BR112019009744B1 - SYSTEM AND METHOD FOR GENERATING AND MAINTAINING A MAGNETIC FIELD WITH A REVERSE FIELD CONFIGURATION (FRC) - Google Patents

Abstract

The present invention relates to systems and methods that facilitate the formation and maintenance of FRCs with superior stability, as well as particle confinement, energy and flow and, more particularly, systems and methods that facilitate the formation and maintenance of FRCs with high energy energies. system and improved lift utilizing neutral beam injection and high harmonic fast wave electron heating.

Description

FIELD OF TECHNIQUE

[001] The embodiments described herein generally relate to magnetic plasma confinement systems having a field-reverse configuration (FRC) and, more particularly, to systems and methods that facilitate the formation and maintenance of FRCs with superior stability as well as confinement. of particles, energy and flow and, more particularly, to systems and methods that facilitate the heating of high harmonic fast wave electrons in FRCs.

BASICS OF THE INVENTION

[002] The field reverse configuration (FRC) belongs to a class of magnetic plasma confinement topologies known as compact toroids (CT). The FRC exhibits predominantly poloidal magnetic fields and has zero or small self-generated toroidal fields (see M. Tuszewski, Nucl. Fusion 28, 2033 (1988)). The attractions of such a configuration are its simple geometry for ease of construction and maintenance, a natural unrestricted diverter to facilitate energy extraction and ash removal, and very high β (β is the ratio of mean plasma pressure to mean of the magnetic field within the FRC), i.e. high power density. The high β nature is advantageous for economical operation and the use of advanced aneutronic fuels such as D-He3 and p-B11.

[003] The traditional method of forming a CRF uses field-inverted pinch θ technology (or choke point technology), producing high-density hot plasmas (see A. L. Hoffman and J. T. Slough, Nucl. Fusion 33, 27 (1993)). A variation of this is the translational trapping method, in which plasma created in a "theta-pinch" "source" is more or less immediately ejected from one end into a confinement chamber. The translational plasmoid is then clamped between two strong mirrors at the ends of the chamber (see, e.g., H. Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191 (1995)). Once in the confinement chamber, various heating and current drive methods can be applied such as beam injection (neutral or neutralized), rotating magnetic fields, RF or ohmic heating etc. This separation of source and confinement functions offers engineering advantages for potential future fusion reactors. FRCs have proven to be extremely robust, resilient to dynamic formation, translation, and violent capture events. Furthermore, they show a tendency to assume a preferred plasma state (see, e.g., H. Y. Guo, A. L. Hoffman, K. E. Miller, and L. C. Steinhauer, Phys. Rev. Lett. 92, 245001 (2004)). There has been significant progress in the last decade in the development of other formation methods: fusion The traditional method of forming a CRF uses field-inverted pinch technology, producing high-density hot plasmas ( see A. L. Hoffman and J. T. Slough, Nucl. Fusion 33, 27 (1993)). A variation of this is the translational trapping method, in which plasma created in a theta-pinch “source” is more or less immediately ejected from one end into a confinement chamber. The translational plasmoid is then clamped between two strong mirrors at the ends of the chamber (see, e.g., H. Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191 (1995)). Once in the confinement chamber, various heating and current drive methods can be applied such as beam injection (neutral or neutralized), rotating magnetic fields, RF or ohmic heating etc. This separation of source and confinement functions offers engineering advantages for potential future fusion reactors. FRCs have proven to be extremely robust, resilient to dynamic formation, translation, and violent capture events. Furthermore, they show a tendency to assume a preferred plasma state (see, e.g., H. Y. Guo, A. L. Hoffman, K. E. Miller, and L. C. Steinhauer, Phys. Rev. Lett. 92, 245001 (2004)). In the last decade, there has been significant progress in developing other FRC formation methods: fusing spheromaks with oppositely oriented helicities (see, e.g., Y. Ono, M. Inomoto, Y. Ueda, T. Matsuyama, and T. Okazaki , Nucl. Fusion 39, 2001 (1999)) and conducting current with rotating magnetic fields (RMF) (see, for example, IR Jones, Phys. Plasmas 6, 1950 (1999)), which also provides additional stability.

[004] Recently, the long-proposed collision fusion technique (see, e.g., DR Wells, Phys. Fluids 9, 1010 (1966)) has been significantly developed: two separate theta-pinches at opposite ends of a confinement chamber simultaneously generates two plasmoids and accelerates the plasmoids towards each other at high speed; they then collide in the center of the confinement chamber and fuse to form a composite FRC. In the successful construction and operation of one of the largest FRC experiments to date, the conventional collision fusion method produced stable, long-lived, high-flow, high-temperature FRCs (see, e.g., M. Binderbauer, H.Y. Guo , M Tuszewski et al., Phys. Rev. Lett. 105, 045003 (2010)).

[005] FRCs consist of a torule of closed field lines within a separatrix, and an annular edge layer on the open field lines outside the separatrix. The edge layer coalesces into jets beyond the length of the FRC, providing a natural divertor. The FRC topology coincides with that of a Field Reversed Mirror plasma. However, a significant difference is that the FRC plasma has a β of about 10. The inherent low internal magnetic field provides a certain population of inherent kinetic particles, that is, particles with large larmor radii, comparable to the smaller radius of the FRC. It is these strong kinetic effects that appear to contribute, at least partially, to the overall stability of past and present FRCs, such as those produced in the collision fusion experiment.

[006] Past FRC experiments tended to be dominated by convective losses with energy confinement largely determined by particle transport. Particles diffuse mainly radially out of the separatrix volume and are then lost axially into the edge layer. Consequently, FRC confinement depends on the properties of both closed and open field line regions. The particle diffusion time outside the separatrix scales as T± ~ a2/D± (a ~ rs/4, where rs is the central separatrix radius) and D± is an FRC diffusivity characteristic such as D± ~ 12.5 pie , with pie representing the gyration and ion radii, evaluated in an externally applied magnetic field. The TH edge layer particle confinement time is essentially an axial transit time in past FRC experiments. At steady state, the balance between particle radial and axial losses produces a separatrix density gradient length δ ~ (D±TII)1/2 The FRC particle confinement time scales (T±TII)1/2 for Previous FRCs that have substantial density in the separatrix (see, e.g., M. TUSZEWSKI, “Reverse Field Configurations,” Nucl. Fusion 28, 2033 (1988)).

[007] Another disadvantage of previous FRC system designs is the lack of efficient electron heating regimes other than neutral beam injection, which tends to have low electron heating efficiency due to the energy dampening mechanism in the electrons through collision. of electron ions.

[008] In light of the foregoing, it is therefore desirable to improve the maintenance of FRCs in order to use steady-state FRCs with high power systems as a pathway to a reactor core for the fusion of light cores for future power generation.

SUMMARY OF THE INVENTION

[009] The embodiments provided herein are directed to systems and methods that facilitate the formation and maintenance of FRCs with superior stability as well as particle, energy and flow confinement and, more particularly, to systems and methods that facilitate the formation and maintenance of FRCs with high system energies and improved lift and, more particularly, to systems and methods that facilitate the heating of high harmonic fast wave electrons in FRCs. According to one embodiment of the present disclosure, a method for generating and maintaining a magnetic field with a field reverse configuration (FRC) comprising forming an FRC around a plasma in a confinement chamber by injecting a plurality of neutral beams into the FRC plasma at an angle toward the midplane of the confinement chamber and launching fast high harmonic waves in radio frequency bands into the FRC plasma to heat electrons in the FRC plasma core.

[010] According to another embodiment of the present disclosure, the method also includes maintaining the FRC at or approximately a constant value without falling and raising the plasma electron temperature to above approximately 1.0 keV by launching fast high harmonic waves at radiofrequency bands for the FRC plasma at an angle from the middle through the plane of the confinement chamber.

[011] Heating electrons through fast high harmonic waves in radio frequency bands advantageously reduces the loss of fast ion charge exchange and improves plasma confinement, as well as increasing the efficiency of driving the plasma current, which increases with the electron temperature Te.

[012] According to another embodiment of the present disclosure, the method also comprises injecting compact toroidal (CT) plasmas from the first and second CT injectors into the FRC plasma at an angle toward the midplane of the confinement chamber, in that the first and second CT injectors are diametrically opposed on opposite sides of the midplane of the confinement chamber.

[013] According to an embodiment of the present disclosure, a system for generating and maintaining a magnetic field with a field reverse configuration (FRC) comprising a confinement chamber, first and second diametrically opposed FRC forming sections coupled to the confinement chamber first and second, first and second divertors coupled to the first and second forming sections, one or more of a plurality of plasma guns, one or more polarization electrodes, and first and second mirror plugs, wherein the plurality of plasma guns includes first and second axial plasma guns operatively coupled to the first and second divertors, the first and second forming and confinement chamber sections, wherein the one or more polarization electrodes are positioned within the one or more confinement chambers, first and second forming sections and first and second divertors and wherein the first and second mirror plugs are positioned between the first and second forming sections and the first and second divertors, a joint 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 angled toward a midplane of the confinement chamber, a magnetic system comprising a plurality of quasi-dc (quasi-dc) coils positioned at around the confinement chamber, the first and second forming sections, and the first and second divertors, and first and second sets of quasi-dc mirror coils positioned between the first and second forming sections and the first and second divertors, and one or more antennas coupled to the confinement chamber to launch fast high harmonic waves in radio frequency bands for heating electrons in the FRC plasma core within the confinement chamber.

[014] According to another embodiment of the present disclosure, the system also comprises first and second compact torus (CT) injectors coupled to the confinement chamber at an angle toward the midplane of the confinement chamber, wherein the first and second CT injectors are diametrically opposed on opposite sides of the midplane of the confinement chamber.

[015] The systems, methods, characteristics and advantages of the exemplary modalities will be or will become apparent to one skilled in the art after analysis of the following figures and detailed description. All such additional methods, features and advantages are intended to be included in this specification and to be protected by the appended claims. It is also intended that the claims are not limited to requiring the details of exemplary embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

[016] The attached drawings, which are included as part of the present report, illustrate the example embodiments at present and, together with the general description provided above and the detailed description of the example embodiments provided below, serve to explain and teach the principles of the present modalities.

[017] Figure 1 illustrates particle confinement in the present FRC system under a high performance FRC regime (HPF) versus under a conventional FRC regime (CR), and versus other conventional FRC experiments.

[018] Figure 2 illustrates the components of the present FRC system and the magnetic topology of a CRF produced in the present FRC system.

[019] Figure 3A illustrates the basic layout of the present FRC system, viewed from above, including the preferred arrangement of the central confinement vessel, forming section, divertors, neutral beams, electrodes, plasma guns, mirror plugs and injector. granule.

[020] Figure 3B illustrates the central confining container seen from above and showing the neutral beams arranged at an angle normal to the greatest axis of symmetry in the central confining container.

[021] Figure 3C illustrates the central confining vessel viewed from above and showing the neutral beams arranged at a smaller than normal angle to the major axis of symmetry in the central confining vessel and directed to inject particles toward the midplane of the central containment container.

[022] Figures 3D and 3E illustrate top and perspective views, respectively, of the basic arrangement of an alternative embodiment of the present FRC system, including the preferred arrangement of the central confinement vessel, forming section, internal and external divertors, neutral beams arranged at a smaller angle than normal to the main axis of symmetry in the central confining vessel, electrodes, plasma guns and mirror plugs.

[023] Figure 4 illustrates a schematic of the components of a pulsed power system for the forming sections.

[024] Figure 5 illustrates an isometric view of an individual pulsed power formation skid.

[025] Figure 6 illustrates an isometric view of one of a forming tube assembly.

[026] Figure 7 illustrates a partial isometric sectional view of the neutral beam system and key components.

[027] Figure 8 illustrates an isometric view of the neutral beam arrangement in the confinement chamber.

[028] Figure 9 illustrates a partial sectional isometric view of a preferred arrangement of the Ti and Li junction systems.

