Systems and methods for improved support for high performance frc and high harmonic fast wave electron heating in high performance frc

Abstract

Systems and methods to facilitate the formation and maintenance of FRCs with excellent stability and particle, energy, and flux confinement, and more particularly, systems and methods to facilitate the formation and maintenance of FRCs with elevated system energy and improved support using neutral beam injection and high-harmonic fast-wave electron heating.

Description

[0001] This application is a divisional application of Chinese Patent Application No. 201780070992.7 (PCT Application No. PCT / US2017 / 061860), filed on November 15, 2017, entitled "System and method for improved support of high-performance FRC and high-order harmonic fast wave electronic heating in high-performance FRC". Technical Field

[0002] The embodiments described herein generally relate to magnetic plasma confinement systems with anti-field configurations (FRCs), and more specifically to systems and methods that facilitate the formation and maintenance of FRCs with excellent stability and particle, energy and flux confinement, and even more specifically to systems and methods that facilitate high-order harmonic fast-wave electron heating in FRCs. Background Technology

[0003] The reverse field configuration (FRC) belongs to a category of magnetoplasmic confinement topologies called compact toroidal (CT) topologies. FRCs primarily exhibit a poloidal magnetic field and possess a self-generated toroidal field that is zero or small (see M. Tuszewski, Nucl. Fusion 28, 2033 (1988)). The appeal of this configuration lies in its simple geometry, facilitating construction and maintenance, allowing for naturally unconstrained divertors that are beneficial for energy extraction and de-ashing, and its very high β (β is the ratio of the average plasma pressure to the average magnetic field pressure within the FRC), i.e., high power density. The high β characteristic is advantageous for economical operation and for the use of advanced, neutron-free fuels (such as D-He). 3 and pB 11 It is advantageous.

[0004] The conventional method for forming an FRC uses a field-reverse theta-pinch technique to generate a hot, high-density plasma (see AL Hoffman and JTSlough, Nucl. Fusion 33, 27 (1993)). A variation of this is the moving trapping method, in which the plasma generated in the angularly pinched “source” is ejected more or less immediately from one end into the confinement chamber. The moving plasma puff is then trapped between two strong mirrors at the end of the chamber (see, e.g., H. Himura, S. Okada, S. Sugimoto and S. Goto, Phys. Plasmas 2, 191 (1995)). Once in the confinement chamber, various heating and current-driven methods can be applied, such as beam injection (neutral or neutral), rotating magnetic fields, RF, or ohmic heating. This separation of the source and confinement functions provides key engineering advantages for potential future nuclear fusion reactors. FRCs have proven to be very robust and adaptable to dynamic formation, movement, and violent trapping events. Furthermore, they show a tendency to exhibit preferred plasma states (see, for example, HY Guo, AL Hoffman, KEMiller and LCSteinhauer, Phys. Rev. Lett. 92, 245001 (2004)). Significant progress has been made in the development of other FRC formation methods over the past decade: combining spherical marks with anti-helical properties (see, for example, Y. Ono, M. Inomoto, Y. Ueda, T. Matsuyama and T. Okazaki, Nucl. Fusion 39, 2001 (1999)) with current driven by a rotating magnetic field (RMF) (see, for example, IR Jones, Phys. Plasmas 6, 1950 (1999)), which also provides additional stability.

[0005] Recently, the collision-merging technique, proposed long ago (see, for example, DR. Wells, Phys. Fluids 9, 1010 (1966)), has been significantly further developed: two separate angular clamps at opposite ends of a confinement chamber simultaneously generate two plasma clumps and accelerate them toward each other at high speed; they then collide and merge at the center of the confinement chamber to form a composite FRC. In the construction and successful operation of one of the largest FRC experiments to date, the conventional collision-merging method has been shown to produce stable, long-lived, high-flux, high-temperature FRCs (see, for example, M. Binderbauer, HY. Guo, M. Tuszewski, et al., Phys. Rev. Lett. 105, 045003 (2010)).

[0006] The FRC comprises a loop of closed field lines within the interface and a ring-shaped edge layer on an open field line just outside the interface. The edge layers merge into jets exceeding the length of the FRC, providing a natural divertor. The FRC topology is consistent with that of field-reversing mirror plasmas. However, a significant difference is that the FRC plasma has a β of approximately 10. The inherently low internal magnetic field provides certain inherent dynamical particle populations, i.e., particles with large Larmor radii comparable to the small radius of the FRC. It is these strong dynamical effects that contribute at least in part to the overall stability of past and present FRCs (such as those produced in collision-merging experiments).

[0007] Past FRC experiments tended to be dominated by convection losses, where energy confinement was largely determined by particle transport. Particles diffuse radially out of the interface volume and then axially in the edge layer. Therefore, FRC confinement depends on the properties of both closed and open fieldline regions. The timescale of particle diffusion to the interface is τ ~ a. 2 / D(a~r s / 4, where r s (where D is the radius of the central interface), and D is the characteristic FRC diffusivity, such as D ~ 12.5ρ. ie , where ρ ie This represents the ion gyroradius, which is evaluated under an externally applied magnetic field. The edge layer particle confinement time τ... / / In past FRC experiments, the axial transport time was essentially the factor. In steady state, the balance between radial and axial particle losses produces the interface density gradient length δ (Dτ). / / ) 1 / 2 For past FRC particles with a relatively high density at the interface, the FRC particle confinement timescale is (τ-τ). / / ) 1 / 2 (See, for example, M. TUSZEWSKI, “Field Reversed Configurations”, Nucl. Fusion 28, 2033 (1988)).

[0008] Another drawback of existing FRC system designs is the lack of an effective electronic heating mechanism (regime) other than neutral beam injection. Due to the mechanism of power damping of electrons through ion-electron collisions, it tends to have poor electronic heating efficiency.

[0009] In light of the foregoing, it is desirable to improve support for FRC in order to use steady-state FRCs with elevated energy systems as a pathway to reactor cores for light nuclear fusion for future generations of energy. Summary of the Invention

[0010] The embodiments provided herein relate to systems and methods that facilitate the formation and maintenance of FRCs with excellent stability and particle, energy, and flux confinement, and more specifically to systems and methods that facilitate the formation and maintenance of FRCs with increased system energy and improved support, and more specifically to systems and methods that facilitate high-harmonic fast-wave electron heating in FRCs. According to embodiments of this disclosure, a method for generating and maintaining a magnetic field having a reverse field configuration (FRC) includes: forming an FRC with respect to a plasma in a confinement chamber; injecting a plurality of neutral beams at an angle toward the intermediate plane of the confinement chamber into the FRC plasma; and emitting high-harmonic fast waves in the radio frequency range into the FRC plasma for electron heating in the core of the FRC plasma.

[0011] According to another embodiment of this disclosure, the method further includes: maintaining the FRC at a constant or approximately constant value without decaying and raising the plasma electron temperature to above approximately 1.0 keV by emitting high-order harmonic fast waves in the radio frequency range into the FRC plasma at an angle relative to the intermediate through-plane of the confinement chamber.

[0012] Heating electrons via high-harmonic fast waves in the radio frequency range advantageously reduces fast ion charge exchange losses and improves plasma confinement, and also increases plasma current drive efficiency, which increases with electron temperature Te.

[0013] According to another embodiment of this disclosure, the method further includes: injecting compact ring (CT) plasma at an angle from first and second CT injectors toward the mid-plane of the confinement chamber into the FRC plasma, wherein the first and second CT injectors are exactly opposite each other on opposite sides of the mid-plane of the confinement chamber.

[0014] According to embodiments of this disclosure, a system for generating and maintaining a magnetic field having a reverse field configuration (FRC) includes: a confinement chamber; first and second opposing FRC generation sections coupled to the first and second confinement chambers; first and second divertors coupled to the first and second generation sections; one or more of the following: a plurality of plasma guns, one or more bias electrodes, and first and second 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 generation sections, and the confinement chamber; wherein one or more bias electrodes are positioned within one or more of the following: the confinement chamber, the first and second generation sections, and the first and second divertors; and wherein... The system includes: first and second mirror plugs positioned between first and second generation sections and first and second divertors; a gettering system coupled to the confinement chamber and the first and second divertors; multiple neutral atom beam injectors coupled to the confinement chamber and angled toward the midplane of the confinement chamber; a magnetic system including multiple quasi-DC coils positioned around the confinement chamber, the first and second generation sections, and the first and second divertors, with a first set and a second set of quasi-DC mirror coils positioned between the first and second generation sections and the first and second divertors; and one or more antennas coupled to the confinement chamber to transmit high-order harmonic fast waves in the radio frequency range for electronic heating of the core of the FRC plasma within the confinement chamber.

[0015] According to another embodiment of this disclosure, the system further includes: first and second compact ring (CT) injectors, which are angledly connected to the constraint chamber toward the intermediate plane of the constraint chamber, wherein the first and second CT injectors are exactly opposite each other on opposite sides of the intermediate plane of the constraint chamber.

[0016] The systems, methods, features, and advantages of the exemplary embodiments will become apparent to those skilled in the art upon review of the following accompanying drawings and detailed description. It is intended that all such additional methods, features, and advantages are included within this description and protected by the appended claims. It is also intended that the claims are not limited to the details required for the exemplary embodiments. Attached Figure Description

[0017] The accompanying drawings, which are included as a part of this specification, illustrate the exemplary embodiments of the invention and, together with the general description given above and the detailed description of the exemplary embodiments given below, serve to explain and teach the principles of the embodiments.

[0018] Figure 1 The illustration shows the particle confinement in this FRC system under the high-performance FRC mechanism (HPF) compared to the conventional FRC mechanism (CR) and compared to other conventional FRC experiments.

[0019] Figure 2 The diagram illustrates the components of this FRC system and the magnetic topology of the FRCs that can be generated in this FRC system.

[0020] Figure 3A The diagram illustrates the basic layout of this FRC system when viewed from above, including the preferred arrangement of the central constraint container, generation section, divertor, neutral beam, electrodes, plasma gun, mirror plug, and projectile injector.

[0021] Figure 3B The diagram illustrates the central constraint container as viewed from above, and shows the neutral bundles arranged at an angle orthogonal to the principal axis of symmetry within the central constraint container.

[0022] Figure 3C The illustration shows the central constraint container as viewed from above, and illustrates a neutral beam of particles arranged at an angle less than orthogonal to the principal axis of symmetry within the central constraint container and guided toward the central plane of the central constraint container.

[0023] Figure 3D and 3E Top and perspective views of the basic layout of an alternative embodiment of this FRC system are shown, including a preferred arrangement of the central confinement container, generation section, internal and external divertors, and neutral beam arranged at an angle less than orthogonal to the principal axis of symmetry of the central confinement container, electrodes, plasma gun, and mirror plug.

[0024] Figure 4 The diagram illustrates the components of the pulse power system for generating the pulse.

[0025] Figure 5 The illustration shows an isometric view of a single pulse power forming skid.

[0026] Figure 6 The illustration shows an isometric view of the generating tube assembly.

[0027] Figure 7 The illustration shows partial cross-sectional isometric views of the neutral beam system and key components.

[0028] Figure 8 An isometric view of the neutral bundle arrangement in the constraint chamber is shown.

[0029] Figure 9 The illustration shows a partial cross-sectional isometric view of a preferred arrangement of titanium and lithium intake systems.

[0030] Figure 10 The illustration shows a partial cross-sectional isometric view of a plasma gun installed in a divertor chamber. The associated magnetic mirror plug and divertor electrode assembly are also shown.

[0031] Figure 11 The figure illustrates a preferred arrangement of the annular bias electrode at the axial end of the constraint chamber.

[0032] Figure 12 The diagram illustrates the evolution of the exclusion flux radius in an FRC system obtained from a series of external diamagnetic loops at the two reversed-field-theta-pinch generation sections and at the magnetic probe embedded in the central metal confinement chamber. Time is measured from the moment the synchronizing field in the generation source reverses, and distance z is given relative to the axial midplane of the machine.

