wherein, The steps of merging spherical mark plasmas and forming the FRC plasma include: performing anti-spiral spherical mark merging on the spherical mark plasmas injected from the first and second spherical mark injectors into the confinement chamber.

4. The method according to claim 2 or 3, wherein, The first and second ball-shaped mark injectors include a magnetized coaxial plasma gun (MCPG).

5. The method according to claim 2 or 3, wherein, The first and second ball-shaped mark injectors include a core biased coil system.

6. The method according to claim 5, wherein, The core of the core bias coil system is cast iron with a permeability of 250 H / m.

7. The method according to claim 5, wherein, The core of the iron core bias coil system is 99.9% Fe and has a permeability equal to or greater than 200,000 H / m.

8. The method according to claim 2 or 3, further comprising: The first ball-shaped marker injector and the second ball-shaped marker injector are controlled independently.

9. The method according to claim 8, wherein, The ball-mark plasma ejected from the first ball-mark injector is different from the ball-mark plasma ejected from the second ball-mark injector.

10. The method according to claim 2 or 3, further comprising: The FRC plasma is refueled along the geometric axis of the confinement chamber using one or more ball-mark plasmas from one or more of the first and second ball-mark injectors.

11. The method according to claim 10, wherein, The refeeding step includes: injecting one or more ball-mark plasmas from one or more of the first ball-mark injector and the second ball-mark injector into the FRC plasma in multiple pulses.

12. The method according to claim 2 or 3, further comprising: A multi-pulse spherical mark is formed and injected into the FRC plasma.

13. The method according to any one of claims 1 to 3, wherein, The step of injecting a beam of fast neutral atoms includes one of the following: adjusting the beam energy of a plurality of neutral beams between a first beam energy and a second beam energy, wherein the second beam energy is different from the first beam energy; or adjusting the beam energy of a plurality of neutral beams between a first beam energy and a second beam energy, wherein the second beam energy is different from the first beam energy, and wherein the second beam energy is higher than the first beam energy; or adjusting the beam energy of a plurality of neutral beams between a first beam energy and a second beam energy, wherein the second beam energy is different from the first beam energy, and wherein the plurality of neutral beams switch between the first beam energy and the second beam energy during the duration of the injection emission.

14. The method according to any one of claims 1 to 3, further comprising: A magnetic field is generated within the confinement chamber using a quasi-DC coil extending around the confinement chamber.

15. The method of claim 14, further comprising the following steps: The magnetic flux surface of the FRC is guided to a divertor coupled to the end of the confinement chamber.

16. The method of claim 15, further comprising the following steps: A quasi-DC coil, which is wound around the forming section and extends into the divertor, generates a magnetic field within the divertor.

17. The method of claim 16, further comprising the following steps: A mirror magnetic field is generated within the opposite ends of the confinement chamber using a quasi-DC mirror coil extending around the opposite ends of the confinement chamber.

18. The method of claim 14, further comprising the following steps: A saddle-shaped coil coupled to the confinement chamber generates either a magnetic dipole field or a magnetic quadrupole field within the confinement chamber.

19. The method according to any one of claims 15 to 18, further comprising the step of: The intake system is used to adjust the inner surfaces of the constraint chamber and the divertor.

20. The method according to claim 19, wherein, The air intake system includes either a titanium deposition system or a lithium deposition system.

21. The method according to any one of claims 1 to 3, further comprising the following steps: Controlling the radial electric field distribution in the edge layer of the FRC plasma.

22. The method according to claim 21, wherein, The step of controlling the radial electric field distribution in the edge layer of the FRC includes: applying a potential distribution to a set of open flux surfaces of the FRC using bias electrodes.

23. The method according to claim 2 or 3, further comprising: injecting sphere-mark plasma having a magnetic flux greater than 20 mWb from the first sphere-mark injector and the second sphere-mark injector, or injecting sphere-mark plasma having a magnetic flux greater than 25-30 mWb from the first sphere-mark injector and the second sphere-mark injector.

24. A system for generating and maintaining a magnetic field having a field-reversed configuration (FRC), the system comprising: Restraint chamber First and second divertors, coupled to the confinement chamber, First and second diameter-opposite ball-mark injectors are coupled to the first and second divertors to generate ball-mark plasma and to translate the ball-mark plasma axially toward the mid-plane of the confinement chamber. Multiple neutral atom beam injectors are coupled to the confinement chamber and oriented to inject neutral atom beams toward the midplane of the confinement chamber at an angle less than orthogonal to the longitudinal axis of the confinement chamber. A magnetic system comprising a plurality of quasi-DC coils positioned around the confinement chamber and the first and second divertors; a first set and a second set 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 confinement chamber and the first and second divertors. The intake system, coupled to the confinement chamber and the first and second divertors, 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 the confinement chamber and one or more of the first and second divertors, and Two or more saddle-shaped coils are coupled to the constraint chamber.

25. A system for generating and maintaining a magnetic field having a field-reversed configuration (FRC), the system comprising: Restraint chamber First and second divertors, coupled to the confinement chamber, First and second diameter-opposite ball-shaped injectors, coupled to the first and second divertors. A plurality of bias electrodes and one or more of first and second mirror plugs, wherein one or more bias electrodes are positioned within the constraint chamber and one or more of the first and second divertors, and wherein the first and second mirror plugs are positioned between the constraint chamber and the first and second divertors. The intake system, coupled to the confinement chamber and the first and second divertors, Multiple neutral atom beam injectors, coupled to the confinement chamber and oriented at an angle toward the midplane of the confinement chamber, and The magnetic system includes a plurality of quasi-DC coils positioned around the confinement chamber and the first and second divertors, and a first set and a second set of quasi-DC mirror coils positioned between the confinement chamber and the first and second forming sections. The system is configured to generate FRC when a neutral beam is injected into the plasma and to maintain the FRC without decay. The first and second ball-mark injectors are configured to inject ball-mark plasma axially toward the midplane of the confinement chamber to merge and form FRC plasma.

26. The system according to claim 25, wherein, The first and second ball-mark injectors are configured to form a first and second ball-mark plasma with anti-helical properties and inject them into the confinement chamber.

27. The system according to any one of claims 24 to 26, wherein, The first and second ball-shaped mark injectors include a magnetized coaxial plasma gun (MCPG).

28. The system according to any one of claims 24 to 26, wherein, The first and second ball-shaped mark injectors include a core biased coil system.

29. The system according to claim 28, wherein, The core of the core bias coil system is cast iron with a permeability of 250 H / m.

30. The system according to claim 28, wherein, The core of the iron core bias coil system is 99.9% Fe, and its permeability is equal to or greater than 200,000 H / m.

31. The system according to any one of claims 24 to 26, wherein, The first ball-shaped marker injector and the second ball-shaped marker injector are independently controllable.

32. The system according to claim 31, wherein, The first and second ball-mark injectors are configured to inject more than one ball-mark plasma into the confinement chamber in multiple pulses.

33. The system according to any one of claims 24 to 26, wherein, Multiple neutral beams are adjustable between a first beam energy and a second beam energy, wherein the second beam energy is different from the first beam energy, and wherein the beam energy of the multiple neutral beams is switchable between the first beam energy and the second beam energy during the duration of injection emission.

34. The system according to any one of claims 24 to 26, further comprising: The first and second diameter opposite-diameter reverse field angle clamping formation sections are inserted between the first and second divertors and the confinement chamber.

35. The system of claim 34, further comprising: The third and fourth divertors are inserted between the first and second diameter-opposite reverse field angle compression forming sections and the confinement chamber.

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