[029] Figure 10 illustrates a partial isometric sectional view of a plasma gun installed in the diverter chamber. Also shown are the associated magnetic mirror plug and a set of diverter electrodes.

[030] Figure 11 illustrates a preferred layout of an annular polarization electrode at the axial end of the confinement chamber.

[031] Figure 12 illustrates the evolution of the excluded flux radius in the FRC system obtained from a series of external diamagnetic loops in the two field reverse theta pinch formation sections and magnetic probes embedded within the central metal confinement chamber. The time is measured from the instant of synchronized field reversal at the forming sources, and the distance z is given relative to the axial plane of the machine.

[032] Figures 13, 13A, 13, 13 and 13D illustrate data from a representative non-sustained, non-HPF discharge in the present FRC system. Shown as functions of time are (Figure 13A) midplane excluded flux radius, (Figure 13B) 6 chord integrated line density from the CO2 midplane interferometer, (Figure 13C) inverted Abel density radial profiles from the CO2 interferometer and (Figure 13D) total pressure equilibrium plasma temperature.

[033] Figure 14 illustrates the axial profiles of the excluded flow at selected times for the same discharge of the current FRC system shown in Figure 13A, 13B, 13C and 13D.

[034] Figure 15 illustrates an isometric view of the saddle coils mounted outside the confinement chamber.

[035] Figures 16A, 16B, 16C and 16D illustrate the correlations between the useful life of the FRC and the pulse length of the injected neutral beams. As shown, longer beam pulses produce longer FRCs.

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

[037] Figures 18A, 18B, 18C and 18D illustrate data from a representative HPF, non-sustained discharge in the present FRC system. Shown as functions of time are (Figure 18A) midplane excluded flux radius, (Figure 18B) 6 line-integrated density strings from the CO2 midplane interferometer, (Figure 18C) inverted Abel density radial profiles from the CO2 interferometer and (Figure 18D) total pressure equilibrium plasma temperature.

[038] Figure 19 illustrates the confinement of the flow as a function of the electron temperature (Te). Represents a graphical representation of a recently established upscaling regime for HPF discharges.

[039] Figure 20 illustrates the FRC lifetime corresponding to the pulse length of angled and non-angled injected neutral beams.

[040] Figures 21A, 21B, 21C, 21D and 21E illustrate the pulse length of angle-injected neutral beams and the lifetime of FRC plasma parameters of plasma radius, plasma density, plasma temperature and flow corresponding to the pulse length of the angular injected neutral beams.

[041] Figures 22A and 22B illustrate the basic layout of a compact toroidal (CT) injector.

[042] Figures 23A and 23B illustrate the central confinement container showing the CT injector mounted therein.

[043] Figures 24A and 24B illustrate the basic layout of an alternative embodiment of the CT injector having a bypass tube coupled to it.

[044] Figure 25 illustrates the central confining vessel viewed from above and showing the neutral beams arranged at a smaller angle than normal to the major axis of symmetry in the central confining vessel and directed to inject particles towards the midplane of the central containment vessel and showing antennas from which high harmonic fast waves propagate at a smaller than normal angle to the major axis of symmetry in the central containment vessel and are directed to propagate from the midplane of the containment vessel central for plasma electron heating.

[045] Figures 26A and 26B illustrate a complete radial density profile and a complete radial electron temperature profile of an FRC plasma of the present FRC system.

[046] Figures 27A to 27D illustrate radial profiles of system equilibrium and characteristic frequency in the midplane (Z = 0) of the present FRC system.

[047] Figures 28A to 28C illustrate observations of energy absorption and mode conversion under microwave electron heating conditions at 8GHz in an FRC plasma of the present FRC system.

[048] Figures 29A to 29F illustrate observations of energy absorption and mode conversion under microwave electron heating conditions at 50GHz in an FRC plasma of the present FRC system.

[049] Figures 30A to 30C illustrate observations of energy absorption under 0.5 GHz whistler wave electron heating conditions in an FRC plasma of the present FRC system.

[050] Figure 31 illustrates a density and wave propagation profile in an FRC plasma of the present FRC system.

[051] Figure 32 illustrates a poloidal flow profile and wave propagation in an FRC plasma of the present FRC system.

[052] Figure 33 illustrates an exemplary density profile and wave propagation trajectory in an FRC plasma of the present FRC system.

[053] Figure 34 illustrates an exemplary w/wci [D] profile and wave propagation trajectory in an FRC plasma of the present FRC system.

[054] Figure 35 illustrates the exemplary power damping with the wave propagation distance in an FRC plasma of the present FRC system.

[055] Figure 36 illustrates an exemplary energy absorption profile in an FRC plasma of the present FRC system.

[056] Figures 37A and 37B illustrate exemplary radial profiles of the energy density in an FRC plasma of the present FRC system.

[057] Figure 38 illustrates an exemplary 2D profile of the damping power density in an FRC plasma of the present FRC system.

[058] Figure 39 illustrates an exemplary power damping profile in an FRC plasma of the present FRC system.

[059] Figure 40 illustrates an exemplary finite ion Larmor radius profile in an FRC plasma of the present FRC system.

[060] Figure 41 illustrates an exemplary energy absorption profile in an FRC plasma of the present FRC system.

[061] Figure 42 illustrates an exemplary profile of an FRC plasma of the present FRC system.

[062] It should be noted that numbers are not necessarily drawn to scale and that elements of similar structures or functions are generally represented by similar reference numbers for illustrative purposes throughout the figures. It should also be noted that the figures are intended only to facilitate the description of the various embodiments described herein. The numbers do not necessarily describe all aspects of the teachings disclosed herein and do not limit the scope of the claims.

DETAILED DESCRIPTION

[063] The modalities provided here are directed to systems and methods that facilitate the formation and maintenance of FRCs with superior stability, as well as particle, energy and flow confinement. Some of the present embodiments are directed to systems and methods that facilitate the formation and maintenance of FRCs with high energies and temperatures and system support using neutral beam injection and high harmonic wave electron heating.

[064] Representative examples of the embodiments described herein, which examples utilize many of these features and additional teachings, separately and in combination, will now be described in greater detail with reference to the accompanying drawings. This detailed description is intended simply to teach one skilled in the art more details for practicing preferred aspects of the present teachings and is not intended to limit the scope of the invention. Accordingly, the combinations of features and steps disclosed in the following detailed description may not be necessary to practice the invention in the broadest sense and, rather, are taught merely to describe particularly representative examples of the present teachings.

[065] Furthermore, the various features of the representative examples and the dependent claims may be combined in ways that are not specifically enumerated specifically, in order to provide additional useful embodiments of the present teachings. Furthermore, it is expressly noted that all features disclosed in the description and/or claims are intended to be disclosed separately and independently from one another for purposes of original disclosure, as well as for the purpose of narrowing down the claimed subject matter independent of the compositions of the features. in the embodiments and/or claims. It is also expressly noted that all ranges of values or indications of groups of entities disclose all possible intermediate values or intermediate entities for purposes of original disclosure as well as for the purpose of narrowing the subject matter claimed.

[066] Before turning to systems and methods that facilitate the heating of harmonic fast-wave electrons in FRC plasmas, a commentary is provided on systems and methods for forming and maintaining high-performance FRCs with superior stability as well as superior confinement of particles, energy, and flow over conventional FRCs, as well as a commentary on systems and methods for forming and maintaining high-performance FRCs at or about a constant value without decreasing. These high-performance FRCs provide a pathway for a whole range of applications, including compact neutron sources (for medical isotope production, nuclear waste remediation, materials research, radiography and neutron tomography), compact photon sources (for production and chemical processing), bulk separation and enrichment systems, and reactor cores for the fusion of light nuclei for future energy generation.

[067] Various auxiliary systems and modes of operation were explored to assess whether there is a superior confinement regime in FRCs. These efforts have led to innovative discoveries and the development of a high-performance FRC paradigm described here. In accordance with this new paradigm, current systems and methods combine a number of new ideas and means to dramatically improve FRC confinement as illustrated in Figure 1, as well as provide stability control without negative side effects. As discussed in greater detail below, Figure 1 represents particle confinement in an FRC 10 system described below (see Figures 2 and 3), operating under a High Performance FRC (HPF) regime to form and maintain a FRC versus operating according to a conventional CR to form and maintain a CRF, and against particle confinement according to conventional regimes to form and maintain a CRF used in other experiments. This disclosure will outline and detail the FRC 10 system's innovative individual components and methods, as well as their collective effects.

FRC System Vacuum System

[068] Figures 2 and 3 represent a schematic system of the present FRC 10. The FRC system 10 includes a central confinement container 100 surrounded by two diametrically opposed inverted field forming sections theta pinch 200 and, in addition to the forming sections 200 , two 300 diversion chambers to control neutral density contamination and impurity. The present FRC 10 system is constructed to accommodate ultra-high vacuum and operate at typical base pressures of 10-8 torr. Such vacuum pressures require the use of double-pumped mating flanges between mating components, metal rings, high-purity inner walls, as well as careful initial conditioning of all parts prior to assembly, such as physical and chemical cleaning followed by 24 hours. vacuum cooking at 250°C and cleaning with hydrogen glow discharge.

[069] The theta pinch inverted field formation sections 200 are standard inverted field theta pinches (FRTPs), albeit with an advanced pulsed power formation system commented in detail below (see Figures 4 to 6). Each 200 forming section is made from standard opaque industrial grade quartz tubes that feature an inner lining of 2 millimeters of ultrapure quartz. The confinement chamber 100 is made of stainless steel to allow for a plurality of radial and tangential ports; It also serves as a flux conservator on the time scale of the experiments described below and limits fast magnetic transients. Vacuums are created and maintained within the FRC 10 system with a suite of dry scroll grinding pumps, molecular turbocharger pumps and cryo pumps.

Magnetic System

[070] The magnetic system 400 is illustrated in Figures 2 and 3. Figure 2, among other features, illustrates an FRC magnetic flux and density contours (as functions of radial and axial coordinates) belonging to a FRC 450 that can be produced by the FRC 10 system. These contours were obtained by a 2-D resistive Hall-MHD numerical simulation using code developed to simulate systems and methods corresponding to the FRC 10 system, and are in agreement with measured experimental data. As seen in Figure 2, the FRC 450 within a separatrix 561 consists of a torus of closed field lines on the inside 453 of the FRC 450 within a separatrix 451, and of an annular edge layer 456 on the open field lines 452 outside. of the separator 451. The edge layer 456 mixes into jets 454 beyond the FRC length, providing a natural diverter.

[071] The main magnetic system 410 includes a series of quasi-dc coils 412, 414 and 416 that are situated at particular axial positions along the components, i.e. along the confinement chamber 100, the forming sections 200 and of the divertors 300, of the FRC system 10. The quasi-dc coils 412, 414 and 416 are powered by quasi-dc switching power supplies and produce basic magnetic polarization fields of about 0.1 T in the confinement chamber 100, in the forming sections 200 and divertors 300. In addition to the quasi-dc coils 412, 414, and 416, the main magnetic system 410 includes quasi-dc mirror coils 420 (powered by switching supplies) between each end of the confinement chamber 100 and adjacent forming sections 200. Quasi-dc mirror coils 420 provide magnetic mirror ratios of up to 5 and can be independently energized for balance shaping control. Additionally, mirror plugs 440 are positioned between each of the forming sections 200 and divertors 300. Mirror plugs 440 comprise compact quasi-dc mirror coils 430 and mirror plug coils 444. -cc 430 include three coils 432, 434 and 436 (powered by switching sources) that produce additional guide fields to focus the magnetic flux surfaces 455 to the small diameter passage 442 passing through the mirror plug coils 444. Mirror plug coils 444, which surround small diameter passage 442 and are powered by LC pulsed power circuits, produce strong magnetic mirror fields of up to 4 T. The purpose of this coil arrangement is to tightly wind and guide surfaces of magnetic flux 455 and end-flow plasma jets 454 in the remote chambers 310 of the divertors 300. Finally, a set of saddle coil “antennas” 460 (see Figure 15) is located outside the confinement chamber 100, two of each side of the midplane, and are powered by energy sources. The 460 saddle coil antennas can be configured to provide a quasi-static dipole or quadrupole magnetic field of about 0.01 T to control rotational instabilities and/or electron current control. The 460 saddle coil antennas can flexibly provide magnetic fields that are symmetrical or non-symmetrical with respect to the midplane of the machine, depending on the direction of the applied currents.