[0033] Figure 13A , Figure 13B , Figure 13C and Figure 13D The figure illustrates data from a representative non-HPF, unsupported discharge from this FRC system. Data shown as a function of time is ( Figure 13A The exclusion flux radius at the intermediate plane, Figure 13B The six chords of the line integration density from the mid-plane CO2 interferometer, Figure 13C Abelian inversion density radial distribution from CO2 interferometer data, and ( Figure 13D The total plasma temperature from pressure equilibrium.

[0034] Figure 14 The diagram illustrates the... Figure 13A , Figure 13B , Figure 13C and Figure 13D The diagram shows the axial distribution of the discharge flux of the same discharge in this FRC system at the selected time.

[0035] Figure 15 The illustration shows an isometric view of a saddle-shaped coil installed outside the constraint chamber.

[0036] Figure 16A , Figure 16B , Figure 16C and Figure 16D The diagram illustrates the correlation between FRC lifetime and the pulse length of the injected neutral beam. As shown, longer beam pulses result in longer-lived FRCs.

[0037] Figure 17A , Figure 17B , Figure 17C and Figure 17D The individual and combined effects of different components of the FRC system on FRC performance and the achievement of the HPF mechanism.

[0038] Figure 18A , Figure 18B , Figure 18C and Figure 18DThe figure illustrates representative HPF and unsupported discharge data from this FRC system. Data shown as a function of time is ( Figure 18A The exclusion flux radius at the intermediate plane, Figure 18B The six chords of the line integration density from the mid-plane CO2 interferometer, Figure 18C Abelian inverse density radial distribution from CO2 interferometer data, and ( Figure 18D The total plasma temperature from pressure equilibrium.

[0039] Figure 19 The figure illustrates the flux constraint as a function of electron temperature (Te). It represents a graphical representation of the newly established superior scaling mechanism for HPF discharge.

[0040] Figure 20 The figure illustrates the FRC lifetime corresponding to the pulse lengths of injected neutral beams that are non-angled and angled.

[0041] Figure 21A , Figure 21B , Figure 21C , Figure 21D and Figure 21E The diagram illustrates the lifetime of FRC plasma parameters (pulse length, plasma radius, plasma density, plasma temperature) for an angled injected neutral beam, and the magnetic flux corresponding to the pulse length of the angled injected neutral beam.

[0042] Figure 22A and Figure 22B The diagram illustrates the basic layout of a compact ring (CT) injector.

[0043] Figure 23A and Figure 23B The illustration shows a central constraint container and a CT injector installed into it.

[0044] Figure 24A and Figure 24B The illustration shows the basic layout of an alternative embodiment of a CT injector with a drift tube attached thereto.

[0045] Figure 25 The illustration shows the central confinement container as viewed from above, and illustrates a neutral beam of particles arranged at an angle less than orthogonal to the principal axis of symmetry in the central confinement container and guided toward the central plane of the central confinement container. An antenna is also shown from which high-order harmonic fast waves propagate at an angle less than orthogonal to the principal axis of symmetry in the central confinement container and are guided to propagate from the central plane of the central confinement container for heating plasma electrons.

[0046] Figure 26A and Figure 26BThe diagram illustrates the complete radial density distribution and complete radial electron temperature distribution of the FRC plasma in this FRC system.

[0047] Figures 27A-27D The diagram illustrates the radial distribution of the system equilibrium and characteristic frequencies at the midplane (Z=0) of this FRC system.

[0048] Figures 28A-28C The illustration shows the observation of power absorption and mode switching in the FRC plasma of this FRC system under microwave electronic heating conditions at 8 GHz.

[0049] Figures 29A-29F The illustration shows the observation of power absorption and mode switching in the FRC plasma of this FRC system under microwave electronic heating conditions at 50 GHz.

[0050] Figures 30A-30C The illustration shows the observation of power absorption in the FRC plasma of this FRC system under electronic heating conditions at a 0.5 GHz whistle wave.

[0051] Figure 31 The diagram illustrates the density distribution and wave propagation in the FRC plasma of this FRC system.

[0052] Figure 32 The diagram illustrates the poloidal flux distribution and wave propagation in the FRC plasma of this FRC system.

[0053] Figure 33 An exemplary density distribution and wave propagation trajectory in the FRC plasma of this FRC system are illustrated.

[0054] Figure 34 The illustration shows an exemplary ω / ω in the FRC plasma of this FRC system. ci[D] Distribution and wave propagation trajectory.

[0055] Figure 35 The illustration shows an exemplary power damping in the FRC plasma of this FRC system as the wave propagates.

[0056] Figure 36 An exemplary power absorption density in the FRC plasma of this FRC system is illustrated.

[0057] Figure 37A and Figure 37B An exemplary radial distribution of power density in the FRC plasma of this FRC system is illustrated.

[0058] Figure 38 An exemplary 2D distribution of damped power density in the FRC plasma of this FRC system is illustrated.

[0059] Figure 39 An exemplary power damping distribution in the FRC plasma of this FRC system is illustrated.

[0060] Figure 40 An exemplary finite-ion Larmor radius distribution in the FRC plasma of this FRC system is illustrated.

[0061] Figure 41 An exemplary power absorption distribution in the FRC plasma of this FRC system is illustrated.

[0062] Figure 42 An exemplary distribution of the FRC plasma in this FRC system is illustrated.

[0063] It should be noted that the drawings are not necessarily drawn to scale, and throughout the drawings, elements with similar structures or functions are often represented by similar reference numerals for illustrative purposes. It should also be noted that the drawings are intended only to facilitate the description of the various embodiments described herein. The drawings do not necessarily depict every aspect of the teachings disclosed herein and do not limit the scope of the claims. Detailed Implementation

[0064] The embodiments provided herein relate to systems and methods that facilitate the formation and maintenance of FRCs with excellent stability and particle, energy, and flux confinement. Some of these embodiments involve systems and methods that utilize neutral beam injection and high-harmonic fast-wave electron heating to facilitate the formation and maintenance of FRCs with increased system energy and temperature, as well as improved support.

[0065] Representative examples of the embodiments described herein will now be described in more detail with reference to the accompanying drawings. These examples utilize many of these additional features and teachings, individually and in combination. This detailed description is intended only to teach those skilled in the art further details for practicing the preferred aspects of this teaching and is not intended to limit the scope of the invention. Therefore, in the broadest sense, the combination of features and steps disclosed in the following detailed description may not be necessary for practicing the invention, but rather is merely a teaching to specifically describe representative examples of this teaching.

[0066] Furthermore, various features of the representative examples and dependent claims may be combined in a manner not specifically and explicitly enumerated to provide additional useful embodiments of this teaching. Moreover, it is expressly stated that, for the purposes of the original disclosure and for the purpose of limiting the claimed subject matter independently of the composition of features in the embodiments and / or claims, all features disclosed in the specification and / or claims are intended to be disclosed separately and independently of each other. It is also expressly stated that, for the purposes of the original disclosure and for the purpose of limiting the claimed subject matter, all indications of value ranges or entity groups disclose every possible intermediate value or intermediate entity.

[0067] Before moving on to systems and methods favorable for high-harmonic fast-wave electron heating in FRC plasmas, this paper discusses systems and methods for forming and maintaining high-performance FRCs with superior stability and excellent particle, energy, and flux confinement compared to conventional FRCs, as well as systems and methods for forming and maintaining high-performance FRCs without decay at constant or approximately constant values. Such high-performance FRCs provide pathways to a wide range of applications, including compact neutron sources (for medical isotope production, nuclear waste management, materials research, neutron radiography, and tomography), compact photon sources (for chemical production and processing), mass separation and enrichment systems, and reactor cores for photonuclear fusion for future energy generation.

[0068] Various auxiliary systems and operating modes have been developed to evaluate the existence of superior constraint mechanisms in FRC. These efforts have led to groundbreaking findings and the development of the high-performance FRC paradigm described in this paper. Based on this new paradigm, this system and method combine a number of novel ideas and techniques to... Figure 1 The results show a significant improvement in FRC constraint and provide stability control without negative side effects. As discussed in more detail below, Figure 1 The particle constraint in the FRC system 10 described below is depicted (see Figure 2 (and Figure 3), compared to operation based on the conventional mechanism CR used in other experiments for forming and maintaining FRC, and compared to particle constraints based on the conventional mechanism for forming and maintaining FRC, it operates based on the high-performance FRC (HPF) mechanism for forming and maintaining FRC. This disclosure will outline and detail the innovative individual components of the FRC system 10 and the method, as well as their combined effect.

[0069] FRC System

[0070] Vacuum system

[0071] Figure 2Figure 3 illustrates a schematic diagram of the FRC system 10. The FRC system 10 includes a central confinement container 100 surrounded by two opposing anti-field angles constricting the generating portion 200, and two divertor chambers 300 located outside the generating portion 200. The divertor chambers 300 are used to control neutral density and impurity contamination. The FRC system 10 is configured to accommodate ultra-high vacuum and operates at 10... -8 The typical basic pressure operation of the Tor is achieved through a vacuum pressure system. This vacuum pressure requires the use of a double-pumped mating flange between mating components, a metal O-ring, a high-purity inner wall, and meticulous initial surface treatment of all parts before assembly, such as physical and chemical cleaning, followed by 24 hours of vacuum baking at 250°C and hydrogen glow discharge cleaning.

[0072] The reverse field angle pinch generation section 200 is a standard reverse field angle pinch (FRTP), although it has the advanced pulse power generation system discussed in detail below (see Figures 4 to 6 Each generation section 200 is made of standard opaque industrial-grade quartz tubing, featuring a 2 mm ultrapure quartz liner. The confinement chamber 100 is made of stainless steel to allow for multiple radial and tangential ports; it also serves as a flux conserver on the timescales of the experiments described below and confines rapid magnetic transients. A vacuum is generated and maintained within the FRC system 10 using a set of dry vortex low-vacuum pumps, turbomolecular pumps, and cryogenic pumps.

[0073] Magnetic system

[0074] Figure 2 The magnetic system 400 is illustrated in Figure 3. Among other features, Figure 2 The illustration shows the FRC flux and isodensity lines (as a function of radial and axial coordinates) belonging to the FRC 450, which can be generated by the FRC system 10. These isodensity lines were obtained through a 2-D resistive Hall-MHD digital simulation using code developed to simulate the system and methods corresponding to the FRC system 10 and are in good agreement with measured experimental data. Figure 2 As seen, the FRC 450 includes a loop of closed field lines within the interface 451 at the interior 453 of the FRC 450, and an annular edge layer 456 just outside the interface 451 on the open field line 452. The edge layer 456 merges into a jet 454 outside the length of the FRC, thereby providing a natural divertor.

[0075] The main magnetic system 410 includes a series of quasi-DC coils 412, 414, and 416 located at specific axial positions along the components of the FRC system 10 (i.e., along the constraint chamber 100, the generation section 200, and the divertor 300). The quasi-DC coils 412, 414, and 416 are fed by a quasi-DC switching power supply and generate a fundamental magnetic offset field of approximately 0.1T in the constraint chamber 100, the generation section 200, and the divertor 300. In addition to the quasi-DC coils 412, 414, and 416, the main magnetic system 410 also includes a quasi-DC mirror coil 420 (fed by a switching power supply) between either end of the constraint chamber 100 and the adjacent generation section 200. The quasi-DC mirror coil 420 provides a magnetic mirror ratio of up to 5 and can be independently excited for balanced forming control. Additionally, a mirror plug 440 is positioned between each of the generation section 200 and the divertor 300. The mirror plug 440 includes a compact quasi-DC mirror coil 430 and a mirror plug coil 444. The quasi-DC mirror coil 430 includes three coils 432, 434, and 436 (fed by a switching power supply) that generate an additional guiding field to focus the magnetic flux surface 455 toward the small-diameter channel 442 passing through the mirror plug coil 444. The mirror plug coil 444, which surrounds the small-diameter channel 442 and is fed by an LC pulse power supply circuit, generates a strong magnetic mirror field up to 4T. The purpose of this entire coil arrangement is to tightly bind and guide the magnetic flux surface 455 and the plasma jet 454 flowing at the ends into the distal chamber 310 of the divertor 300. Finally, a set of saddle-shaped coil "antennas" 460 (see...) Figure 15 Located outside the confinement chamber 100, two antennas are positioned on each side of the intermediate plane and fed by a DC power supply. The saddle-shaped coil antenna 460 can be configured to provide a quasi-static magnetic dipole or quadrupole field of approximately 0.01 T for controlling rotational instability and / or electron flow control. Depending on the direction of the applied current, the saddle-shaped coil antenna 460 can flexibly provide a magnetic field that is symmetrical or antisymmetrical about the intermediate plane of the machine.

[0076] Pulse power generation system

[0077] The pulse power generation system 210 operates based on a modified angular pinch principle. There are two systems, each providing energy to one of the generation sections 200. Figures 4 to 6The main building blocks and arrangement of the generation system 210 are illustrated. Generation system 210 includes a modular pulsed power arrangement comprising individual units (i.e., skids) 220, each energizing a subset of coils 232 of a strip assembly 230 (i.e., a strip), the strip assembly 230 being wound around a generation quartz tube 240. Each skid 220 includes a capacitor 221, an inductor 223, a fast high-current switch 225, and an associated trigger 222, as well as a dump circuitry 224. In total, each generation system 210 stores capacitive energy between 350 and 400 kJ, providing up to 35 GW of power to form and accelerate FRC. Coordinated operation of these components is achieved via state-of-the-art trigger and control systems 222 and 224, which allow for synchronized timing between generation systems 210 at each generation section 200 and minimize switching jitter to tens of nanoseconds. The advantage of this modular design is its flexible operation: FRC can be formed in the field and then accelerated and injected (= static formation) or formed and accelerated simultaneously (= dynamic formation).

[0078] Neutral beam injector

[0079] A neutral atom beam 600 was deployed on the FRC system 10 to provide heating and current drive, as well as to generate fast particle pressure. Figure 3A , Figure 3B and Figure 8 As shown, the individual beamlines include neutral atom beam injector systems 610 and 640, which are positioned around the central confinement chamber 100 and tangential to the FRC plasma (and perpendicular to or orthogonal to the principal axis of symmetry in the central confinement chamber 100) to parametrically inject fast particles with collisional parameters, such that the target trapping region is well located within the interface 451 (see...). Figure 2 Each injector system 610 and 640 is capable of injecting up to 1 MW of neutral beam power into FRC plasmas with particle energies between 20 and 40 keV. Systems 610 and 640 are based on a positive ion porous extraction source and utilize geometric focusing, inertial cooling of the ion extraction grid, and differential pumping. Aside from using different plasma sources, the main difference between systems 610 and 640 lies in their physical design to accommodate their respective mounting locations, thus enabling both side and top injection capabilities. Typical components of these neutral beam injectors are... Figure 7 The side injector system 610 is illustrated in detail. For example... Figure 7As shown, each individual neutral beam system 610 includes an RF plasma source 612 located at the input end (replaced by an arc source in system 640), with a magnetic shield 614 covering this end. An ion source and an accelerating grid 616 are coupled to the plasma source 612, and a gate valve 620 is positioned between the ion source and the accelerating grid 616 and the neutralizer 622. A deflecting magnet 624 and an ion dump 628 are located between the neutralizer 622 and an aiming device 630 at the exit end. The cooling system includes two cryogenic refrigerators 634, two cryogenic plates 636, and an LN2 shield 638. This flexible design allows operation over a wide range of FRC parameters.

[0080] An alternative configuration for the neutral atom beam injector 600 is one in which fast particles are injected tangentially to the FRC plasma, but at an angle A less than 90° relative to the principal axis of symmetry in the central confinement container 100. These types of orientations of the beam injector 615 are... Figure 3C As shown in the diagram. Additionally, the beam injectors 615 can be oriented such that beam injectors 615 on either side of the central plane of the central confinement container 100 inject their particles toward the central plane. Ultimately, the axial position of these beam systems 600 can be selected to be closer to the central plane. These alternative injection embodiments favor a more central feeding option, which provides better beam coupling and higher capture efficiency of the injected fast particles. Furthermore, depending on the angle and axial position, this arrangement of the beam injectors 615 allows for more direct and independent control over the axial elongation and other characteristics of the FRC 450. For example, injecting the beam at a shallow angle A relative to the main axis of symmetry of the container will produce an FRC plasma with a longer axial extension and a lower temperature, while selecting a more perpendicular angle A will result in a plasma with a shorter axial extension but a hotter temperature. In this way, the injection angle A and position of the beam injectors 615 can be optimized for different purposes. Furthermore, this angled orientation and positioning of the beam injector 615 allows beams with higher energies (which are generally more advantageous for depositing more power with less beam divergence) to be injected into a lower magnetic field than would otherwise be necessary to capture such a beam. This is due to the fact that the azimuth component of the energy determines the fast ion orbital scale (which gradually becomes smaller with decreasing injection angle relative to the principal axis of symmetry of the container at constant beam energy). Moreover, angled injection toward the midplane, with the axial beam position close to the midplane, improves beam-plasma coupling, even during the injection period when the FRC plasma shrinks or otherwise axially contracts.

[0081] Go to Figure 3D and Figure 3EAnother alternative configuration of the FRC system 10, in addition to the angled beam injector 615, includes an internal divertor 302. The internal divertor 302 is positioned between the generation section 200 and the confinement chamber 100 and is substantially similar in construction and operation to the external divertor 300. This includes the internal divertor 302, which features a rapidly switching magnetic coil, being effectively idled during the formation process so that the generated FRC can pass through it as it moves toward the midplane of the confinement chamber 100. Once the generated FRC has passed through the internal divertor 302 and entered the confinement chamber 100, the internal divertor is activated to operate substantially similarly to the external divertor and isolates the confinement chamber 100 from the generation section 200.

[0082] Projectile Injector

[0083] To provide a means of injecting new particles and better controlling the FRC particle stock, a 12-tube projectile injector 700 was employed on the FRC system 10 (see, for example, I. Vinyar et al., “Pellet Injectors Developed at PELIN for JET, TAE, and HL-2A,” Proceedings of the 26th Symposium on Nuclear Fusion Science and Technology, 09 / 27–10 / 01 (2010)). Figure 3 illustrates the layout of the projectile injector 700 on the FRC system 10. Cylindrical projectiles (D~1mm, L~1-2mm) were injected into the FRC at velocities ranging from 150 to 250 km / s. Each individual projectile contained approximately 5 × 10⁻⁶ particles. 19 One hydrogen atom, which is comparable to the number of FRC particles.

[0084] Inhalation system

[0085] It is well known that neutral aura gases are a serious problem in all confinement systems. The charge exchange and recovery (release of cold impurity material from the walls) processes can have devastating effects on energy and particle confinement. Furthermore, any high density of neutral gas at or near the edge will lead to the rapid loss of injected large-orbit (high-energy) particles or at least a severely shortened lifetime (large orbits are defined as orbits on the scale of the FRC topology, or at least orbit radii much larger than the length of the characteristic magnetic field gradient), a fact detrimental to all high-energy plasma applications, including nuclear fusion heated via an auxiliary beam.

[0086] Surface treatment is a means of controlling or reducing the adverse effects of neutral gases and impurities in a confinement system. For this purpose, the FRC system 10 presented herein employs titanium and lithium deposition systems 810 and 820, which coat the plasma-facing surfaces of the confinement chamber (or container) 100 and divertors 300 and 302 with films of titanium and / or lithium (tens of micrometers thick). The coating is achieved via vapor deposition. Solid lithium and / or titanium are evaporated and / or sublimated and sprayed onto nearby surfaces to form the coating. The source is an atomic furnace with a guide nozzle (in the case of lithium) 822 or a heated solid sphere with a guide shroud (in the case of titanium) 812. Lithium evaporator systems typically operate in continuous mode, while titanium sublimators mostly operate intermittently between plasma operations. These systems operate at temperatures above 600°C to achieve rapid deposition rates. Multiple strategically positioned evaporator / sublimator systems are necessary to achieve good wall coverage. Figure 9 The preferred arrangement of getter deposition systems 810 and 820 in FRC system 10 is shown in detail. The coating acts as an getter surface and effectively pumps hydrogen-like atomic and molecular impurities (H and D). The coating also reduces other typical impurities such as carbon and oxygen to insignificant levels.

[0087] Mirror plug

[0088] As described above, the FRC system 10 adopts, for example Figure 2And the grouped mirror coils 420, 430, and 444 shown in Figure 3. The first group of mirror coils 420 is located at both axial ends of the constraint chamber 100 and is excited independently of the DC constraint, forming, and divertor coils 412, 414, and 416 of the main magnetic system 410. The first group of mirror coils 420 primarily helps guide and axially contain the FRC 450 during merging and provides balanced forming control during support. The first group of mirror coils 420 generates a nominally higher magnetic field (approximately 0.4 to 0.5 T) than the central constraint field generated by the central constraint coil 412. The second group of mirror coils 430, comprising three compact quasi-DC mirror coils 432, 434, and 436, is located between the generating section 200 and the divertor 300 and is driven by a common switching power supply. Mirror coils 432, 434, and 436, together with a more compact pulsed mirror plug coil 444 (fed by a capacitive power supply) and a physical contraction 442, form a mirror plug 440, which provides a narrow, low-gas conduction path with a very high magnetic field (between 2 and 4 T and a rise time of approximately 10 to 20 ms). The most compact pulsed mirror coil 444 has a compact radial dimension, a 20 cm aperture, and a similar length compared to the meter-plus-scale orifice and pancake-shaped design of the confined coils 412, 414, and 416. The mirror plug 440 serves multiple purposes: (1) the coils 432, 434, 436, and 444 are tightly bundled and guide the magnetic flux surface 452 and the end-flow plasma jet 454 into the remote divertor chamber 300. This ensures that the emitted particles properly reach the divertor 300 and that there is a continuous flux surface 455 extending from the open field line 452 region of the central FRC 450 all the way to the divertor 300. (2) The physical constriction section 442 in the FRC system 10 provides an obstruction to the flow of neutral gas from the plasma gun 350 placed in the divertor 300, and the coils 432, 434, 436 and 444 allow the magnetic flux surface 452 and the plasma jet 454 to pass through the physical constriction section 442. Similarly, the constriction section 442 prevents the backflow of gas from the generation section 200 to the divertor 300, thereby reducing the number of neutral particles that must be introduced into the entire FRC system 10 when the FRC is started. (3) The strong axial mirror generated by the coils 432, 434, 436 and 444 reduces axial particle loss and thus reduces parallel particle diffusivity on the open field line.

[0089] exist Figure 3D and Figure 3E In the alternative configuration shown, a set of low-profile necking coils 421 are positioned between the internal divertor 302 and the generating section 200.

[0090] Axial plasma gun

[0091] The plasma flow from the gun 350, which is installed in the divertor chamber 310 of the divertor 300, is intended to improve stability and neutral beam performance. (See Figure 3 and...) Figure 10 As shown, the gun 350 is mounted on an axis within chamber 310 of the divertor 300 and generates plasma flowing along open flux line 452 within the divertor 300 and toward the center of the confinement chamber 100. The gun 350 operates with a high-density gas discharge in a gasket-stacked channel and is designed to generate fully ionized plasma of several thousand amperes for 5 to 10 ms. The gun 350 includes a pulsed magnetic coil that matches the output plasma flow to the desired size of the plasma in the confinement chamber 100. The gun 350 is characterized by a channel with an outer diameter of 5 to 13 cm and an inner diameter of up to approximately 10 cm, and provides a discharge current of 10-15 kA at 400-600 V, with an internal magnetic field between 0.5 and 2.3 T.