Pulsed Energy Formation System

[072] Pulsed power formation systems 210 operate on a modified theta-pinch principle. There are two systems that power one of the forming sections 200. Figures 4 through 6 illustrate the main building blocks and arrangement of the forming systems 210. The forming system 210 is comprised of a modular pulsed power arrangement consisting of individual units (= skids) 220 that energize a subset of coils 232 of a set of loops 230 (= strips) that surround the formation of quartz tubes 240. Each skid is comprised of capacitors 221, inductors 223, fast high current switches 225 and associated trigger 222 and discharge circuit 224. In total, each forming system 210 stores between 350 to 400 kJ of capacitive energy, which provides up to 35 GW of power to form and accelerate the FRCs. Coordinated operation of these components is achieved through a prior art firing control system 222 and 224 that allows synchronized timing between the forming systems 210 in each forming section 200 and minimizes switching jitter to tens of nanoseconds. The advantage of this modular design is its flexible operation: FRCs can be formed in situ and then accelerated and injected (= static forming) or formed and accelerated at the same time (= dynamic forming).

Neutral Beam Injectors

[073] Neutral atom beams 600 are deployed in the FRC system 10 to provide heating and current drive, as well as to develop rapid particle pressure. As shown in Figures 3A, 3B and 8, individual beam lines comprising neutral atom beam injector systems 610 and 640 are located around the central confinement chamber 100 and inject fast particles tangentially to the FRC plasma (and perpendicular or at an angle normal to the main axis of symmetry in the central confinement vessel 100) with an impact parameter such that the target capture zone is well within the separator 451 (see Figure 2). Each 610 and 640 injector system is capable of injecting up to 1 MW of neutral beam power into the FRC plasma with particle energies between 20 and 40 keV. The 610 and 640 systems are based on positive ion multi-aperture extraction sources and utilize geometric focusing, inertial cooling of the ion extraction grids, and differential pumping. In addition to using different plasma sources, the 610 and 640 systems are primarily differentiated by their physical design to suit their respective mounting locations, producing side and top injection capabilities. Typical components of these neutral beam injectors are specifically illustrated in Figure 7 for side injector systems 610. As shown in Figure 7, each individual neutral beam system 610 includes an RF plasma source 612 at an input end (this is replaced by an arc source in systems 640) with a magnetic screen 614 covering the end. An optical ion source and acceleration grids 616 is coupled to a plasma source 612 and a gate valve 620 is positioned between the optical source and acceleration grids 616 and a neutralizer 622. A deflection magnet 624 and an ion discharge 628 are located between the neutralizer 622 and a aiming device 630 at the exit end. A cooling system comprises two 634 cryogenic coolers, two 636 cryogenic panels and a 638 LN2 cover. This flexible design allows operation over a wide range of FRC parameters.

[074] An alternative configuration for the neutral atom beam injectors 600 is to inject the fast particles tangentially to the FRC plasma, but with an angle A of less than 90° relative to the main axis of symmetry in the central confinement vessel 100 These types of beam injector orientations 615 are shown in Figure 3C. Furthermore, the beam injectors 615 may be oriented such that the beam injectors 615 on each side of the midplane of the central confinement container 100 inject their particles toward the midplane. Finally, the axial position of these beam systems 600 can be chosen closer to the midplane. These alternative injection modalities facilitate a more central supply option, which provides better beam coupling and greater retention efficiency of the injected fast particles. Furthermore, depending on the axial angle and position, this arrangement of the 615 beam injectors allows for more direct and independent control of the axial elongation and other characteristics of the FRC 450. For example, injecting the beams at a shallow angle A relative to the main axis of the container will create an FRC plasma with greater axial extension and lower temperature, while choosing a more perpendicular angle A will lead to an axially shorter but hotter plasma. In this way, the injection angle A and the location of the beam injectors 615 can be optimized for different purposes. Furthermore, such angulation and positioning of the beam injectors 615 may allow beams of higher energy (which is generally more favorable for depositing more power with less beam divergence) to be injected into lower magnetic fields than would be required to intercept such beams. . This is due to the fact that it is the azimuthal component of the energy that determines the fast ion orbit scale (which becomes progressively smaller as the injection angle relative to the main axis of symmetry of the container is reduced at constant beam energy ). Furthermore, injection angled toward the midplane and with axial beam positions close to the midplane improves plasma beam coupling, even as the FRC plasma shrinks or contracts axially during the injection period.

[075] Returning to Figures 3D and 3E, another alternative configuration of the FRC system 10 includes the internal divertors 302 in addition to the angled beam injectors 615. The internal divertors 302 are positioned between the forming sections 200 and the confinement chamber 100, and are configured and operate substantially similar to the external divertors 300. The internal divertors 302, which include fast-switching magnetic coils, are effectively inactive during the forming process to allow the forming FRCs to pass through the internal divertors 302 as the FRCs of formation translate to the midplane of the confinement chamber 100. Once the formation FRCs pass through the internal divertors 302 into the confinement chamber 100, the internal divertors are activated to operate in substantially the same manner as the external divertors and isolate the confinement chamber 100 from the forming sections 200.

Granule Injector

[076] To provide a means to inject new particles and better control the FRC particle inventory, a 12-barrel 700 bead injector (see, for example, I. Vinyar et al., “Bead Injectors Developed at PELIN for JET , TAE and HL-2A, “Proceedings of the 26th Fusion Science and Technology Symposium, 9/27 to 1/10 (2010)) is used in the FRC 10 system. Figure 3 illustrates the layout of the 700 bead injector in the FRC 10 system. Cylindrical granules (D ~ 1 mm, L ~ 1 - 2 mm) are injected into the FRC with a speed in the range of 150 to 250 km/s. Each individual bead contains about 5 x 1019 hydrogen atoms, which is comparable to the FRC particle inventory.

Meeting Systems

[077] It is well known that neutral halo gas is a serious problem in all containment systems. Charge exchange and recycling processes (release of cold impurity material from the wall) can have a devastating effect on energy and particle confinement. Furthermore, any significant density of neutral gas at or near the edge will lead to immediate losses or at least severe reduction in the lifetime of large-orbit (high-energy) injected particles (large-orbit refers to particles with orbits on the FRC topology scale or at least orbital radius much larger than the characteristic magnetic field gradient length scale) - a fact that is detrimental to all energetic plasma applications, including fusion via auxiliary beam heating.

[078] Surface conditioning is a means by which the harmful effects of neutral gas and impurities can be controlled or reduced in a containment system. To this end, the FRC system 10 provided herein employs titanium and lithium deposition systems 810 and 820 that coat the plasma-facing surfaces of the confinement chamber (100) and divertors 300 and 302 with films (tens of micrometers in diameter). thickness) of Ti and/or Li. Coatings are achieved through vapor deposition techniques. Solid Li and/or Ti are evaporated and/or sublimated and sprayed onto nearby surfaces to form the coatings. The sources are atomic furnaces with guide nozzles (in the case of Li) 822 or heated spheres of solid with guide shroud (in the case of Ti) 812. Li evaporator systems typically operate in continuous mode while Ti sublimators are operated intermittently between plasma operation. The operating temperatures of these systems are above 600°C to achieve fast deposition rates. To achieve good wall coverage, multiple strategically located evaporator/sublimator systems are required. Figure 9 details a preferred arrangement of receiving deposition systems 810 and 820 in the FRC system 10. The coatings act as collection surfaces and effectively pump out atomic and molecular hydrogen species (H and D). The coatings also reduce other typical impurities such as carbon and oxygen to negligible levels.

Mirror Plugs

[079] As stated above, the FRC system 10 employs sets of mirror coils 420, 430, and 444 as shown in Figures 2 and 3. A first set of mirror coils 420 is located at the two axial ends of the confinement chamber 100 and is energized independently of the DC confinement, forming, and diverter coils 412, 414, and 416 of the main magnetic system 410. The first set of mirror coils 420 primarily helps direct and axially contain the FRC 450 during melting and provides shaping control. balance during support. The first set of mirror coils 420 produces nominally higher magnetic fields (about 0.4 to 0.5 T) than the central confining field produced by the central confining coils 412. The second set of mirror coils 430, which includes three compact quasi-dc mirror coils 432, 434 and 436, is located between the forming sections 200 and the divertors 300 and are driven by a common switching power supply. Mirror coils 432, 434, and 436, together with the more compact pulsed mirror plug coils 444 (powered by a capacitive power supply) and physical constriction 442 form mirror plugs 440 that provide a conductance path of low, narrow gas with very high magnetic fields (between 2 to 4 T with rise times of about 10 to 20 ms). The more compact pulsed mirror coils 444 are of compact radial dimensions, 20 cm diameter and similar length, compared to the meter plus scale bore and plate design of the confining coils 412, 414 and 416. The purpose of the mirror plugs 440 are multiple: (1) Coils 432, 434, 436, and 444 tightly enclose and guide magnetic flux surfaces 452 and end-flow plasma jets 454 into remote diverter chambers 300. This ensures that exhaust particles reach the divertors 300 appropriately and that there are continuous flow surfaces 455 that trace from the open field line 452 of the central region of the FRC 450 all the way to the divertors 300. (2) The physical constrictions 442 in the FRC system 10, through which the coils 432, 434, 436 and 444 allow the passage of the magnetic flux surfaces 452 and the plasma jets 454, provide an impediment to the flow of neutral gas from the plasma guns 350 that sit on the divertors 300. In the same vein, the constrictions 442 prevent the backflow of gas from the formation sections 200 to the divertors 300, thus reducing the number of neutral particles that must be introduced throughout the FRC system 10 when starting a FRC. (3) The strong axial mirrors produced by coils 432, 434, 436 and 444 reduce axial particle losses and thus reduce the diffusivity of parallel particles at open field lines.

[080] In the alternative configuration shown in Figures 3D and 3E, a set of low-profile retention coils 421 is positioned between the internal divertors 302 and the formation sections 200.

Axial Plasma Guns

[081] The plasma flows from guns 350 mounted in the diverter chambers 310 of the divertors 300 are intended to improve the stability and performance of the neutral beam. The guns 350 are mounted on the shaft within the chamber 310 of the divertors 300 as illustrated in Figures 3 and 10 and produce plasma flowing along the open flow lines 452 in the diverter 300 and toward the center of the confinement chamber 100. The guns 350 operate on a high-density gas discharge in a stack channel and are designed to generate several kiloamperes of fully ionized plasma for 5 to 10 ms. Guns 350 include a pulsed magnetic coil that matches the output plasma current with the desired plasma size in confinement chamber 100. Technical parameters of guns 350 are characterized by a channel with an outer diameter of 5 to 13 cm and up to approximately 10 cm in internal diameter and provide a discharge current of 10-15 kA at 400-600 V with an internal magnetic field between 0.5 and 2.3 T.

[082] Gun plasma streams can penetrate the magnetic fields of the mirror plugs 440 and flow into the forming section 200 and confinement chamber 100. The efficiency of plasma transfer through the mirror plug 440 increases with decreasing distance between gun 350 and plug 440 and making plug 440 wider and shorter. Under reasonable conditions, each 350 gun can deliver approximately 1022 protons/s through the 2 to 4 T of 440 mirror plugs with elevated ion and electron temperatures of about 150 to 300 eV and about 40 to 50 eV, respectively. The 350 guns provide significant replenishment of the 456 FRC edge layer, and improved total FRC particle confinement.