[0092] The gun plasma flow can penetrate the magnetic field of the lens plug 440 and flow into the generation section 200 and the confinement chamber 100. As the distance between the gun 350 and the plug 440 decreases, and by making the plug 440 wider and shorter, the efficiency of plasma transfer through the lens plug 440 increases. Under suitable conditions, the gun 350 can deliver approximately 10 plasmas each at high ion and electron temperatures of approximately 150 to 300 eV and approximately 40 to 50 eV, respectively. 22 One proton / s through the 2 to 4T mirror plug 440. Gun 350 provides significant refeeding of the FRC edge layer 456, as well as improved overall FRC particle confinement.

[0093] To further increase the plasma density, a gas box can be used to inject additional gas into the plasma stream from gun 350. This technique allows for a several-fold increase in the injected plasma density. In FRC system 10, the gas box mounted on the divertor 300 side of mirror plug 440 improves the refeeding of FRC edge layer 456, the formation of FRC 450, and plasma line-tying.

[0094] Considering all the adjustment parameters discussed above, and also considering that it is possible to operate with only one gun or with two guns, it is easy to see that a wide range of operating modes can be obtained.

[0095] bias electrode

[0096] The electrical bias voltage on the open flux surface can provide a radial potential that causes an azimuth angle E×B movement. This provides a control mechanism similar to turning a knob to control the rotation of the open fieldline plasma and the actual FRC core 450 via velocity shear. To achieve this control, the FRC system 10 employs various electrodes strategically placed in various parts of the machine. Figure 3 depicts the bias electrodes positioned in preferred locations within the FRC system 10.

[0097] In principle, there are four types of electrodes: (1) point electrodes 905 in the confinement chamber 100, which contact specific open field lines 452 at the edge of the FRC 450 to provide local charging; (2) annular electrodes 900 between the confinement chamber 100 and the generation section 200, to charge the far-edge flux layer 456 in an azimuth-symmetrical manner; (3) a stack of concentric electrodes 910 in the divertor 300 to charge multiple concentric flux layers 455 (where the selection of layers is controllable by adjusting the divertor magnetic field by adjusting the coil 416 to terminate the desired flux layer 456 on the appropriate electrode 910); and finally (4) the anode 920 of the plasma gun 350 (see Figure 10 It itself (its open flux surface 455 is intercepted near the interface of FRC 450). Figure 10 and Figure 11 Some typical designs for some of these electrodes are shown.

[0098] In all cases, these electrodes are driven by a pulsed or DC power supply at voltages up to approximately 800V. Depending on the electrode size and the flux surface they intersect with, currents in the range of kiloamperes can be drawn.

[0099] FRC system's unsupported operations - standard mechanisms

[0100] Standard plasma formation on the FRC system 10 follows a well-developed reverse-field angular pinch technique. A typical process for starting the FRC begins by driving quasi-DC coils 412, 414, 416, 420, 432, 434, and 436 to steady-state operation. Then, the RFTP pulse power circuit of the pulse power generation system 210 drives the pulsed fast reverse magnetic field coil 232 to generate a temporary reverse bias of approximately -0.05T in the generation section 200. At this time, a predetermined amount of neutral gas is injected at 9–20 psi into the two formation volumes defined by the quartz chambers 240 of the (north and south) generation sections 200 via a set of azimuth-oriented puff-vales located at the outer ends of the generation section 200. Next, a small RF (~several hundred kHz) field is generated from a set of antennas on the surface of the quartz tubes 240 to generate pre-ionization within the neutral gas column in the form of a localized seed ionization region. This is followed by theta-ringing modulation of the current in the driving pulse fast reverse magnetic field coil 232, which results in more comprehensive pre-ionization of the gas column. Finally, the main pulse power group of the pulse power generation system 210 is activated to drive the pulse fast reverse magnetic field coil 232, thereby generating a forward bias field of up to 0.4T. This step can be sequential in time, so that a forward bias field is generated uniformly along the length of the generation tube 240 (static formation), or it can achieve continuous creeping field modulation along the axis of the generation tube 240 (dynamic formation).

[0101] Throughout this formation process, the actual field reversal in the plasma occurs rapidly within approximately 5 μs. The multi-gigawatt pulsed power supplied to the formed plasma readily generates thermal FRCs, which are then ejected from the generation section 200 via time-sequential modulation (magnetic creep) of the applied forward magnetic field or by a temporary increase in current in the last coil of coil group 232 near the axial outer end of the generation tube 210 (forming an axial magnetic field gradient pointing axially toward the confinement chamber 100). The two (north and south) generated FRCs thus formed and accelerated then extend into the larger-diameter confinement chamber 100, where a quasi-DC coil 412 generates a forward bias field to control radial expansion and provide a balanced external magnetic flux.

[0102] Once the north- and south-generated FRCs reach the vicinity of the midplane of confinement chamber 100, the FRCs collide. During the collision, the axial kinetic energy of the north- and south-generated FRCs is largely thermalized as the FRCs eventually merge into a single FRC 450. A large set of plasma diagnostics is available in confinement chamber 100 to investigate the equilibrium of the FRC 450. Typical operating conditions in FRC system 10 produce a composite FRC with an interface radius of approximately 0.4 m and an axial extension of approximately 3 m. Further characteristics include an external magnetic field of approximately 0.1 T and approximately 5 × 10⁻⁶ T / m². 19 m -3 The plasma density and total plasma temperature are as high as 1 keV. Without any support, i.e., without heating and / or current driving via neutral beam injection or other auxiliary means, the lifetime of these FRCs is limited to about 1 ms, with an inherent characteristic decay time.

[0103] Experimental data without supporting operations - conventional mechanism

[0104] Figure 12 This shows a typical time evolution excluding the flux radius rΔФ, which is close to the interface radius r. s The diagram illustrates the dynamics of the angular pinch-and-merge process in FRC 450. Two separate plasma blobs (north and south) are generated simultaneously and then move at supersonic speeds of v. Z The plasma is accelerated away from the corresponding generating portion 200 at speeds of approximately 250 km / s and collides near the intermediate plane at z = 0. During the collision, the plasma clump is axially compressed, followed by rapid radial and axial expansion, before finally merging to form FRC 450. The radial and axial dynamics of the merged FRC 450 are shown through detailed density distribution measurements and tomographic imaging based on a radiometer.

[0105] Representative unsupported discharge data from FRC system 10 Figure 13A , Figure 13B , Figure 13C and Figure 13D The FRC is shown as a function of time. The FRC begins at t = 0. The discharge flux radius at the axial midplane of the machine is... Figure 13A As shown in the figure. This data was obtained from an array of magnetic probes located directly within the stainless steel wall of the confinement chamber, which measured the axial magnetic field. The steel wall is a good flux retainer on this discharge timescale.

[0106] Figure 13B The line integral density is shown in the figure, from a 6-string CO2 / He-Ne interferometer located at z=0. Taking into account the vertical (y) FRC shift, as measured by radiometric tomography, Abel inversion yielded... Figure 13CThe FRC exhibits isodense lines. After some axial and radial oscillations during the first 0.1 ms, it stabilizes with a hollow density distribution. This distribution is fairly flat and has a considerable density along the axis, as is required for typical 2-D FRC equilibration.

[0107] Figure 13D The total plasma temperature is shown, which originates from pressure equilibrium and is in perfect agreement with Thomson scattering and spectroscopic measurements.

[0108] Analysis of the entire exclusion flux array indicates that the shape of the FRC interface (approximate by the axial distribution of exclusion flux) gradually evolves from a racetrack shape to an ellipse. Figure 14 The evolution shown is consistent with the gradual magnetic reconnection from two to a single FRC. In fact, a rough estimate suggests that in this particular case, approximately 10% of the magnetic flux of the two initial FRCs reconnects during the collision.

[0109] The FRC length steadily decreased from 3m to approximately 1m during the FRC's lifespan. Figure 14 This visible shortening indicates that convective energy loss primarily dominates the FRC confinement. As the plasma pressure within the interface decreases faster than the external magnetic pressure, the magnetic field line tension in the end region axially compresses the FRC, thereby restoring axial and radial balance. (See Figure 13 and...) Figure 14 The discharge discussed in the paper, when the FRC equilibrium declines, the FRC magnetic flux, particle stock, and thermal energy (approximately 10 mWb, 7 × 10⁻⁶ ... 19 The number of particles and 7 kJ decreased by approximately an order of magnitude within the first millisecond.

[0110] Supported Operations - HPF Mechanism

[0111] Figures 12 to 14 The example shown is a feature of attenuated FRC without any support. However, several techniques have been deployed on FRC system 10 to further improve the FRC constraints (core and edge layers) to the HPF mechanism and support this configuration.

[0112] Neutral bundle

[0113] First, the fast (H) neutral particle is perpendicular to B. zBeams from eight neutral beam injectors 600 are injected. Beams of fast neutral particles generated from the north and south are injected at the moment they merge into a single FRC 450 in confinement chamber 100. The fast ions, primarily generated by charge exchange, have electron-inductively coupled accelerator orbits that increase the azimuth current of the FRC 450 (having a principal radius on the scale of the FRC topology or at least much larger than the length scale of the characteristic magnetic field gradient). After a partial discharge (0.5 to 0.8 ms after ingress emission), a sufficiently large fast ion population significantly improves the stability and confinement properties of the inner FRC (see, for example, MWIBinderbauer and N. Rostoker, Plasma Phys. 56, Part 3, 451 (1996)). Furthermore, from a support perspective, the beams from the neutral beam injectors 600 are also the primary means of driving the current and heating the FRC plasma.

[0114] In the plasma mechanism of FRC system 10, fast ions are primarily slowed down by plasma electrons. In the early portion of the discharge, the typical orbital slowing time for fast ions is 0.3–0.5 ms, resulting in significant FRC heating, primarily of electrons. Fast ions exhibit large radial drift outside the interface due to the inherently low internal FRC magnetic field (averaging approximately 0.03 T for an external axial field of 0.1 T). If the neutral gas density outside the interface is too high, the fast ions will be susceptible to charge exchange losses. Therefore, wall suction and other techniques deployed on FRC system 10 (such as the plasma gun 350 and mirror plug 440, which, among other things, aid in gas control) tend to minimize edge neutral particles and enable the necessary establishment of a fast ion flow.

[0115] Projectile injection

[0116] When a significant rapid ion population is established within the FRC 450, frozen H or D pellets are injected from the pellet injector 700 into the FRC 450 with higher electron temperatures and longer FRC lifetimes to support the FRC particle stock of the FRC 450. The expected ablation timescale is sufficiently short to provide a large source of FRC particles. This rate can also be increased by expanding the surface area of ​​the injector, which is achieved by breaking individual pellets into smaller fragments in the injection tube or canister of the pellet injector 700 and before entering the confinement chamber 100. This is achieved by increasing the friction between the pellet and the wall of the injection tube by tightening the bend radius of the final section of the injection tube just before entering the confinement chamber 100. By varying the activation sequence and rate of the 12 canisters (injection tubes) and the fragmentation, it is possible to tune the pellet injection system 700 to provide exactly the desired level of particle stock support. This, in turn, helps maintain the internal dynamic pressure within the FRC 450 and the supported operation and lifetime of the FRC 450.

[0117] Once the ablated atoms encounter a large amount of plasma in the FRC 450, they become completely ionized. The resulting cold plasma component is then heated by collisions with the inherent FRC plasma. The energy necessary to maintain the desired FRC temperature is ultimately supplied by the beam injector 600. In this sense, the projectile injector 700, together with the neutral beam injector 600, forms a system that maintains steady state and supports the FRC 450.

[0118] CT injector

[0119] As an alternative to the projectile injector, a compact ring (CT) injector is provided, primarily for feeding reverse field configuration (FRC) plasma. The CT injector 720 includes a magnetized coaxial plasma gun (MCPG), such as... Figure 22A and Figure 22B As shown, it includes a coaxial cylindrical inner electrode 722 and an outer electrode 724, a bias coil 726 positioned inside the inner electrode, and an electrical break 728 on the opposite end of the discharge of the CT injector 720. Gas is injected through a gas injection port 730 into the space between the inner electrode 722 and the outer electrode 724, and a spherical marker plasma is thereby generated by the discharge and ejected from the gun by the Lorentz force. Figure 23A and Figure 23BAs shown, a pair of CT injectors 720 are connected to the confinement container 100 near the midplane and on opposite sides of the midplane to inject CT into the central FRC plasma within the confinement container 100. Similar to the neutral beam injector 615, the discharge ends of the CT injectors 720 are directed at an angle relative to the longitudinal axis of the confinement container 100 toward the midplane of the confinement container 100.

[0120] In alternative embodiments, such as Figure 24A and Figure 24B As shown, the CT injector 720 includes a drift tube 740, which comprises an elongated cylindrical tube coupled to the discharge end of the CT injector 720. As depicted, the drift tube 740 includes drift tube coils 742 positioned around the tube and spaced apart along the tube's axial direction. A plurality of diagnostic ports 744 are depicted along the length of the tube.

[0121] The advantages of the CT injector 720 are: (1) control and adjustability of particle stock via injected CT; (2) deposition of hot plasma (instead of frozen projectiles); (3) the ability of the system to operate in repeat-rate mode to allow for continuous feeding; and (4) the ability of the system to recover some magnetic flux because the injected CT carries an embedded magnetic field. In an embodiment for experimental use, the inner diameter of the outer electrode is 83.1 mm and the outer diameter of the inner electrode is 54.0 mm. The surface of the inner electrode 722 is preferably coated with tungsten to reduce impurities exiting the electrode 722. As depicted, a bias coil 726 is mounted within the inner electrode 722.

[0122] In recent experiments, supersonic CT movement speeds up to ~100 km / s were achieved. Other typical plasma parameters are as follows: electron density ~5 × 10²¹ m⁻³, electron temperature ~30-50 eV, and particle stock ~0.5-1.0 × 10¹⁹. The high dynamic pressure of the CT allows the injected plasma to penetrate deeply into the FRC and deposit particles within the interface. In recent experiments, FRC particle feeding has resulted in a ~10-20% FRC particle stock being provided via the CT injector, successfully demonstrating that feeding can be easily implemented without disrupting the FRC plasma.

[0123] Saddle coil

[0124] To achieve steady-state current drive and maintain the required ion flow, it is desirable to prevent or significantly reduce electron spin acceleration caused by electron-ion friction (due to momentum transfer between ion electrons caused by collisions). The FRC system 10 utilizes an innovative technique to provide electron breakup via an externally applied static magnetic dipole or quadrupole field. This is achieved through… Figure 15This is achieved using the external saddle-shaped coil 460 depicted in the diagram. A radial magnetic field applied laterally from the saddle-shaped coil 460 induces an axial electric field in the rotating FRC plasma. The resulting axial electron flow interacts with the radial magnetic field, thereby generating an azimuth-breaking force on the electrons, F... θ =-σV ee <|B r | 2 For typical conditions in FRC system 10, the magnetic dipole (or quadrupole) field required within the plasma only needs to be on the order of 0.001 T to provide sufficient electron breakup. The corresponding external field of approximately 0.015 T is small enough not to cause significant fast particle loss or otherwise negatively affect confinement. In fact, the applied magnetic dipole (or quadrupole) field helps suppress instabilities. Combined with tangential neutral beam injection and axial plasma injection, the saddle coil 460 provides an additional level of control regarding current maintenance and stability.

[0125] Mirror plug

[0126] The design of the pulse coil 444 within the mirror plug 440 allows for the local generation of a high magnetic field (2 to 4 T) with a moderate (approximately 100 kJ) capacitive energy. To form the typical magnetic field for this operation of the FRC system 10, all field lines within the forming volume pass through the contraction section 442 at the mirror plug 440, as... Figure 2 The field lines indicate that no plasma wall contact occurs. Furthermore, the mirror plug 440, connected in series with the quasi-DC divertor magnet 416, can be adjusted to guide the field lines onto the divertor electrode 910, or to spread the field lines in a cusp configuration (not shown). The latter improves stability and suppresses parallel electron thermal conduction.

[0127] The mirror plug 440 itself also contributes to neutral gas control. The mirror plug 440 allows for better utilization of the deuterium gas filled into the quartz tube during FRC formation, as the small gas conduction (a meager 500 L / s) of the gas backflow into the divertor 300 is significantly reduced by the plug. Most of the residual filling gas within the generation tube 210 is rapidly ionized. Furthermore, the high-density plasma flowing through the mirror plug 440 provides effective neutral particle ionization, thus providing an effective gas barrier. As a result, most of the neutral particles recovered from the FRC edge layer 456 in the divertor 300 do not return to the confinement chamber 100. Additionally, most of the neutral particles associated with the operation of the plasma gun 350 (discussed below) will be confined within the divertor 300.

[0128] Finally, the mirror plug 440 is intended to improve the confinement of the FRC edge layer. Using a mirror ratio (plug / confinement magnetic field) in the range of 20 to 40, and utilizing a length of 15 m between the north and south mirror plugs 440, the edge layer particle confinement time τ is... ||Increased by up to an order of magnitude. Improved τ || This easily increases the FRC ion confinement.

[0129] Assume that the radial diffusion (D) particle loss from the interface volume 453 is equal to the axial loss (τ) from the edge layer 456. || If the equilibrium is achieved, then (2πr) is obtained. s L s )(Dn s / δ)=(2πr s L s δ)(n s / τ || Therefore, the density gradient length at the interface can be rewritten as δ=(Dτ) || ) 1 / 2 Here r s L s and n s These are the interface radius, interface length, and interface density, respectively. The FRC particle confinement time is τ. N =[πr s 2 L s <n>] / [(2πr s L s )(Dn s / δ)]=(<n> / n s )(τ L τ || ) 1 / 2 , where τ L =a 2 / D and a=r s / 4. Physically, improving τ || This leads to an increase in δ (a decrease in the interface density gradient and drift parameter), and thus a reduction in FRC particle loss. The overall improvement in FRC particle constraints is generally slightly less than the quadratic, because n s With τ || Increase.

[0130] τ || The significant improvement also requires that the edge layer 456 remain very stable (i.e., without the n=1 groove, firehose, or other MHD instabilities typical of open systems). The use of the plasma gun 350 provides this preferred edge stability. In this sense, the mirror plug 440 and the plasma gun 350 form an effective edge control system.

[0131] plasma gun

[0132] The plasma gun 350 improves the stability of the FRC emission jet 454 through coil bundling. Gun plasma from the plasma gun 350 is generated without azimuth angular momentum, which has proven useful in controlling FRC rotational instability. Thus, the gun 350 is an efficient means of controlling FRC stability without requiring older quadrupole stabilization techniques. As a result, the plasma gun 350 makes it possible to utilize the beneficial effects of fast particles, or to use advanced hybrid dynamics FRC mechanisms as outlined in this disclosure. Therefore, the plasma gun 350 enables the FRC system 10 to operate with a saddle-shaped coil current that is just sufficient for electron breakup, but below a threshold that would lead to FRC instability and / or significant fast particle diffusion.

[0133] As mentioned in the discussion of mirror plugs above, if τ can be significantly improved || The supplied gun plasma will then be related to the edge layer particle loss velocity (~10). 22 The lifetime of the plasma generated by the gun in FRC system 10 is in the millisecond range. In fact, considering a plasma with n... e ~10 13 cm -3 The plasma, with a density of approximately 200 eV and an ion temperature of approximately 200 eV, is confined within a gun plasma with end-mirror plugs at 440°. The trapping length L and mirror ratio R are approximately 15 m and 20, respectively. The mean free path of the ions due to Coulomb collisions is λ. ii ~6×10 3 cm, and, because λ ii Since lnR / R < L, the ions are confined within the gas dynamic mechanism. The plasma confinement time in this mechanism is τ. gd ~RL / 2V s ~2ms, where V s That is the ion sound velocity. For comparison, for these plasma parameters, the conventional ion confinement time would be τ. c ~0.5τ ii (lnR+(lnR) 0.5 ~0.7 ms. In principle, anomalous transverse diffusion can shorten the plasma confinement time. However, in FRC system 10, if we assume Bohmian diffusion rate, the estimated transverse confinement time for gun plasma is τ. ⊥ >τ gd ~2ms. Therefore, the gun will provide significant refeeding of the FRC edge layer 456 and improved overall FRC particle confinement.

[0134] Furthermore, the gun plasma flow can be turned on in approximately 150 to 200 microseconds, allowing for use during FRC startup, movement, and merging into confinement chamber 100. If turned on near t ~ 0 (FRC main bank start-up), the gun plasma helps support the dynamically formed and merged FRC 450. The combined particle stock from the generated FRC and from the gun is sufficient for neutral beam trapping, plasma heating, and long-term support. If turned on at t in the range of -1 to 0 ms, the gun plasma can be used to fill the quartz tube 210 with plasma or ionize the gas filled into the quartz tube, thus allowing FRC formation with reduced or even zero gas filling. The latter may require sufficiently cold generated plasma to allow for rapid diffusion of the reverse bias magnetic field. If turned on at t < -2 ms, the plasma flow can be used for tens of microseconds. 13 cm -3 The target plasma density filling generation section 200 and the formation of the confinement chamber 100 and the confinement region are approximately 1 to 3 m. 3 The field line volume is sufficient to allow a neutral beam to be established before the arrival of the FRC. The generated FRC can then be formed and moved into the resulting confined container plasma. In this way, the plasma gun 350 enables a wide variety of operating conditions and parameter mechanisms.

[0135] Electrical bias

[0136] Controlling the radial electric field distribution in the edge layer 456 benefits FRC stability and confinement in various ways. With the aid of innovative biasing components deployed in the FRC system 10, it is possible to apply a variety of carefully considered potential distributions to a set of open flux surfaces penetrating the machine from a region completely outside the central confinement region in the confinement chamber 100. In this way, radial electric fields can be generated precisely outside the FRC 450 across the edge layer 456. These radial electric fields then alter the azimuth rotation of the edge layer 456 and achieve its confinement via E×B velocity shear. Thus, any differential rotation between the edge layer 456 and the FRC core 453 can propagate into the FRC plasma interior via shear. As a result, controlling the edge layer 456 directly affects the FRC core 453. Furthermore, since free energy in plasma rotation can also cause instabilities, this technique provides a direct means of controlling the initiation and growth of instabilities. In the FRC system 10, appropriate edge biasing provides effective control over open field line propagation and rotation, as well as FRC core rotation. The positions and shapes of the various provided electrodes 900, 905, 910, and 920 allow for control of different sets of flux surfaces 455 at different and independent potentials. In this way, a large number of different electric field configurations and intensities can be achieved, each with a different characteristic effect on plasma performance.

[0137] The key advantage of all these innovative biasing techniques lies in the fact that they can influence the performance of the core and edge plasmas from the complete outside of the FRC plasma, i.e., without requiring any physical components to come into contact with the central hot plasma (contact would have a significant impact on energy, flux, and particle loss). This has a major beneficial impact on the performance of the HPF concept and all its potential applications.

[0138] Experimental Data - HPF Operation

[0139] Fast particles injected via beam from the neutral beam gun 600 play a crucial role in enabling the HPF mechanism. Figure 16A , Figure 16B , Figure 16C and Figure 16D This fact is illustrated. The figure depicts a set of curves showing how FRC lifetime correlates with beam pulse length. All other operating conditions were kept constant for all discharges including this study. The data are averaged over multiple emissions and therefore represent typical performance. It is clearly evident that a longer beam duration results in a longer-lived FRC. Considering this evidence, along with other diagnostics during this study, it demonstrates that the beam increases stability and reduces losses. The correlation between beam pulse length and FRC lifetime is not perfect because beam trapping becomes inefficient at certain plasma sizes; that is, not all injected beam is intercepted and trapped when the physical dimensions of FRC 450 are shortened. The shortening of the FRC is primarily due to the fact that, for a given experimental setup, the net energy loss from the FRC plasma during discharge (approximately 4 MW midway through the discharge) is slightly greater than the total power fed into the FRC via the neutral beam (approximately 2.5 MW). Positioning the beam closer to the midplane of container 100 will tend to reduce these losses and extend the FRC lifetime.