[083] To further increase the density of the plasma, a gas box could be used to blow additional gas into the plasma stream from the guns 350. This technique allows for a several-fold increase in the density of the injected plasma. In the FRC system 10, a gas box installed on the diverter side 300 of the mirror plugs 440 improves FRC 456 edge layer replenishment, FRC 450 formation, and plasma line attachment.

[084] Considering all the adjustment parameters discussed above and also considering that operation with just one or both guns is possible, it is clear that a wide spectrum of operating modes is accessible.

Polarization Electrodes

[085] Electrical polarization of open flow surfaces can provide radial potentials that give rise to E x B azimuthal motion that provides a control mechanism, analogous to turning a knob, to control the rotation of the open field line plasma, as well as the actual core of the FRC 450 via speed shear. To carry out this control, the FRC 10 system employs several electrodes strategically placed in various parts of the machine. Figure 3 shows the polarization electrodes positioned in preferred locations within the FRC 10 system.

[086] In principle, there are 4 classes of electrodes: (1) point electrodes 905 in the confinement chamber 100 that contact particular open field lines 452 at the edge of the FRC 450 to provide local charging, (2) annular electrodes 900 between confinement chamber 100 and forming sections 200 to load far-edge flow layers 456 in an azimuthally symmetrical fashion, (3) concentric electrode stacks 910 on divertors 300 to load multiple concentric flow layers 455 (wherein layer selection is controllable by adjusting the coils 416 to adjust the magnetic field of the diverter to terminate the desired flux layers 456 at the appropriate electrodes 910) and finally (4) the anodes 920 (see Figure 10) of the spray guns themselves. plasma 350 (which intersect internal open flow surfaces 455 near the FRC separator 450). Figures 10 and 11 show some typical designs for some of them.

[087] In all cases, these electrodes are driven by power sources or pulsed at voltages up to about 800 V. Depending on the size of the electrode and which flow surfaces are intercepted, currents can be traced in the kilo-amperage range .

Non-Sustained Operation of the FRC System - Conventional Regime

[088] Standard plasma formation in the FRC 10 system follows the well-developed reverse field theta-pinch technique. A typical process for starting an FRC begins by driving quasi-dc coils 412, 414, 416, 420, 432, 434, and 436 into steady-state operation. The RFTP pulsed power circuits of the pulsed power forming systems 210 then drive the fast pulse inverted magnetic field coils 232 to create a temporary inverted bias of about -0.05 T in the forming sections 200. At this point, a predetermined amount of neutral gas at 9 to 20 psi is injected into the two formation volumes defined by the quartz tube chambers 240 of the formation sections (north and south) 200 through a set of azimuthal-oriented vaporization valves on the flanges located at the outer ends of the forming sections 200 Next, a small RF field (~hundreds of kilohertz) is generated from an array of antennas on the surface of the quartz tubes 240 to create pre-ionization in the form of local regions of ionization of seeds within neutral gas columns. This is followed by applying a theta ringing modulation to the current driving the fast-pulsing inverted magnetic field coils 232, which leads to a more global pre-ionization of the gas columns. Finally, the main pulsed power banks of the pulsed power formation systems 210 are driven to drive pulsed fast inverted magnetic field coils 232 to create a forward bias field of up to 0.4 T. This step can be sequenced in time. such that the polarized field is generated uniformly along the length of the forming tubes 240 (static forming) or such that a consecutive peristaltic field modulation is achieved along the axis of the forming tubes 240 (dynamic forming).

[089] Throughout this formation process, the real field inversion in the plasma occurs quickly, in about 5 μs. The multi-gigawatt pulsed power delivered to the forming plasma readily produces hot FRCs that are then ejected from the forming sections 200 through the application of a sequenced modulation of the direct magnetic field (magnetic peristalsis) or temporarily increased currents in the last coils of coil sets. 232 near the axial outer ends of the forming tubes 210 (forming an axial magnetic field gradient that points axially toward the confinement chamber 100). The two formation FRCs (north and south) thus formed and accelerated expand into the larger diameter confinement chamber 100, where quasi-dc coils 412 produce a forward-biased field to control radial expansion and provide flow. external magnetic balance.

[090] Once the north and south formation FRCs come close to the midplane of the confinement chamber 100, the FRCs collide. During the collision, the axial kinetic energies of the north and south forming FRCs are largely thermal as the FRCs merge into a single FRC 450. A large suite of plasma diagnostics is available in the confinement chamber 100 to study the equilibria of the FRC 450. Typical operating conditions in the FRC 10 system produce composite FRCs with separation radii of about 0.4 m and about 3 m in axial extension. Other features are external magnetic fields of around 0.1 T, plasma densities of around 5x1019 m-3 and total temperature in the plasma of up to 1 keV. Without any sustain, i.e. without conducting heat and/or current through neutral beam injection or other auxiliary means, the lifetime of these FRCs is limited to about 1 ms, the decay time of the inherent characteristic configuration. .

Experimental Data from Non-Sustained Operation - Conventional Regime

[091] Figure 12 shows a typical time evolution of the excluded flux radius, rΔΦ, which approaches the separatrix radius, rs, to illustrate the dynamics of the FRC 450 theta-pinch merger process. south) individual plasmoids are produced simultaneously and then accelerated out of the respective formation sections 200 at a supersonic speed, vZ ~ 250 km/s, and collide near the midplane at z = 0. During the collision, the plasmoids compress axially , followed by rapid radial and axial expansion, before eventually merging to form an FRC 450. The radial and axial dynamics of the FRC 450 merger are evidenced by detailed density profile measurements and bolometer-based tomography.

[092] Data from a representative non-sustained discharge of the FRC 10 system are shown as functions of time in Figures 13A, 13B, 13C and 13D. The FRC starts at t = 0. The excluded flow radius in the axial midplane of the machine is shown in Figure 13A. This data is obtained from an array of magnetic probes, located within the stainless steel wall of the confinement chamber, which measure the axial magnetic field. The steel wall is a good flow conservator on the time scales of this discharge.

[093] The line-integrated densities are shown in Figure 13B, from a 6-string CO2/He-Ne interferometer located at z = 0. Considering the vertical displacement (y) of the FRC, measured by bolometric tomography, the inversion of Abel produces the density contours of Figures 13C. After a few axial and radial squirts during the first 0.1 ms, the FRC settles into a hollow density profile. This profile is quite flat, with substantial on-axis density, as required by typical 2-D FRC equilibria.

[094] The total plasma temperature is shown in Figure 13D, derived from pressure equilibrium and fully consistent with Thomson scattering and spectroscopy measurements.

[095] Analysis of the entire set of excluded flows indicates that the shape of the FRC separatrix (approximated by the axial profiles of the excluded flow) gradually evolves from racetrack to elliptical. This evolution, shown in Figure 14, is consistent with a gradual magnetic reconnection from two to a single FRC. In fact, rough estimates suggest that at this particular instant about 10% of the FRC's two initial magnetic fluxes reconnect during the collision.

[096] The FRC length shrinks steadily from 3 to about 1 m during the lifetime of the FRC. This shrinkage, visible in Figure 14, suggests that predominantly convective energy loss dominates the confinement of the FRC. As the plasma pressure inside the separatrix decreases faster than the external magnetic pressure, the magnetic field line tension in the end regions compresses the FRC axially, restoring axial and radial balance. For the discharge discussed in Figures 13 and 14, the magnetic flux, particle inventory, and thermal energy of the FRC (about 10 mWb, 7x1019 particles, and 7 kJ, respectively) decrease by approximately an order of magnitude in the first millisecond, when the discharge balances. FRC appears to decrease.

Sustained Operation - HPF Regime

[097] The examples in Figures 12 to 14 are characteristic of decaying FRCs without any support. However, several techniques are deployed in the FRC 10 system to further improve the confinement of FRC (inner core and edge layer) to the HPF regime and maintain the configuration.

Neutral Beams

[098] Firstly, the fast neutrals (H) are injected perpendicular to the Bz in the beams of the eight neutral beam injectors 600. The fast neutral beams are injected from the moment the north and south formation FRCs merge in the chamber of confinement 100 in an FRC. 450. Fast ions, created primarily by charge exchange, have betatron orbits (with primary radii on the FRC topology scale or at least much larger than the characteristic magnetic field gradient length scale) that add to the azimuthal current of the FRC 450. After a fraction of the discharge (after 0.5 to 0.8 ms on trigger), a sufficiently large fast ionic population significantly improves the stability and confinement properties of the internal FRC (see, e.g., MW Binderbauer and N .Rostoker, Plasma Phys. 56, part 3). 451 (1996)). Additionally, from a sustainment perspective, the beams from the neutral beam injectors 600 are also the primary means for driving current and heating the FRC plasma.

[099] In the plasma regime of the FRC 10 system, fast ions slow down mainly in plasma electrons. During the initial part of a discharge, typical in-orbit deceleration times of fast ions are 0.3 to 0.5 ms, which results in significant heating of FRC, particularly electrons. Fast ions make large radial excursions outside the separatrix because the internal magnetic field of the FRC is inherently low (around 0.03 T on average for an external axial field of 0.1 T). The fast ions would be vulnerable to loss of charge exchange if the density of the neutral gas was too high outside the separator. Therefore, wall gettering and other techniques (such as the 350 plasma gun and 440 mirror plugs that contribute, among other things, to gas control) deployed in the FRC system tend to minimize edge neutrals and enable the necessary accumulation of fast ion current.

Granule Injection

[0100] When a significant population of fast ions is built up within the FRC 450, with higher electron temperatures and longer FRC lifetimes, frozen H or D beads are injected into the FRC 450 from the bead injector 700 to sustain the FRC particle inventory from FRC 450. The anticipated ablation time scales are sufficiently short to provide a significant source of FRC particles. This rate can also be increased by increasing the surface area of the injected part by breaking the individual bead into smaller fragments while in the injection pipes or tubes of the bead injector 700 and before entering the confinement chamber 100, a step that can be achieved by increase the friction between the bead and the walls of the injection tube by tightening the radius of curvature of the last segment of the injection tube immediately before entering the confinement chamber 100. Due to the variation in the firing sequence and the rate of the 12 cylinders ( injection tubes) as well as fragmentation, it is possible to adjust the granule injection system 700 to provide just the desired level of particle inventory support. In turn, this helps maintain internal kinetic pressure in the FRC 450 and the sustained operation and service life of the FRC 450.

[0101] Once the separated atoms encounter significant plasma in FRC 450, they become fully ionized. The resulting cold plasma component is then collisionally heated by the inherent FRC plasma. The energy required to maintain a desired temperature of the FRC is ultimately supplied by the beam injectors 600. In this sense, the bead injectors 700 together with the neutral beam injectors 600 form the system that maintains a fixed state and sustains the FRC 450.

CT Injector

[0102] As an alternative to the bead injector, a compact toroid injector (CT) is provided, mainly for feeding field-reversed configuration plasmas (FRCs). The CT injector 720 comprises a magnetized coaxial plasma gun (MCPG) which, as shown in Figures 22A and 22B, includes coaxial inner and outer cylindrical electrodes 722 and 724, a bias coil positioned within the inner electrode 726, and an electrical break 728 at one end opposite the discharge of the CT injector 720. Gas is injected through a gas injection port 730 into a space between the inner and outer electrodes 722 and 724 and a Spheromak-type plasma is generated from it by discharge and pushed out of the pistol by Lorentz force. As shown in Figures 23A and 23B, a pair of CT injectors 720 are coupled to the containment vessel 100 near and on opposite sides of the midplane of the vessel 100 to inject CTs into the central FRC plasma within the containment vessel 100. The end of Discharges from the TC injectors 720 are directed toward the midplane of the containment vessel 100 at an angle to the longitudinal axis of the containment vessel 100, similar to neutral beam injectors 615.

[0103] In an alternative embodiment, the CT injector 720, as shown in Figures 24A and 24B, includes a bypass tube 740 comprising an elongated cylindrical tube coupled to the discharge end of the CT injector 720. As depicted, the bypass tube 740 includes bypass tube coils 742 positioned around and axially spaced along the tube. A plurality of diagnostic ports 744 are represented along the length of the tube.

[0104] The advantages of the CT 720 injector are: (1) control and adjustability of the particle inventory per injected CT; (2) hot plasma is deposited (instead of cryogenic beads); (3) the system can be operated in repeat rate mode to allow continuous supply; (4) the system can also restore some magnetic flux as the injected CTs carry built-in magnetic field. In one embodiment for experimental use, the inner diameter of an outer electrode is 83.1 mm and the outer diameter of an inner electrode is 54.0 mm. The surface of the internal electrode 722 is preferably coated with tungsten so as to reduce impurities leaving the electrode 722. As described, the polarization coil 726 is mounted within the internal electrode 722.

[0105] In recent experiments, a supersonic CT translational speed of up to ~100 km/s has been achieved. Other typical plasma parameters are as follows: electron density ~ 5 x 1021 m-3, electron temperature ~ 30-50 eV and particle inventory of ~ 0.5-1.0 x 1019. The high kinetic pressure of TC allows the injected plasma to penetrate deep into the FRC and deposit particles within the separatrix. In recent experiments, fueling of FRC particles resulted in ~10-20% of the FRC particle inventory being supplied by the CT injectors successfully demonstrating that fueling can be readily accomplished without disrupting the FRC plasma.

Saddle Coils

[0106] To achieve steady-state current drive and maintain the required ion current, it is desirable to prevent or significantly reduce electron rotation due to electron-ion frictional force (resulting from momentary electron transfer from collision ion ). The FRC 10 system utilizes an innovative technique to provide electron splitting via an externally applied static magnetic dipole or quadrupole field. This is achieved through the external saddle coils 460 depicted in Figure 15. The transversely applied radial magnetic field of the saddle coils 460 induces an axial electric field in the rotating FRC plasma. The resulting axial electron current interacts with the radial magnetic field to produce an azimuthal breaking force on the electrons, Fθ = -oVeθ<|Brl2>. For typical conditions in the FRC 10 system, the applied magnetic dipole (or quadrupole) field required within the plasma need only be of order 0.001 T to provide adequate electron splitting. The corresponding external field of about 0.015 T is small enough not to cause appreciable loss of fast particles or adversely affect confinement. In fact, the applied magnetic dipole (or quadrupole) field contributes to suppressing instabilities. In combination with tangential neutral beam injection and axial plasma injection, 460 saddle coils provide an additional level of control with regards to current maintenance and stability.

Mirror Plugs

[0107] The design of the pulsed coils 444 within the mirror plugs 440 allows for the local generation of high magnetic fields (2 to 4 T) with modest capacitive energy (about 100 kJ). For formation of magnetic fields typical of the present operation of the FRC system 10, all field lines within the formation volume are passing through the constrictions 442 in the mirror plugs 440, as suggested by the magnetic field lines in Figure 2 and wall contact. of plasma does not occur. Additionally, the mirror plugs 440 in tandem with the quasi-dc splitter magnets 416 can be adjusted to guide the field lines to the diverter electrodes 910, or widen the field lines in an end-cusp configuration (not shown). The latter improves stability and suppresses parallel electron thermal conduction.

[0108] Mirror plugs 440 themselves also contribute to neutral gas control. The mirror plugs 440 allow better utilization of the deuterium gas blown into the quartz tubes during FRC formation, since the gas flow to the divertors 300 is significantly reduced by the small conductance of the plugs (a meager 500 L/ s) . Most of the residual gas swollen within the forming tubes 210 is rapidly ionized. Furthermore, the high-density plasma flowing through the mirror plugs 440 provides efficient neutral ionization, hence an effective gas barrier. As a result, most of the neutrals recycled in the divertors 300 of the FRC edge layer 456 do not return to the confinement chamber 100. Furthermore, the neutrals associated with the operation of the plasma guns 350 (as discussed below) will be primarily confined to the divertors 300 .

[0109] Finally, mirror plugs 440 tend to improve confinement of the FRC edge layer. With mirror ratios (plug/confinement magnetic fields) in the range of 20 to 40 and with a length of 15 m between the north and south mirror plugs 440, the TH edge layer particle confinement time increases up to a order of magnitude. Improving TH readily increases FRC particle confinement.

[0110] Assuming that the loss of diffuse radial particles (D) from the volume of the separator 453, balanced by the axial loss (th) of the edge layer 456, we obtain (2πrsLs)(Dns/δ) = (2πrsLsδ)(ns /Tii), from which the length of the separatrix density gradient can be rewritten as δ = (DTH)1/2 Here rs, Ls and ns are separatrix radius, separatrix length and separatrix density, respectively. The confinement time of the FRC particle is tN = [πrs2Ls<n>]/[(2πrsLs)(Dns/δ)] = (<n>/ns)(T±Tii)1/2, where T± = a2/ D with a=rs/4. Physically, improving TH leads to increased δ (reduced separatrix density gradient and drift parameter) and therefore reduced FRC particle loss. The overall improvement in FRC particle confinement is generally somewhat less than quadratic, because ns increases with TH.

[0111] A significant improvement in TH also requires that the edge layer 456 remains fully stable (i.e., no n = 1 spline, firehose, or other MHD instability typical of open systems). The use of 350 plasma guns provides this preferred onboard stability. In this sense, the mirror plugs 440 and the plasma gun 350 form an effective onboard control system.

Plasma Pistols

[0112] Plasma Guns 350 have improved the stability of FRC 454 exhaust jets by line tying. The pistol plasmas of the 350 Plasma Guns are generated without azimuthal angular momentum, which proves to be useful in controlling FRC rotational instabilities. As such, 350 pistols are an effective means of controlling FRC stability without the need for the older quadrupole stabilization technique. As a result, Plasma Guns 350 make it possible to take advantage of the beneficial effects of fast particles or access the advanced hybrid kinetic FRC regime as described in this description. Therefore, the 350 plasma guns allow the FRC 10 system to be operated with saddle coil currents just suitable for electron splitting, but below the threshold that would cause FRC instability and/or lead to rapid and dramatic particle diffusion. .

[0113] As mentioned in the above Mirror Plug comment, if th could be significantly improved, the gun plasma provided would be comparable to the edge layer particle loss rate. (~1022/s). The lifetime of the plasma produced by the cannon in the FRC 10 system is in the millisecond range. In fact, consider the gun plasma with density ne ~ 1013 cm-3 and ionic temperature of about 200 eV, confined between the end mirror plugs 440. The trap length L and mirror ratio R is approximately 15 m and 20 , respectively. The ion mean free path due to Coulomb collisions is Xii ~ 6x103 cm and, since XülnR/R < L, the ions are confined in the gas dynamic regime. The plasma confinement time in this regime is Tgd ~ RL/2Vs ~ 2 ms, where Vs is the ion sound speed. For comparison, the classical ion confinement time for these plasma parameters would be Tc ~ 0.5Tii(lnR + (lnR)0-5) ~ 0.7 ms. Anomalous transverse diffusion can, in principle, shorten the plasma confinement time. However, in the FRC 10 system, if we assume the Bohm diffusion rate, the estimated transverse confinement time for the gun plasma is T± > Tgd ~ 2 ms. Thus, the guns would provide significant replenishment of the FRC 456 edge layer, and improved total FRC particle confinement.

[0114] Additionally, gun plasma currents can be turned on in about 150 to 200 microseconds, which allows for use in FRC starting, translation and fusion in confinement chamber 100. If turned on around t ~ 0 (FRC main bank initiation), pistol plasmas help support the dynamically formed and merged FRC 450. The combined particle inventories of the formation FRCs and the guns are suitable for neutral beam trapping, plasma heating, and long sustain. If activated at t in the range of -1 to 0 ms, gun plasmas can fill the 210 quartz tubes with plasma or ionize the inflated gas in the quartz tubes, thus allowing the formation of reduced or even zero gas FRC. The latter may require formation plasma cold enough to allow rapid diffusion of the reversed polarization magnetic field. If turned on at t < -2 ms, the plasma currents could fill the field line volume of about 1 to 3 m3 of the formation and confinement regions of the formation sections 200 and the confinement chamber 100 with a target plasma density. of 1013 cm 3, sufficient to allow the neutral beam to accumulate before the arrival of the FRC. The formation of FRCs could then be formed and translated into the plasma resulting from the confinement vessel. In this way, the 350 plasma guns allow for a wide variety of operating conditions and parameter regimes.

Electrical Polarization

[0115] Controlling the radial electric field profile in the edge layer 456 is beneficial in several ways to the stability and confinement of the FRC. By virtue of the innovative biasing components implemented in the FRC 10 system it is possible to apply a variety of deliberate distributions of electrical potentials to a group of open flow surfaces along the machine from areas well outside the central confinement region in the confinement chamber. 100. In this way, radial electric fields can be generated across the edge layer 456 on the outside of the FRC 450. These radial electric fields then modify the azimuthal rotation of the edge layer 456 and effect its confinement through velocity shear. E x B. Any differential rotation between the edge layer 456 and the FRC core 453 can then be transmitted into the FRC plasma by shear. As a result, controlling the 456 edge layer directly impacts the FRC 453 core. Furthermore, because the free energy in plasma rotation can also be responsible for instabilities, this technique provides a direct means to control the initiation and growth of instabilities. . In the FRC 10 system, appropriate edge polarization provides effective control of the transport and rotation of the open field line, as well as the rotation of the FRC core. The location and shape of the various provided electrodes 900, 905, 910 and 920 allow control of different groups of flow surfaces 455 and at different and independent potentials. In this way, a wide range of different electric field configurations and strengths can be realized, each with a different characteristic impact on plasma performance.

[0116] A key advantage of all these innovative polarization techniques is the fact that the behavior of the plasma core and edge can be affected from outside the FRC plasma, i.e. there is no need to bring any physical components into contact with the central hot plasma (which would have severe implications for energy, flow and particle losses). This has a huge beneficial impact on performance and all possible applications of the HPF concept.

Experimental Data - Operation HPF

[0117] Fast particle injection via neutral beam gun beams 600 plays an important role in enabling the HPF regime. Figures 16A, 16B, 16C and 16D illustrate this fact. A set of curves is depicted that shows how the lifetime of the FRC is correlated with the length of the beam pulses. All other operating conditions are held constant for all discharges comprising this study. The data is averaged over many shots and therefore represents typical behavior. It is evident that longer beam duration produces longer FRCs. Looking at this evidence, as well as other diagnostics during this study, it is demonstrated that the beams increase stability and reduce losses. The correlation between beam pulse length and FRC duration is not perfect, because the beam trap becomes inefficient below a certain plasma size, i.e., as the FRC 450 shrinks in physical size, nor all injected beams are intercepted and retained. The FRC contraction is mainly due to the fact that the net energy loss (~4 MW halfway through discharge) from the FRC plasma during discharge is somewhat greater than the total energy fed into the FRC via neutral beams ( ~2.5 MW) for the particular experimental setup. Locating the beams at a location closer to the midplane of the container 100 would tend to reduce these losses and extend the service life of the FRC.

[0118] Figures 17A, 17B, 17C and 17D illustrate the effects of different components to achieve the HPF regime. Shows a family of typical curves representing the lifetime of the FRC 450 as a function of time. In all cases, a constant and modest amount of beam power (about 2.5 MW) is injected throughout the duration of each discharge. Each curve is representative of a different combination of components. For example, operation of the FRC system 10 without any mirror plugs 440, plasma guns 350, or gettering from gettering systems 800 results in rapid onset of spin instability and loss of FRC topology. Adding just the 440 mirror plugs delays the onset of instabilities and increases confinement. Using the combination of 440 mirror plugs and a 350 plasma gun further reduces instabilities and increases the service life of the FRC. Finally the addition of gettering (Ti in this case) on top of the 350 gun and 440 plugs produces the best results - the resulting FRC is free of instabilities and exhibits the longest service life. It is clear from this experimental demonstration that the complete combination of components produces the best effect and provides the beams with the best target conditions.