[0140] Figure 17A , Figure 17B , Figure 17C and Figure 17DThe diagram illustrates the impact of different components on achieving the HPF mechanism. It shows a series of typical curves depicting the lifetime of the FRC 450 as a function of time. In all cases, a constant, moderate beam power (approximately 2.5 MW) is injected for the entire duration of each discharge. Each curve represents a different combination of components. For example, operating the FRC system 10 without any mirror plug 440, plasma gun 350, or getter from the getter system 800 results in a rapid onset of rotational instability and loss of FRC topology. Adding only the mirror plug 440 delays the onset of instability and increases constraint. The combination of the mirror plug 440 and plasma gun 350 further reduces instability and increases FRC lifetime. Finally, adding getter in addition to the gun 350 and plug 440 (in this case, titanium) produces the best results—the resulting FRC is instable and exhibits the longest lifetime. This experiment clearly demonstrates that the complete combination of components produces the best results and provides optimal target conditions for the beam.

[0141] like Figure 1 As shown in the figure, the newly discovered HPF mechanism exhibits significantly improved transmission performance. Figure 1 The diagram illustrates the change in particle confinement time in FRC system 10 between the conventional and HPF mechanisms. As can be seen, it has been improved by more than 5 times in the HPF mechanism. Furthermore, Figure 1 The particle confinement time in FRC System 10 is described in detail relative to that in existing conventional FRC experiments. Regarding these other machines, the HPF mechanism of FRC System 10 has improved confinement by factors between 5 and close to 20. Last and foremost, the characteristics of confinement scaling in FRC System 10 under the HPF mechanism are significantly different from all existing measurements. Prior to establishing the HPF mechanism in FRC System 10, various empirical scaling rules were derived from data in existing FRC experiments to predict confinement times. All of these scaling rules depend primarily on the ratio R... 2 / ρ i Where R is the radius of the zero magnetic field (an imprecise measurement of the physical scale of the machine), and ρ i It is the Larmor radius of the ion evaluated in an externally applied field (an imprecise measurement of the applied magnetic field). From Figure 1 It is clear that long confinement in conventional FRC is only possible under conditions of large machine size and / or high magnetic fields. Operating an FRC system using a conventional FRC mechanism tends to follow these conversion rules, such as... Figure 1 As shown in the figure. However, the HPF mechanism is extremely superior and demonstrates that much better confinement can be obtained without large machine size or high magnetic fields. More importantly, from Figure 1 It is also clear that the HPF mechanism results in improved confinement time with a reduced plasma size compared to the CR mechanism. A similar trend is observed for flux and energy confinement time, which have increased by more than 3–8 times in FRC System 10, as described below. Therefore, the breakthrough in the HPF mechanism enables the support and maintenance of FRC equilibrium in FRC System 10 and future higher-energy machines using moderate beam power, lower magnetic fields, and smaller dimensions. These improvements are accompanied by lower operating and construction costs and reduced engineering complexity.

[0142] For further comparison, Figure 18A , Figure 18B , Figure 18C and Figure 18D Data on representative HPF mechanism discharges from FRC system 10 as a function of time are shown. Figure 18A The flux exclusion radius at the intermediate plane is depicted. For these longer timescales, the conductive steel wall is no longer such a good flux retainer, and the magnetic probe inside the wall is adequately responsible for the diffusion of magnetic flux through the steel by probe amplification outside the wall. Compared with typical performance in conventional mechanism CR, such as Figure 13A , Figure 13B , Figure 13C and Figure 13D As shown, the HPF mechanism operating mode exhibits a lifespan that is more than 400% longer.

[0143] Figure 18B The figure shows a representative chord of the line integral density trace, and Figure 18C The image shows its Abelian inversion complement and isodensity lines. For example... Figure 13A , Figure 13B , Figure 13C and Figure 13D As shown, compared to the conventional FRC mechanism CR, the plasma penetration pulse is much calmer, indicating very stable operation. Figure 18D As shown, the peak density is also slightly lower in HPF emission—a result of the hotter overall plasma temperature (up to twice as high).

[0144] for Figure 18A , Figure 18B , Figure 18C and Figure 18D The corresponding discharge illustrated in the figure has energy, particle, and flux confinement times of 0.5 ms, 1 ms, and 1 ms, respectively. At the reference time of 1 ms before entering the discharge, the stored plasma energy is 2 kJ while the loss is approximately 4 MW, making this target highly suitable for neutral beam support.

[0145] Figure 19This paper summarizes all the advantages of the newly established experimental HPF flux constraint transformation form. For example... Figure 19 As can be seen, based on measurements taken before and after t = 0.5 ms (i.e., t ≤ 0.5 ms and t > 0.5 ms), for a given interface radius (r) s Flux confinement (and similarly, particle and energy confinement) is approximately at the electron temperature (T). e Conversion of the square of T. e This strong conversion, a positive power (and not a negative power), is the complete opposite of the conversion exhibited by conventional tokamas, where confinement is typically inversely proportional to a power of the electron temperature. This conversion is a direct result of the HPF state and the large-orbital (i.e., orbitals on the FRC topological scale and / or at least on the characteristic magnetic field gradient length scale) ion population. Fundamentally, this new conversion substantially favors high operating temperatures and enables the realization of relatively moderately sized reactors.

[0146] Leveraging the advantages of the HPF mechanism, neutral beam-driven FRC support or steady-state can be achieved, meaning that overall plasma parameters such as plasma thermal energy, total particle number, plasma radius and length, and magnetic flux can be maintained at reasonable levels without substantial attenuation. For comparison, Figure 20 Plot A shows data as a function of time for a representative HPF mechanism discharge from FRC system 10, and Plot B shows data as a function of time for a projected representative HPF mechanism discharge from FRC system 10, where FRC 450 is supported and the duration of the neutral beam pulse does not decay. For Plot A, a neutral beam with a total power in the range of approximately 2.5–2.9 MW is injected into FRC 450 for an active beam pulse length of approximately 6 ms. The plasma diamagnetic lifetime depicted in Plot A is approximately 5.2 ms. More recent data show that a plasma diamagnetic lifetime of approximately 7.2 ms can be obtained using an active beam pulse length of approximately 7 ms.

[0147] As mentioned above Figure 16A , Figure 16B , Figure 16C and Figure 16D As noted, the correlation between beam pulse length and FRC lifetime is not perfect because beam trapping becomes inefficient at certain plasma sizes; that is, not all injected beams are intercepted and trapped when the physical dimensions of the FRC 450 are shortened. The shortening or attenuation of the FRC is primarily due to the fact that, for a given experimental setup, the net energy loss from the FRC plasma during discharge (approximately 4 MW midway through the discharge) is slightly greater than the total power fed into the FRC via the neutral beam (approximately 2.5 MW). (See also: [link to relevant information]). Figure 3C As noted, angled beam injection from the neutral beam gun 600 toward the midplane improves beam-plasma coupling, even if the FRC plasma shortens or otherwise contracts axially during the injection period. Furthermore, appropriate projectile feeding will maintain the necessary plasma density.

[0148] Curve B represents the results of a simulated run using an active beam pulse length of approximately 6 ms and a total beam power slightly greater than approximately 10 MW from the neutral beam injector 600, where the neutral beam is to inject H (or D) neutral particles with a particle energy of approximately 15 keV. The equivalent current injected by each particle in the beam is approximately 110 A. For Curve B, the beam injection angle relative to the device axis is approximately 20° less than normal, with a target radius of 0.19 m. The injection angle can be varied within the range of less than normal 15°–25°. The beam will be injected at an azimuth angle in a co-current direction. The net lateral force and net axial force from the neutral beam momentum injection should be minimized. As in the case of Curve A, fast (H) neutral particles generated from north and south form FRCs that merge into a single FRC at moment 450 from the neutral beam injector 600.

[0149] The simulations that form the basis of plot B use a multidimensional Hall-MHD solver for background plasma and equilibrium, a fully dynamic Monte Carlo solver for energy beam components and all scattering processes, and numerous coupled transport formulas for all plasma types to model the interactive loss processes. The transport components are empirically calibrated and widely used as benchmarks against experimental databases.

[0150] As shown in plot B, the steady-state diamagnetic lifetime of the FRC 450 will be the length of the beam pulse. However, it is important to note that the key correlation plot B shows that the plasma or FRC begins to decay when the beam is turned off, not before. The decay will be similar to that observed in discharges not assisted by the beam (which may be on the order of 1 ms beyond the beam turn-off time) and is simply a reflection of the characteristic decay time of the plasma driven by intrinsic loss processes.

[0151] Go to Figure 21A , Figure 21B , Figure 21C , Figure 21D and Figure 21EThe experimental results illustrated in the figure indicate the achievement of FRC support or steady-state by an angled neutral beam, meaning that overall plasma parameters (such as plasma radius, plasma density, plasma temperature, and magnetic flux) are maintained at constant levels without decay related to the NB pulse duration. For example, these plasma parameters remain essentially constant for ~5+ ms. This plasma performance, including support characteristics, is strongly correlated with the NB pulse duration, with diamagnetic persistence even milliseconds after NB termination due to accumulated fast ions. As illustrated, the plasma performance is limited only by the pulse length constraint caused by the finite energy stored in the associated power sources of many critical systems (such as the NB injector and other system components).

[0152] High-order harmonic fast wave electronic heating

[0153] As mentioned above Figure 3A , Figure 3B , Figure 3C , Figure 3D , Figure 3E and Figure 8 As mentioned, the neutral atom beam 600 is deployed on the FRC system 10 to provide heating and current drive, as well as to generate rapid particle pressure. The individual beamlines, including the neutral atom beam injector system 600, are located around the central confinement chamber 100, and as... Figure 3C , Figure 3D and Figure 3E As shown, neutral particles are preferably injected at an angle toward the midplane of the confinement chamber 100. To improve FRC support and demonstrate the rise of FRC to high plasma temperatures and increased system energy, this FRC system 10 includes a neutral beam injector (NBI) system 600 with increased power and extended pulse length, for example, for exemplary purposes only, with a power of approximately 20+ MW and a pulse length of up to 30 ms.

[0154] However, neutral beam injection tends to have poor electron heating efficiency due to the power damping mechanism of electrons via ion-electron collisions. The unique characteristics of the FRC plasma in this FRC system 10 make heating the electrons in the core of the FRC plasma extremely challenging; these unique characteristics include, for example, the plasma's anomalously high density (ω within the interface). pe >30ω ceFurthermore, the magnetic field in the plasma core rapidly drops to zero. Conventional electron heating scenarios are unsuitable for FRC plasmas due to poor wave accessibility to the plasma core, such as electron cyclotron resonance frequency (or its second or third harmonic) heating, which is widely used in tokamas, stellarators, and mirror machines. Other electron heating scenarios (such as electron Bernstein waves, upper mixed resonance waves, and whistle waves) encounter similar problems or have low heating efficiency when applied to FRC plasmas.

[0155] In an exemplary embodiment, the FRC system 10 includes high-order harmonic fast-wave electron heating to increase the plasma electron temperature and thus further improve FRC support. Figure 25 As shown, the FRC system 10 includes one or more antennas 650, such as, for example, a phased array antenna with four (4) bands, which are deployed on the FRC system 10 and configured to propagate high-harmonic fast waves in the radio frequency range into the FRC plasma in the confinement container 100 to provide electron heating from about 150 eV to above about 1 keV in the core of the FRC plasma. In an exemplary embodiment, the antenna 650 will include an about 2 MW RF system in the range of about 15-25 MHz. Heating electrons via high-harmonic fast waves in the radio frequency range advantageously reduces fast ion charge exchange losses and improves plasma confinement, and increases plasma current drive efficiency, which increases with electron temperature Te.