[0119] As shown in Figure 1, the newly discovered HPF regime exhibits dramatically improved transport behavior. Figure 1 illustrates the change in particle confinement time in the FRC 10 system between the conventional regime and the HPF regime. As can be seen, it improved by more than a factor of 5 on the HPF regimen. Additionally, Figure 1 details the particle confinement time in the FRC 10 system relative to the particle confinement time in previous conventional FRC experiments. Relative to these other machines, the FRC 10 system's HPF regime improved confinement by a factor of between 5 and close to 20. Finally, and most importantly, the nature of the FRC 10 system's scale of confinement in the HPF regime is dramatically different. of all previous measurements. Prior to the establishment of the HPF regime in the FRC 10 system, several empirical scaling laws were derived from data to predict confinement times in previous FRC experiments. All these scaling rules depend mainly on the ratio R2/pi, where R is the radius of the zero magnetic field (a measure free of the physical scale of the machine) and pi is the ion Larmor radius evaluated in the externally applied field (the measure lost of the applied magnetic field). It is clear from Figure 1 that prolonged confinement in conventional FRCs is only possible at large machine size and/or high magnetic field. Operating the FRC 10 system in the CRC of the conventional FR regime tends to follow these scaling rules, as indicated in Figure 1. However, the HPF regime is far superior and shows that much better confinement is possible without large machines or high magnetic fields. . More importantly, it is also clear from Figure 1 that the HPF regime results in improved confinement time with reduced plasma size compared to the CR regime. Similar trends are also visible for flow and energy confinement times, as described below, which have also increased by a factor of 3 to 8 in the FRC 10 system. The advancement of the HPF regime therefore allows the use of modest beam power , lower magnetic fields and smaller size to sustain and maintain FRC balances in the FRC 10 system and future high energy machines. Hand in hand with these improvements, operating and construction costs are lower, as well as reduced engineering complexity.

[0120] For further comparison, Figures 18A, 18B, 18C and 18D show data from a representative HPF regime discharge in the FRC 10 system as a function of time. Figure 18A shows the excluded flow radius in the midplane. For these longer time scales, the driving steel wall is no longer a good flux conservator and the in-wall magnetic probes are augmented with out-of-wall probes to adequately account for magnetic flux diffusion through the steel. Compared to typical performance in conventional duty CR, as shown in Figures 13A, 13B, 13C, and 13D, the HPF duty operating mode exhibits more than 400% longer lifetime.

[0121] A representative chord of the line integrated density trace is shown in Figure 18B with its inverted complement Abel, the density contours, in Figure 18C. Compared to the conventional CR FRC regime, as shown in Figures 13A, 13B, 13C and 13D, the plasma is more mobile along the pulse, indicative of very stable operation. The peak density is also somewhat lower in HPF shots - this is a consequence of the higher total plasma temperature (up to a factor of 2), as shown in Figure 18D.

[0122] For the respective discharge illustrated in Figures 18A, 18B, 18C and 18D, the energy, particle and flow confinement times are 0.5 ms, 1 ms and 1 ms, respectively. At a reference time of 1 ms on discharge, the stored plasma energy is 2 kJ, while losses are about 4 MW, making this target very suitable for neutral beam sustainment.

[0123] Figure 19 summarizes all the advantages of the HPF regime in the form of a newly established experimental HPF flow confinement schedule. As can be seen in Figure 19, based on measurements made before and after t = 0.5 ms, i.e., t < 0.5 ms and t > 0.5 ms, flow confinement (and similarly, flow confinement particles and energy confinement) increases with the square of the Electron Temperature (Te) for a given separator radius (rs). This strong scaling with a positive power of Te (and not a negative power) is completely opposite to that exhibited by conventional “tokomaks”, where confinement is typically inversely proportional to some power of the electron temperature. The manifestation of this scale is a direct consequence of the HPF state and the large orbit (i.e., orbits on the scale of the FRC topology and/or at least the characteristic magnetic field gradient length scale) ion population. Fundamentally, this new scale substantially favors high operating temperatures and allows for relatively modest-sized reactors.

[0124] With the advantages of the HPF regime, sustain or steady state FRC driven by neutral beams is achievable, meaning that the overall plasma parameters such as plasma thermal energy, total number of particles, plasma radius and length as well as magnetic flux are sustainable at reasonable levels without substantial decay. For comparison, Figure 20 shows data in plot A for a representative HPF regime discharge in the FRC 10 system as a function of time and in plot B for a representative HPF regime discharge projected in the FRC 10 system as a function of time where the FRC 450 is sustained without decay through the duration of the neutral beam pulse. For graph A, neutral beams with total power in the range of about 2.5 to 2.9 MW were injected into the FRC 450 for an active beam pulse length of about 6 ms. The diamagnetic plasma lifetime represented in graph A was about 5.2 ms. More recent data shows that a plasma diamagnetic lifetime of about 7.2 ms is achievable with an active beam pulse length of about 7 ms.

[0125] As noted above with respect to Figures 16A, 16B, 16C and 16D, the correlation between beam pulse length and FRC lifetime is not perfect because beam trapping becomes inefficient below a certain size plasma, that is, as the FRC 450 shrinks not all injected beams are intercepted and trapped. The contraction or decay of the FRC is mainly due to the fact that the net energy loss (- 4 MW at half discharge) of the FRC plasma during discharge is slightly greater than the total energy fed into the FRC through the neutral beams. (- 2.5 MW) for the specific experimental setup. As noted in connection with Figure 3C, angled beam injection from neutral beam guns 600 to the midplane improves beam plasma coupling even as the FRC plasma contracts or otherwise contracts axially during the period of injection. Furthermore, adequate supply of beads will maintain the required plasma density.

[0126] Chart B is the result of simulations performed using an active beam pulse length of about 6 ms and total beam power from the Neutral Beam Guns 600 of just over 10 MW, where neutral beams inject neutral H ( or D) with particle energy of about 15 keV. The equivalent current injected by each of the beams is about 110 A. For plot B, the beam injection angle to the device axis was about 20° less than normal with a target radius of 0.19 m . The injection angle can be changed within the range of 15° to 25° below normal. The beams must be injected in the azimuthally concurrent direction. The lateral force and axial force of neutral beam moment injection must be minimized. As in graph A, fast neutrals (H) are injected from the neutral beam injectors 600 from the moment the north and south formation FRCs merge in the confinement chamber 100 into a single FRC 450.

[0127] The simulations in which the foundation for graph B utilize multidimensional “hall-MHD” solvers for the plasma and background equilibrium, fully kinetic Monte-Carlo based solvers for the energetic beam components and all scattering processes , as well as a series of coupled transport equations for all plasma species to model interactive loss processes. The transport components are empirically calibrated and extensively compared with an experimental database.

[0128] As shown by graph B, the fixed-state diamagnetic lifetime of the FRC 450 will be the length of the beam pulse. However, it is important to note that the main correlation plot B shows that when the beams are turned off, the plasma or FRC begins to decay at that time, but not before. The decay will be similar to that observed in discharges that are not beam-assisted - probably on the order of 1 ms beyond the beam off time - and is simply a reflection of the characteristic decay time of the plasma driven by intrinsic loss processes.

[0129] Returning to Figures 21A, 21B, 21C, 21D and 21E, the experimental results illustrated in the figures indicate obtaining FRC lift or fixed state driven by angular neutral beams, that is, global plasma parameters such as plasma radius, density of plasma, plasma temperature as well as magnetic flux are sustainable at constant levels without decay in correlation with the duration of the NB pulse. For example, such plasma parameters are essentially being held constant for ~5+ ms. This plasma performance, including the sustain feature, correlates strongly with NB pulse duration, with diamagnetism persisting up to several milliseconds after NB termination due to the accumulation of fast ions. As illustrated, plasma performance is limited only by pulse length constraints that arise from the finite energies stored in the associated power supplies of many critical systems, such as NB injectors, as well as other system components.

High harmonic fast wave electron heating

[0130] As noted above in connection with Figures 3A, 3B, 3C, 3D, 3E and 8, neutral atom beams 600 are deployed in the FRC system 10 to provide heating and driving current, as well as to develop rapid particle pressure. . Individual beam lines comprising neutral atom beam injection systems 600 are located around the central confinement chamber 100 and, as shown in Figures 3C, 3D and 3E, are preferably angled to inject neutral particles toward the midplane. of the confinement chamber 100. To improve FRC sustain and demonstrate FRC rise for high plasma temperatures and high system energies, the current FRC 10 system includes a high power Neutral Beam Injector (NBI) 600 system and expanded pulse length, e.g. for exemplary purposes only, power of about 20+ MW with up to a pulse length of 30 ms.

[0131] Neutral beam injection, however, tends to have low electron heating efficiency due to the energy dampening mechanism in electrons through ion-electron collision. The unique characteristics of an FRC plasma of the present FRC 10 system, for example, the plasma being usually excessively dense (®pe > 30 c>ce within the separatrix) and the magnetic field rapidly falling to zero in the plasma core, extremely challenging to heat electrons in the nucleus of FRC plasmas. Conventional electron heating scenarios, such as the electron-cyclotron resonant frequency (or its second or third harmonics), which is widely used in tokamaks, stellarators and mirror machines, cannot be adapted to FRC plasmas due to poor wave accessibility to plasma. Other electron heating scenarios, such as electric Bernstein waves, higher hybrid resonant waves, and whistler waves, encounter similar problems or exhibit low heating efficiency when applied to FRC plasmas.

[0132] In an exemplary embodiment, the present FRC system 10 includes heating by fast wave electrons of high harmonics to raise plasma electron temperatures and thus further improve FRC sustainment. As shown in Figure 25, the present FRC system 10 includes one or more antennas 650, such as, for example, a phased array antenna with four (4) loops, deployed in the FRC system 10 and configured to propagate fast harmonic waves. high radio frequency variations in the FRC plasma in the containment vessel 100 to provide electron heating in the FRC plasma core of about 150 eV to about 1 keV. In an exemplary embodiment, the antennas 650 would comprise about a 2 MW RF system at about 15 to 25 Mhz. Heating of electrons through high harmonic fast waves in radio frequency bands advantageously reduces charge exchange loss and improves confinement of the plasma, as well as increases the efficiency of the plasma current, which increases with electron temperature Te.

[0133] Simulations of electron heating in high-performance FRC plasmas, such as the FRC plasma of the current FRC 10 system, were performed in the following scenarios: (1) higher hybrid resonance frequency (50 GHz); (2) electron-cyclotronic resonance (ECR) frequency (28 GHz); (3) electrical Bernstein waves (EBW) with frequencies of 2.45 GHz, 5 GHz, 8 GHz and 18 GHz; (4) whistle waves at 0.5 GHz; (5) HHFW at 15 MHz The simulation results clearly showed that the HHFW regime not only has an extremely strong single-pass energy absorption (~100%), but also has very good wave accessibility in the core of FRC plasmas. These simulations indicated that the conflict between good wave accessibility and efficient energy damping in electrons is resolved using this high harmonic fast wave heating (HHFW), which has been successfully adapted to dense spherical beta tokamak (ST) plasmas such as NSTX for the electron core heating and off-axis current drive experiments.

[0134] The HHFW heating mechanism includes both electron Landau damping (LD) (where the force acting on electrons is FLD = eE//) and transit time magnetic pumping (TTMP or MP) (where the force is FMP = -V//(μB//)). Here e and μ are the electron charge and magnetic moment, and E // and B // are the parallel components of the fast-wave electric and magnetic field, respectively. Conventional heating of fast-wave electrons in tokamak plasmas requires wave-parallel phase velocity Vph // = w/k // « VTe electron thermal velocity) for any significant absorption via dominated LD; MP does not contribute significantly to electron damping and can often be neglected. Furthermore, fast wave absorption in tokamak plasmas is weak and therefore it is normally necessary to have strong microwave electron preheating at the electron-cyclotron resonance frequency in order to increase energy absorption. multiple passes. However, in high beta, ST plasmas like NSTX, MP has been found to significantly increase energy absorption in electrons over electron LD alone, and it becomes substantially larger over a larger phase velocity range, w / k // < 2.5 VTe . The combination of MP and LD can lead to 100% single-pass absorption.