[0156] Simulations of electron heating in high-performance FRC plasmas (such as the FRC plasma of this FRC system 10) were performed in the following scenarios: (1) upper hybrid resonant frequency (50 GHz); (2) electron cyclotron resonance (ECR) frequency (28 GHz); (3) electron Bernstein waves (EBW) at frequencies of 2.45 GHz, 5 GHz, 8 GHz, and 18 GHz; (4) whistle waves at 0.5 GHz; and (5) HHFW at 15 MHz. The simulation results clearly show that the mechanism of HHFW not only has extremely strong single-pass power absorption (~100%), but also very good wave accessibility to the core of the FRC plasma. These simulations indicate that the contradiction between good wave accessibility and effective power damping of electrons is resolved by using this high-harmonic fast wave (HHFW) heating, which has been successfully adapted for high-β, superdense spherical tokamak (ST) plasmas, such as NSTX, for core electron heating and off-axis current-driven experiments.

[0157] The heating mechanism of HHFW includes electronic Landau damping (LD) (where the force acting on the electrons is F). LD =eE / / ) and time-transfer magnetic pump (TTMP or MP) (where force is Both. Here, e and μ are the charge and magnetic moment of the electron, and E / / and B / / These are the parallel components of the fast-wave electric and magnetic fields, respectively. For any significant absorption via the dominant LD, conventional fast-wave electronic heating in tokamak plasmas requires a wave-parallel phase velocity V. ph / / ≡ω / k / / ≈V Te (Electron thermal velocity); MP makes no significant contribution to electron damping, and it is generally negligible. Furthermore, fast wave absorption is weak in tokamak plasmas, and therefore strong electron preheating via microwaves at the electron cyclotron resonance frequency is typically required to enhance multipath power absorption. However, in high-β, ST plasmas (such as NSTX), it is found that MP significantly increases electron power absorption only at the electron LD, and it becomes very large in the higher range of phase velocities, ω / k / / ≤2.5V Te The combination of MP and LD can result in 100% single-pass absorption.

[0158] In high-β mechanisms, high-performance FRC plasmas, such as this FRC system 10 (which has approximately 90% β in the core plasma), are used. e In the value), damping is dominated by a magnetic pump, which can be scaled to Im k. ⊥ ∝n e T e B 2 ∝β c And when ω / k / / ≤2.5V Te hour, And the magnetic pump becomes significant. In the simulation of this FRC system 10, T e =150eV, T i =800eV, n e =n i =3.2×10 19 m -3 The magnetic field B = 1000 Gauss, the HHFW has a transmission power of 1 MW and its frequency is chosen to be f = 15 MHz, therefore ω = 2πf = 10ω ci [H]=20ω ci [D]<<ω LH A single-pass absorption greater than 99% was achieved, and the HHFW power damping for electrons was shown to be as high as 90%. The power damped on ions or by collisions can be less than 5%, respectively. Furthermore, the radial distribution of power deposition for electrons, ions, and by collisions has been shown within the interface layer of the FRC plasma, where more than 60% of the HHFW power is damped.

[0159] Figure 26A and 26B The diagram illustrates the complete radial density distribution and complete radial electron temperature distribution of the FRC plasma in this FRC system 10. The FRC system according to an embodiment of this disclosure is configured according to the parameter and value pairs shown in Table 1.

[0160]

[0161]

[0162] Table 1: Parameters of this FRC system.

[0163] Figures 27A-27D The radial distribution of C-2U equilibrium and characteristic frequencies at the midplane (Z=0) of this FRC system 10 is illustrated. The observed challenge is that within the interface layer, the plasma is excessively dense (ω... pe >30ω ce Furthermore, B rapidly decreases to 0 within a radial distance of 11 cm. All ECR harmonic resonant layers are compacted in a very narrow region, thus allowing microwaves to propagate radially over only a very short distance.

[0164] The following simulation was performed using GENRAY-C ray tracing code for microwave frequency scenarios:

[0165] EBW (2.45GHz, 5GHz, 8GHz, 18GHz and 28GHz);

[0166] Upper mixed resonant frequencies (50GHz, 55GHz);

[0167] Whistle wave frequency (0.5-1.0 GHz)

[0168] Unfortunately, these scenarios cannot resolve the contradiction between wave penetration into the plasma core and the effective power damping of electrons.

[0169] Figures 28A-28C The illustration shows observations of power absorption and mode switching in the FRC plasma of this FRC system 10 under microwave electron Bernstein wave (EBW) electron heating conditions at 8 GHz. Figures 28A-28C Six rays were emitted at different angles, and a clear O->X->B conversion was observed. At the fourth harmonic ECR layer (outside the interface), over 90% of the microwave power was absorbed by electrons; this resulted in highly localized absorption. The EBW mechanism could only heat electrons at the plasma edge and could not penetrate into the plasma core.

[0170] Figures 29A-29FThe illustration shows observations of power absorption and mode switching in the FRC plasma of this FRC system 10 under microwave electronic heating conditions at 50 GHz. Figures 29A-29F In the study, it was observed that the radiation stopped propagating after the O->X->B conversion, and 30% of the microwave power was absorbed.

[0171] Figures 30A-30C The illustration shows the observation of power absorption in the FRC plasma of this FRC system 10 under electron heating conditions at a 0.5 GHz whistle wave. Figures 30A-30C In the study, it was observed that the whistle wave at 0.5 GHz (~1 / 4 fce) exhibited high power absorption but poor wave accessibility. With a large N... / / (Starting from position 16) waves are emitted, and the waves circulate when there is a large magnetic field bending them.

[0172] In contrast to these heating mechanisms, as demonstrated by simulation results, high-harmonic fast-wave heating provides high average β e FRC plasmas (e.g., the FRC plasma of this FRC system 10) have the following characteristics: 1) strong one-way absorption (≈100%); 2) good accessibility to the plasma core; 3) core electron effective power absorption up to 60%; 4) electron power damping dominated by magnetic pumping (TTMP), which can be on the scale of 1m K. L ∝n e T e / B 2 ∝β e .

[0173] Figure 31 The diagram illustrates the density distribution and wave propagation in the FRC plasma of this FRC system 10. Figure 10 In the middle, T e =150eV, while T e (Interface) = 100eV. T i =800eV, while T i (Interface) = 200 eV. Thermionic ions have the same density and distribution as electrons. Fast ion information is not included. Figure 31 middle. Figure 32 The diagram illustrates the poloidal flux distribution and wave propagation in the FRC plasma of this FRC system 10.

[0174] Figure 33 An exemplary density distribution and wave propagation trajectory in the FRC plasma of this FRC system 10 are illustrated. Figure 33 In the middle, T e =150eV, while T e (Interface) = 100eV. T i =800eV, while Ti (Interface) = 200eV. In Figure 33 In this case, f = 6MHz (initial ω / ω ci[D] ~9), with a total power of 1MW. Five rays are emitted at the mid-plane, with the initial n / / between 4 and 6.

[0175] Figure 34 An exemplary ω / ω in the FRC plasma of this FRC system 10 is illustrated. ci[D] Distribution and wave propagation trajectory. Figure 34 For clarity, ω / ω is not displayed. ci[D] The level is greater than 28. The dashed lines in the gaps are magnetic flux lines.

[0176] Figure 35 The illustration shows an exemplary power damping effect as the wave propagation distance in the FRC plasma of this FRC system 10 changes. Figure 35 The middle part includes five rays, each with a different n value between 4 and 6. / / Each ray has a power of 200 kW at the emission point. The region of significant power damping is between 30 cm and 50 cm.

[0177] Figure 36 An exemplary power absorption distribution in the FRC plasma of this FRC system 10 is illustrated. Figure 36 Significant power absorption of ions and electrons was observed when HHFW penetrated through the interface layer.

[0178] Figure 37A and Figure 37B An exemplary radial distribution of power density in the FRC plasma of this FRC system 10 is illustrated. The radial distribution of power density is for the following: (a) total absorption, (b) damping for electrons, (c) damping for ions, and (d) collision damping. Figure 37A In the middle, P total =1000kW, P e =448kW, P i =486kW, and P cl =66kW. In Figure 37B In the middle, P total =999kW, P e =720kW, P i =194kW, and P cl =85kW. 100% one-way absorption was observed during HHFW heating in the plasma core.

[0179] Figure 38 An exemplary 2D distribution of damped power density in the FRC plasma of this FRC system 10 is illustrated.

[0180] Figure 39 An exemplary power damping distribution in the FRC plasma of this FRC system 10 is illustrated. Figure 39 In the study, it was observed that as |B| approaches its minimum, the power damping of the electron increases to its maximum. A very small |E| was observed. / / Therefore, Landau damping has a relatively small effect on power absorption.

[0181] Figure 40 The illustration shows an exemplary finite-ion Larmor radius distribution in the FRC plasma of this FRC system 10. Figure 40 Even when the ion temperature Ti < 1 keV, a significant finite ion Larmor radius effect is observed. Within the interface, Kxρ Larmor >>1. It becomes infinite at the field zero (null) in the intermediate plane (z=0). This can lead to the interaction of thermionic ions with HHFW, and therefore power damping of thermionic ions.

[0182] Figure 41 An exemplary power absorption distribution in the FRC plasma of this FRC system 10 is illustrated. Figure 41 Significant power absorption by hot ions was observed. Cyclotron resonance absorption by ions was also observed, with harmonic numbers n = (11-20). The condition for significant power damping of ions is Kxρ. Larmor >>1 and ω / K < 2V Ti .

[0183] Figure 42 An exemplary profile of the FRC plasma in this FRC system 10 is illustrated. Figure 42 In the meantime, the following changes are observed as the wave propagates a distance: (a) local |B(r, z)| (b) imaginary part of vertical wavenumber Ki (c) |E \\ The ratio of / E| and (d) parallel refractive index n / / .

[0184] Simulations of HHFW heating of the FRC plasma in this FRC system 10 have clearly demonstrated that HHFW heating leads to: 1) 100% one-way power absorption; 2) TTMP is the dominant power absorption mechanism for core electron heating; 3) when the wave parallel phase velocity V ph / / =ω / k / / <V Te At that time, maximum power damping of electrons occurs; and 4) when K×ρ Larm >>1 and ω / k < 2V Ti When the conditions are maintained, significant power absorption by thermionic ions tends to occur.

[0185] According to embodiments of the present disclosure, a method for generating and maintaining a magnetic field having a reverse field configuration (FRC) includes: forming an FRC with respect to a plasma in a confinement chamber, injecting a plurality of neutral beams at an angle toward the intermediate plane of the confinement chamber into the FRC plasma, and heating the electrons of the FRC plasma using a high-order harmonic fast wave propagating into the FRC plasma.

[0186] According to another embodiment of this disclosure, heating electrons include: transmitting a plurality of high-order harmonic fast waves from one or more antennas into an FRC plasma in a confinement chamber.

[0187] According to another embodiment of this disclosure, heating electrons include: transmitting a plurality of high-order harmonic fast waves from one or more antennas into the FRC plasma in the confinement chamber at an emission angle relative to the intermediate plane of the confinement chamber.

[0188] According to another embodiment of this disclosure, the launch angle is in the range of about 15° to about 25° from the mid-plane of the confinement chamber.

[0189] According to another embodiment of this disclosure, the launch angle is close to but less than that orthogonal to the longitudinal axis of the confinement chamber.

[0190] According to another embodiment of this disclosure, one or more antennas are phased array antennas having multiple bands.

[0191] According to another embodiment of this disclosure, the high-order harmonic fast wave is a fast wave in the radio frequency range.

[0192] According to another embodiment of this disclosure, heating the electrons includes heating the electrons from about 150 eV to above about 1 keV.

[0193] According to another embodiment of this disclosure, the method further includes: maintaining the FRC at a constant or approximately constant value without decaying, and raising the plasma electron temperature to above approximately 1.0 keV.

[0194] According to another embodiment of this disclosure, the method further includes: generating a magnetic field within the confinement chamber using a quasi-DC coil extending around the confinement chamber, and generating a mirror magnetic field within the confinement chamber at opposite ends using quasi-DC mirror coils extending around opposite ends of the confinement chamber.