[0135] In high beta regimes such as the high performance FRC plasma of the current FRC 10 system (which has a value of around βe around 90% in the plasma core), the damping is dominated by magnetic pumping, which can be scaled as Im k. α neTe/B2 αβe, and the magnetic pumping becomes significant when 0/k// < 2.5 VTe. In simulations for the current FRC 10 system, Te = 150 eV, Ti = 800 eV, ne = n = 3.2 x 1019 m-3, magnetic field B = 1000 Gauss, HHFW has an initial power of 1 MW and its frequency is selected as f = 15 MHz, therefore 0 = 2πf = 10 0 [H] = 20 0 [D] « 0LH, single-pass absorption greater than 99% was achieved, and the damped HHFW power on the electrons was shown to be as high as 90%. The energy damped in ions or damped by collision can be less than 5%, respectively. Furthermore, radial energy deposition profiles in electrons, ions and collisions showed that more than 60% of the HHFW power is damped within the separator layer of FRC plasmas.

[0136] Figures 26A and 26B illustrate a complete radial density profile and a complete radial electron temperature profile of an FRC plasma of the current FRC system 10. The present FRC system, in accordance with the present embodiments, is configured according to the parameter and pair values shown in Table 1. Table 1: Parameters for the present FRC system

[0137] Figures 27A to 27D illustrate the C-2U equilibrium radial profiles and characteristic frequency in the midplane (Z = 0) of the FRC 10 system. The challenges observed are that, within the separator layer, the plasma is denser (ape > 30 ace) and B quickly drops to 0 at a radial distance of 11 cm. All of the ECR's harmonic resonance layers are packed into a very narrow region, so microwaves can spread radially over a short distance.

[0138] The following simulations were conducted by GENRAY-C ray tracing for the microwave frequency scenarios as follows: EBW (2.45 GHz, 5 GHz, 8 GHz, 18 GHz and 28 GHz); Higher hybrid resonance frequency (50 GHz, 55 GHz); Whistle wave frequency (0.5 - 1.0 GHz).

[0139] Unfortunately, these scenarios are unable to resolve the conflict between wave penetration into the plasma core and efficient energy damping in the electrons.

[0140] As Figures 28A to 28C illustrate observations of energy filtering and emitting electron heat conditions by Microwave Electron Bernstein Wave (EBW) at 8GHz in an FRC plasma of the current system 10. In Figures 28A to 28C, the waves are fired at different angles, observing a clear O->X->B conversion. More than 90% of the microwave energy can be absorbed by electrons in the ECR layer of the 4th harmonic (outside the separator); which results in very localized absorption. The EBW regime can heat only at the plasma edge, it cannot penetrate the plasma core.

[0141] Figures 29A to 29F illustrate the energy absorption and conversion mode observations under 50 GHz microwave heating conditions in an FRC plasma of the present FRC 10 system. In Figures 29A to 29F, it is observed that the rays stop propagating after the O->X->B conversion, and 30% of the microwave power is absorbed.

[0142] Figures 30A-30C illustrate observations of energy absorption under conditions of hissing wave electron heating at 0.5 GHz in an FRC plasma of the present CRF system 10. In Figures 30A-30C, it is observed that wave hiss at 0.5 GHz (~1/4 fce) has high energy absorption but poor wave accessibility. A wave is launched with a large N // (from 16) and the wave rotates when there is a large curvature of the magnetic field.

[0143] In contrast to these heating regimes, high harmonic fast wave heating provides, as demonstrated by simulation results, the following for FRC plasma with high mean e βe (~90%) such as an FRC plasma of the present FRC 10 system: 1) strong single-pass absorption (~100%); 2) good accessibility to the plasma core; 3) efficient energy absorption by core electrons up to 60%; 4) the energy damping in electrons is dominated by magnetic pumping (TTMP), which can be scaled as lm k⊥ x neTe/B2 xβe.

[0144] Figure 31 illustrates a density and wave propagation profile in an FRC plasma of the present FRC 10 system. In Figure 10, Te = 150 eV, while Te (separatrix) = 100 eV. Ti = 800 eV, while Ti (separatrix) = 200 eV. Thermal ions have the same density and profile as electrons. Fast ion information is not included in Figure 31. Figure 32 illustrates a poloidal flow profile and wave propagation in an FRC plasma of the present FRC 10 system.

[0145] Figure 33 illustrates an exemplary density profile and wave propagation trajectory in an FRC plasma of the present RFC 10 system. In Figure 33, Te = 150 eV, while Te (separatrix) = 100 eV. Ti = 800 eV, while Ti (separatrix) = 200 eV. In Figure 33, f = 6 MHz (initial w/wci[D] ~ 9), with total power of 1MW. Five rays are launched in the midplane with initial n// between 4 and 6.

[0146] Figure 34 illustrates an exemplary w/wci [D] profile and wave propagation path in an FRC plasma of the present FRC 10 system. In Figure 34, w/wci [D] levels > 28 are not shown for greater clarity. The dotted lines in the gap are the contour of the magnetic flux.

[0147] Figure 35 illustrates exemplary power damping with the wave propagation distance in an FRC plasma of the current FRC 10 system. In Figure 35, five rays are included with different n // between 4 and 6. Each ray It has 200kW of power at starting point. The region of significant energy damping is between 30cm and 50cm.

[0148] Figure 36 illustrates an exemplary energy absorption profile in an FRC plasma of the present FRC system 10. In Figure 36, significant energy absorption is observed in ions and electrons when HHFWs penetrate through the separator layer.

[0149] Figures 37A and 37B illustrate exemplary radial power density profiles in an FRC plasma of the present CRF system 10. The radial power density profiles are for (a) total absorption, (b) electron damping, (c) ion damping, and (d) collision damping. In Figure 37A, Ptotal = 1000kW, Pe = 448kW, Pi = 486kW and Pcl = 66kW. In Figure 37B, Ptotal = 999kW, Pe = 720kW, Pi = 194kW and Pcl = 85kW. A single-pass absorption of 100% is observed during HHFW heating in the plasma core.

[0150] Figure 38 illustrates an exemplary 2D profile of the damping power density in an FRC plasma of the present FRC system 10.

[0151] Figure 39 illustrates an exemplary power damping profile in an FRC plasma of the current FRC 10 system. In Figure 39, it is observed that the energy damping in electrons increases to a maximum when | B | approaches a minimum. A very small |E///E| therefore, less effect of Landau damping on energy absorption.

[0152] Figure 40 illustrates an exemplary profile of finite ions of radius Larmor in an FRC plasma of the present system FRC 10. In Figure 40, significant effects of finite ions of radius Larmor are observed even when the ionic temperature Ti < 1 keV . Inside the separatrix, Ki x pLarmor >> 1. It goes to infinity in the null field in the midplane (z = 0). This can lead to the interaction of thermal ions with the HHFW, decreasing the potency of the thermal ions.

[0153] Figure 41 illustrates an exemplary energy absorption profile in a FRC plasma of the present CRF system 10. In Figure 41, significant energy absorption by thermal ions is observed. Cyclotron ion resonant absorption is observed with harmonic number n = (11 to 20). The conditions for significant damping of power in the ions are Ki x pLarmor >> 1 and w/Ki < 2VTÍ.

[0154] Figure 42 illustrates an exemplary profile in an FRC plasma of the present FRC system 10. In Figure 42, changes of (a) local |B(r,z)|, (b) imaginary part of the perpendicular wavenumber Ki, (c) ratio of |E\\/ E| and (d) parallel refractive index n// are observed with distance along the wave propagation.

[0155] HHFW heating simulations of an FRC plasma of the present FRC 10 system have clearly demonstrated that HHFW heating results in: 1) 100% single-pass energy absorption; 2) TTMP being dominated energy absorption mechanism for heating core electrons; 3) damping of the maximum power in the electrons that occurs when the parallel phase speed of the wave is Vph // = w/k// < VTe; and, 4) significant energy absorption by thermal ions tending to occur when the conditions of K±x PLarm >> 1 and w/k. < 2 VTÍ are maintained.

[0156] According to one embodiment of the present disclosure, a method for generating and maintaining a magnetic field with a field reverse configuration (FRC) comprising forming a CRF around a plasma in a confinement chamber, injecting a plurality of neutral beams into the FRC plasma at an angle toward the midplane of the confinement chamber and heating electrons from the FRC plasma with fast high harmonic waves propagating in the FRC plasma.

[0157] According to another embodiment of the present disclosure, the heating electrons include launching a plurality of high harmonic fast waves from one or more antennas into the FRC plasma in the confinement chamber.

[0158] According to another embodiment of the present disclosure, the heating electrons include launching a plurality of high harmonic fast waves from one or more antennas to the FRC plasma in the confinement chamber at a midplane launch angle. of the confinement chamber.

[0159] According to another embodiment of the present disclosure, the launch angle is in a range of about 15° to about 25° from the midplane of the confinement chamber.

[0160] According to another embodiment of the present disclosure, the launch angle is close to, but less than normal, a longitudinal axis of the confinement chamber.

[0161] According to another embodiment of the present disclosure, the one or more antennas is a phased array antenna with a plurality of strips.

[0162] According to another embodiment of the present disclosure, high harmonic fast waves are fast waves in radio frequency bands.

[0163] According to another embodiment of the present disclosure, heating of electrons includes heating of electrons from about 150 eV to above about 1 keV.

[0164] According to another embodiment of the present disclosure, the method further includes maintaining the FRC at or about a constant value without decay and raising the temperature of the electron plasma above about 1.0 keV.

[0165] According to another embodiment of the present disclosure, the method further comprises generating a magnetic field within the confinement chamber quasi-dc coils extending over the confinement chamber and a mirror magnetic field within opposite ends of the confinement chamber with quasi-dc mirror coils extending over opposite ends of the confinement chamber.

[0166] According to another embodiment of the present disclosure, the method further comprises generating a magnetic field within the confinement chamber with quasi-dc coils extending over the confinement chamber and a mirror magnetic field within opposite ends. of the confinement chamber quasi-dc coils extending over opposite ends of the confinement chamber.

[0167] According to another embodiment of the present disclosure, formation of the CRF includes forming a CRF in opposition to the first and second forming sections coupled to the confinement chamber and accelerating CRC formation of the first and second forming sections in towards the middle through the plane of the confinement chamber where the two forming FRCs merge to form the FRC.

[0168] According to another embodiment of the present disclosure, formation of the CRF includes forming a forming CRF while accelerating the formation of the CRF toward the midplane of the confinement chamber and forming a forming CRF, then accelerating the CRC formation towards the middle through the plane of the confinement chamber.

[0169] According to another embodiment of the present disclosure, accelerating the FRC formation of the first and second forming sections toward the midplane of the confinement chamber includes passing the FRC formation of the first and second forming sections through the first and second divertors internals coupled to opposite ends of the confinement chamber interposing the confinement chamber and the first and second forming sections.

[0170] According to another embodiment of the present disclosure, passing the FRC formation of the first and second formation sections through the first and second internal divertors includes inactivating the first and second internal divertors when the FRC formation of the first and second formation sections passes through the first and second internal divertors.

[0171] According to another embodiment of the present disclosure, the method further comprises orienting magnetic flux surfaces of the FRC on the first and second internal divertors.

[0172] According to another embodiment of the present disclosure, the method further comprises orienting magnetic flux surfaces of the FRC on the first and second external divertors coupled to the ends of the forming sections.

[0173] According to another embodiment of the present disclosure, the method further comprises generating a magnetic field within the forming sections and the first and second external divertors with quasi-dc coils extending over the forming and divertor sections. .

[0174] According to another embodiment of the present disclosure, the method further comprises generating a magnetic field within the forming sections and the first and second internal divertors with quasi-dc coils extending over the forming and divertor sections.

[0175] According to another embodiment of the present disclosure, the method further comprises generating a mirror magnetic field between the first and second forming sections and the first and second external divertors with quasi-dc mirror coils.

[0176] According to another form of disclosure of the present disclosure, the method further comprises a generation of a mirror plug magnetic field within a construction between a first and second forming section and the first and second external divertors with coils almost -mirror cc extending around the constriction between the formation and divertor sections.

[0177] According to another form of disclosure, the method also comprises generating a mirror magnetic field between a confinement chamber and the first and second internal divertors with quasi-dc coils and generating a check magnetic field between the first and second forming sections and the first and second internal divertors with the low profile quasi-dc check coils.

[0178] According to another form of disclosure of the present invention, the method is still a generation of a magnetic dipole field and a magnetic quadrupole field within the chamber with saddle coils coupled to the chamber.

[0179] According to another form of the present disclosure, the method also comprises conditioning the internal surfaces of the chamber and the internal surfaces of the first and second forming sessions, the first and second divertors interposing the confinement chamber and the first and second forming sections and the first and second external divertors coupled to the first and second forming sections with a gettering system.

[0180] According to another embodiment of the present disclosure, the gettering system includes a titanium deposition system and a lithium deposition system.

[0181] According to another embodiment of the present disclosure, the method also comprises injecting plasma axially into the FRC from the axially mounted plasma guns.

[0182] According to another embodiment of the present disclosure, the method also comprises controlling the radial electric field profile in an edge layer of the FRC.

[0183] According to another embodiment of the present disclosure, controlling the radial electric field profile in an edge layer of the FRC includes applying an electric potential distribution to a group of open-flow surfaces of the FRC with polarization electrodes.

[0184] According to another embodiment of the present disclosure, the method also comprises injecting compact torus (CT) plasmas from first and second CT injectors into the FRC plasma at an angle toward the midplane of the confinement chamber, wherein the first and second CT injectors are diametrically on opposite sides of the midplane of the confinement chamber.

[0185] According to another embodiment of the present disclosure, a system for generating and maintaining a magnetic field with a field reverse configuration (FRC) comprises a confinement chamber, first and second diametrically opposed FRC forming sections coupled to the confinement chamber. confinement, the first and second diametrically opposed divertors coupled to the FRC forming sections, one or more of a plurality of plasma guns, one or more polarization electrodes, and first and second mirror plugs, wherein the plurality of plasma guns includes first and second axial plasma guns operatively coupled to the first and second divertors, first and second forming sections and the confinement chamber, wherein one or more polarization electrodes are positioned within one or more confinement chambers, the first and second forming sections, and the first and second external divertors and wherein the first and second mirror plugs are positioned between the first and second forming sections and the first and second divertors, a gettering system coupled to the confinement chamber and to the first and second divertors, a plurality of neutral atom beam injectors coupled to the confinement chamber and inclined toward a midplane of the confinement chamber, a magnetic system comprising a plurality of quasi-dc coils positioned around the confinement chamber, confinement, the first and second forming sections, and the first and second divertors, and first and second sets of quasi-dc mirror coils positioned between the first and second forming sections and the first and second divertors, and an antenna system positioned around the confinement chamber, in which the antenna system is configured to launch fast high harmonic waves into the FRC plasma to heat plasma electrons.

[0186] According to another embodiment of the present disclosure, the system is configured to generate an FRC and maintain the FRC without decay, while neutral beams are injected into the plasma and raise the plasma electron temperature to about 1.0 keV .

[0187] According to another embodiment of the present disclosure, the antenna system includes one or more antennas positioned to launch the high harmonic fast waves at a launch angle from the midplane of the FRC plasma confinement chamber.

[0188] According to another embodiment of the present disclosure, the launch angle is in a range of about 15° to about 25° from the midplane of the confinement chamber.

[0189] According to another embodiment of the present disclosure, the launch angle is close to, but less than normal, a longitudinal axis of the confinement chamber.

[0190] According to another embodiment of the present disclosure, the antenna system includes phased array antennas with a plurality of strips

[0191] According to another embodiment of the present disclosure, high harmonic fast waves are fast waves in radio frequency bands.

[0192] According to another embodiment of the present disclosure, the system is configured to heat FRC plasma electrons from about 150 eV to above about 1 keV.

[0193] According to another embodiment of the present disclosure, the first and second divertors comprise first and second internal divertors interposing the first and second forming sections and the confinement chamber, and further comprising first and second external divertors coupled to the first and second formation sections, in which the first and second formation sections interpose the first and second internal divertors and the first and second external divertors.

[0194] According to another embodiment of the present disclosure, the system also comprises first and second axial plasma guns operatively coupled to the first and second internal and external divertors, the first and second forming sections and the confinement chamber.

[0195] According to another embodiment of the present disclosure, the system further comprises two or more saddle coils coupled to the confinement chamber.

[0196] According to another embodiment of the present disclosure, the forming section comprises modularized forming systems for generating an FRC and translating it toward a midplane of the confinement chamber.

[0197] According to another embodiment of the present disclosure, the polarization electrodes include one or more of one or more point electrodes positioned within the containment chamber to contact open field lines, a set of annular electrodes between the containment chamber and the first and second forming sections for loading far-edge flow layers in an azimuthally symmetrical manner, a plurality of concentric stacked electrodes positioned on the first and second divertors for loading multiple concentric flow layers, and plasma gun anodes for intercepting open flow.

[0198] According to another embodiment of the present disclosure, the system further comprises first and second compact toroid (CT) injectors coupled to the confinement chamber at an angle toward the midplane of the confinement chamber, wherein the first and second injectors CT are diametrically opposite on opposite sides of the midplane of the confinement chamber.

[0199] The exemplary embodiments provided here, however, are merely intended as illustrative examples and are not intended to be in any way limiting.

[0200] All features, elements, components, functions and steps described with respect to any embodiment provided herein are intended to be freely combinable and substitutable with those of any other embodiment. If a particular feature, element, component, function or step is described with respect to only one embodiment, then it is to be understood that such feature, element, component, function or step may be used with all other embodiments described herein unless explicitly declared otherwise. This paragraph therefore serves as a background and written support for the introduction of claims, at any time, that combine features, elements, components, functions and steps of different embodiments, or that replace features, elements, components, functions and steps of another, even if the following description does not explicitly indicate, in a given case, that such combinations or substitutions are possible. Express mention of all possible combinations and substitutions is unduly burdensome, especially considering that the permissibility of each of these combinations and substitutions will be readily recognized by those skilled in the art upon reading this description.

[0201] In many cases, entities are described here as being coupled to other entities. It should be understood that the terms “coupled” and “connected” (or any of their forms) are used interchangeably in this document and, in both cases, are generic to the direct coupling of two entities (non-negligible intervening entities (e.g. , parasitic) and indirect coupling of two entities (with one or more non-negligible intervening entities). When entities are shown as being directly coupled, or described as coupled without describing any intervening entity, it should be understood that these entities can be indirectly coupled together unless the context clearly dictates otherwise.

[0202] Although the embodiments are susceptible to various modifications and alternative forms, specific examples thereof have been shown in the drawings and are described in detail herein. It should be understood, however, that these embodiments should not be limited to the particular form disclosed, but rather, these embodiments should encompass all modifications, equivalents and alternatives within the spirit of the disclosure. Furthermore, any features, functions, steps or elements of the embodiments may be mentioned in or added to the claims, as well as negative limitations that define the inventive scope of the claims for features, functions, steps or elements that are not in scope within the claims.

Claims (13)

1. Method for generating and maintaining a magnetic field with a field reverse configuration (FRC), CHARACTERIZED by the fact that it comprises the steps of: forming an FRC over a plasma in a confinement chamber, injecting a plurality of neutral beams into the plasma of FRC at an angle toward the midplane of the confinement chamber, and heating electrons of the FRC plasma with high harmonic fast waves propagating in the FRC plasma by launching a plurality of high harmonic fast waves from one or more antennas in the FRC plasma in the confinement chamber at a launch angle in a range of about 15° to about 25° from the midplane of the confinement chamber, wherein the high harmonic fast waves are fast in radio frequency bands. 2. Method, according to claim 1, CHARACTERIZED by the fact that the one or more antennas is a phased array antenna with a plurality of strips. 3. Method, according to claim 1, CHARACTERIZED by the fact that the step of heating the electrons includes heating the electrons from about 150 eV to above about 1 keV. 4. Method according to claim 1, CHARACTERIZED by the fact that it further includes maintaining the FRC at or about a constant value without decay by injecting beams of fast neutral atoms into the FRC plasma in the confinement chamber and raising electron temperatures of plasma to above 1.0. keV. 5. Method according to claim 1, CHARACTERIZED by the fact that it further comprises the step of generating a magnetic field within the confinement chamber with quasi-dc (quasi-dc) coils extending around the confinement chamber and a mirror magnetic field within opposite ends of the confinement chamber with quasi-dc mirror coils extending around the opposite ends of the confinement chamber. 6. Method according to claim 1, CHARACTERIZED by the fact that the step of forming the FRC includes forming a forming FRC in opposing first and second forming sections coupled to the confinement chamber and accelerating the forming FRC from the first and second formation sections towards the middle of the confinement chamber plane where the two formation FRCs merge to form the FRC. 7. System for generating and maintaining a magnetic field with a field reverse configuration (FRC), CHARACTERIZED by the fact that it comprises: a confinement chamber, first and second diametrically opposed FRC forming sections coupled to the confinement chamber, first and second divertors coupled to the first and second forming sections, one or more of a plurality of plasma guns, one or more polarizing electrodes, and first and second mirror plugs, wherein the plurality of plasma guns includes first and second polarizing guns. axial plasma operatively coupled to the first and second divertors, the first and second forming sections and the confinement chamber, wherein the one or more polarization electrodes are positioned within one or more of the confinement chamber, the first and second sections forming sections, and the first and second divertors, and wherein the first and second mirror plugs being positioned between the first and second forming sections and the first and second divertors, a gettering system coupled to the confinement chamber and the first and second divertors, a plurality of neutral atom beam injectors coupled to the confinement chamber and inclined toward a midplane of the confinement chamber, a magnetic system comprising a plurality of quasi-dc (quasi-dc) coils positioned around the chamber of confinement, the first and second forming sections, and the first and second divertors, and first and second sets of quasi-dc mirror coils positioned between the first and second forming sections and the first and second divertors, and a antenna including one or more antennas positioned around the confinement chamber adjacent to the midplane of the confinement chamber, wherein the antenna system is configured to launch fast high harmonic waves into the FRC plasma at a launch angle in a range of about 15° to about 25° from the midplane of the confinement chamber, where high harmonic fast waves are fast waves in radio frequency bands. 8. System according to claim 7, CHARACTERIZED by the fact that the antenna system includes phased array antennas with a plurality of strips. 9. System, according to claim 7, CHARACTERIZED by the fact that the radio frequency of high harmonic fast waves are in radio frequency bands of about 15 to 25 MHz. 10. System according to claim 7, CHARACTERIZED by the fact that the system is configured to heat FRC plasma electrons from about 150 eV to above about 1 keV. 11. System, according to claim 7, CHARACTERIZED by the fact that the system is configured to generate an FRC and maintain the FRC without decay while the neutral beams are injected into the plasma. 12. System, according to claim 11, CHARACTERIZED by the fact that the system is configured to raise FRC plasma electron temperature above about 1 keV. 13. System, according to claim 7, CHARACTERIZED by the fact that the first and second divertors comprise first and second internal divertors interposing the first and second formation sections and the confinement chamber, and further comprise first and second external divertors coupled to the first and second forming sections wherein the first and second forming sections interpose the first and second second internal diverters and the first and second external diverters, and further comprising one or more of the first and second coupled axial plasma guns operatively to the first and second internal and external divertors, the first and second forming sections and the confining chamber, and two or more saddle coils coupled to the confining chamber.