[0195] According to another embodiment of this disclosure, the method further includes: generating a magnetic field within the confinement chamber using a quasi-DC coil extending around the confinement chamber, and generating a mirror magnetic field within the confinement chamber at opposite ends using quasi-DC mirror coils extending around opposite ends of the confinement chamber.

[0196] According to another embodiment of the present disclosure, forming an FRC includes: forming a generating FRC in opposing first and second generating portions, the first and second generating portions being connected to a constraint chamber and causing the generating FRC to accelerate from the first and second generating portions toward a central through-plane of the constraint chamber, and merging two generating FRCs in the constraint chamber to form an FRC.

[0197] According to another embodiment of the present disclosure, forming an FRC includes one of the following: forming a generating FRC while accelerating the generating FRC toward the intermediate plane of the constraint chamber; and forming a generating FRC and then accelerating the generating FRC toward the intermediate through-plane of the constraint chamber.

[0198] According to another embodiment of this disclosure, accelerating the generated FRC from the first and second generating portions toward the intermediate plane of the constraint chamber includes: conveying the generated FRC from the first and second generating portions through first and second internal divertors connected to opposite ends of the constraint chamber, the first and second internal divertors being sandwiched between the constraint chamber and the first and second generating portions.

[0199] According to another embodiment of this disclosure, causing the generated FRC to pass from the first and second generation portions through the first and second internal divertors includes: idling the first and second internal divertors when the generated FRC from the first and second generation portions is transmitted through the first and second internal divertors.

[0200] According to another embodiment of this disclosure, the method further includes: guiding the magnetic flux surface of the FRC into the first and second internal divertors.

[0201] According to another embodiment of this disclosure, the method further includes guiding the magnetic flux surface of the FRC to first and second external divertors coupled to the end of the generating portion.

[0202] According to another embodiment of this disclosure, the method further includes: using a quasi-DC coil extending around the generating portion and the divertor to generate a magnetic field within the generating portion and the first and second external divertors.

[0203] According to another embodiment of this disclosure, the method further includes generating a magnetic field within the generating portion and the first and second internal divertors using a quasi-DC coil extending around the generating portion and the divertor.

[0204] According to another embodiment of this disclosure, the method further includes: generating a mirror magnetic field between the first and second generating portions and the first and second external divertors using a quasi-DC mirror coil.

[0205] According to another embodiment of the present disclosure, the method further includes: using a quasi-DC mirror plug coil extending around a contraction between the generating portion and the divertor to generate a mirror plug magnetic field within the contraction located between the first and second generating portions and the first and second external divertors.

[0206] According to another embodiment of the present disclosure, the method further includes: using a quasi-DC mirror coil to generate a mirror magnetic field between the confinement chamber and the first and second internal divertors, and using a quasi-DC low-profile necking coil to generate a necking magnetic field between the first and second generating portions and the first and second internal divertors.

[0207] According to another embodiment of this disclosure, the method further includes: using a saddle-shaped coil connected to the room to generate one of a magnetic dipole field and a magnetic quadrupole field in the room.

[0208] According to another embodiment of this disclosure, the method further includes: using an intake system to process the inner surface of the chamber and the inner surfaces of the first and second generating portions, the inner surfaces of the first and second divertors sandwiched between the constraint chamber and the first and second generating portions, and the inner surfaces of the first and second external divertors connected to the first and second generating portions.

[0209] According to another embodiment of this disclosure, the intake system includes one of a titanium deposition system and a lithium deposition system.

[0210] According to another embodiment of this disclosure, the method further includes: axially injecting plasma into the FRC from an axially mounted plasma gun.

[0211] According to another embodiment of this disclosure, the method further includes controlling the radial electric field distribution in the edge layer of the FRC.

[0212] According to another embodiment of this disclosure, controlling the radial electric field distribution in the edge layer of the FRC includes applying a potential distribution to a set of open flux surfaces of the FRC using a bias electrode.

[0213] According to another embodiment of this disclosure, the method further includes: injecting compact ring (CT) plasma from first and second CT injectors at an angle toward the mid-plane of the confinement chamber into the FRC plasma, wherein the first and second CT injectors are exactly opposite each other on opposite sides of the mid-plane of the confinement chamber.

[0214] According to another embodiment of this disclosure, a system for generating and maintaining a magnetic field having a reverse field configuration (FRC) includes: a confinement chamber; first and second opposing FRC generation sections coupled to the confinement chamber; first and second opposing divertors coupled to the FRC generation sections; and one or more of the following: a plurality of plasma guns, one or more bias 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 generation sections, and the confinement chamber; wherein one or more bias electrodes are positioned within one or more of the following: the confinement chamber, the first and second generation sections, and the first and second external divertors. The system comprises: first and second mirror plugs positioned between first and second generating sections and first and second divertors; an intake system coupled to the confinement chamber and the first and second divertors; a plurality of neutral atom beam injectors coupled to the confinement chamber and angled toward the central plane of the confinement chamber; a magnetic system comprising a plurality of quasi-DC coils positioned around the confinement chamber, the first and second generating sections, and the first and second divertors; a first set and a second set of quasi-DC mirror coils positioned between the first and second generating sections and the first and second divertors; and an antenna system positioned around the confinement chamber, wherein the antenna system is configured to transmit high-order harmonic fast waves into the FRC plasma to heat plasma electrons.

[0215] According to another embodiment of this disclosure, the system is configured to generate and maintain an FRC without decaying while injecting a neutral beam into the plasma, and to raise the plasma electron temperature to approximately above 1.0 keV.

[0216] According to another embodiment of this disclosure, the antenna system includes one or more antennas positioned to transmit high-order harmonic fast waves into the FRC plasma at a transmission angle relative to the midplane of the confinement chamber.

[0217] According to another embodiment of this disclosure, the launch angle is in the range of approximately 15° to approximately 25° from the mid-plane of the confinement chamber.

[0218] According to another embodiment of this disclosure, the launch angle is close to but less than that orthogonal to the longitudinal axis of the confinement chamber.

[0219] According to another embodiment of this disclosure, the antenna system includes a phased array antenna having multiple bands.

[0220] According to another embodiment of this disclosure, the high-order harmonic fast wave is a fast wave in the radio frequency range.

[0221] According to another embodiment of this disclosure, the system is configured to heat FRC plasma electrons from about 150 eV to above about 1 keV.

[0222] According to another embodiment of the present disclosure, the first and second divertors include first and second internal divertors sandwiched between the first and second generating portions and the constraint chamber, and further include first and second external divertors coupled to the first and second generating portions, wherein the first and second generating portions are sandwiched between the first and second internal divertors and the first and second external divertors.

[0223] According to another embodiment of this disclosure, the system further includes: first and second axial plasma guns operatively coupled to first and second internal and external divertors, first and second generation sections, and a confinement chamber.

[0224] According to another embodiment of this disclosure, the system further includes two or more saddle-shaped coils connected to the constraint chamber.

[0225] According to another embodiment of this disclosure, the generation section includes a modular generation system for generating an FRC and moving the FRC toward the intermediate plane of the constraint chamber.

[0226] According to another embodiment of this disclosure, the bias electrode includes one or more of the following: one or more point electrodes positioned in the confinement chamber to contact the open field lines; a set of annular electrodes between the confinement chamber and the first and second generation portions to charge the far-edge flux layer in an azimuth-symmetrical manner; a plurality of concentrically stacked electrodes positioned in the first and second divertors to charge the plurality of concentric flux layers; and an anode of a plasma gun for intercepting open flux.

[0227] According to another embodiment of this disclosure, the system further includes first and second compact ring (CT) injectors that are angled to the confinement chamber toward the mid-plane of the confinement chamber, wherein the first and second CT injectors are exactly opposite each other on opposite sides of the mid-plane of the confinement chamber.

[0228] However, the example embodiments provided herein are intended merely as illustrative examples and are not in any way limiting.

[0229] All features, elements, components, functions, and steps described with respect to any embodiment provided herein are intended to be freely combined and can be substituted with those from any other embodiment. If certain features, elements, components, functions, or steps are described with respect to only one embodiment, it should be understood that such features, elements, components, functions, or steps can be used with each of the other embodiments described herein, unless otherwise expressly indicated. This paragraph therefore serves at all times as the basis for reference and written support for introducing claims that combine features, elements, components, functions, and steps from different embodiments or substitute features, elements, components, functions, and steps from another embodiment for those from one embodiment, even if the following description does not expressly state in a particular context that such combinations or substitutions are possible. Detailing every possible combination and substitution would be cumbersome, especially considering that those skilled in the art will readily perceive the permissibility of each and every such combination and substitution upon reading this description.

[0230] In many instances, entities are described herein as being connected to other entities. It should be understood that the terms “connection” and “linkage” (or any form thereof) are used interchangeably herein, and in both cases, the term is applicable to a direct connection between two entities (without any non-negligible (e.g., parasitic) intermediate entity) and an indirect connection between two entities (with one or more non-negligible intermediate entities). Where entities are shown as being directly connected, or described as being connected without any intermediate entity described, it should be understood that those entities may also be indirectly connected, unless the context clearly specifies otherwise.

[0231] While the embodiments are susceptible to various modifications and alternatives, specific examples have been shown in the accompanying drawings and described in detail herein. However, it should be understood that these embodiments are not limited to the specific forms disclosed, but rather, they will cover all modifications, equivalents, and alternatives falling within the spirit of this disclosure. Furthermore, any feature, function, step, or element of the embodiments, as well as any negative limitations defining the scope of the invention by features, functions, steps, or elements not within that scope, may be recited in or added to the claims.

Claims

1. A method for maintaining and heating a reverse field configuration (FRC) plasma, the method comprising the steps of: Multiple neutral beams are injected at an angle toward the central plane of the confinement chamber into the FRC plasma within the confinement chamber, and Multiple radio frequency range high-harmonic fast waves are emitted into the FRC plasma from one or more antennas at an emission angle relative to the mid-plane of the confinement chamber.

2. The method according to claim 1, wherein, The launch angle is in the range of 15° to 25° from the mid-plane of the confinement chamber.

3. The method according to claim 1, wherein, The emission angle is less than orthogonal to the longitudinal axis of the confinement chamber.

4. The method according to claim 2, wherein, The one or more antennas are phased array antennas with multiple bands.

5. The method according to claim 1, wherein, The step of transmitting high-harmonic fast waves across multiple radio frequency ranges to the FRC plasma includes heating the FRC plasma electrons from 150 eV to above 1 keV.

6. The method according to claim 1, further comprising: The FRC plasma is maintained at a constant value without decay when a fast neutral atom beam is injected into the FRC plasma in the confinement chamber, and the electron temperature of the FRC plasma is increased to above 1.0 keV.

7. The method of claim 1, further comprising the steps of: generating a magnetic field within the confinement chamber using a quasi-DC coil extending around the confinement chamber, and generating a mirror magnetic field within the opposite ends of the confinement chamber using quasi-DC mirror coils extending around opposite ends of the confinement chamber.

8. The method according to claim 7, further comprising the step of forming the FRC plasma in the confinement chamber.

9. The method according to claim 8, wherein, The steps of forming the FRC plasma include: forming generating FRC plasma in opposing first and second generating sections, the first and second generating sections being coupled to the confinement chamber and accelerating the generating FRC plasma from the first and second generating sections toward a central penetrating plane of the confinement chamber, wherein the two generating FRC plasmas are merged in the confinement chamber to form the FRC plasma.

10. The method according to claim 9, wherein, The steps of forming the FRC include one of the following: forming a generating FRC while accelerating the generating FRC toward the central through-plane of the constraint chamber; And to form a generated FRC, and then accelerate the generated FRC toward the central through-plane of the constraint chamber.

11. The method according to any one of claims 7, the method further comprising the step of: using a saddle coil connected to the chamber to generate one of a magnetic dipole field and a magnetic quadrupole field in the chamber.

12. The method of claim 9, further comprising the steps of: using an air intake system to process the inner surface of the constraint chamber and the inner surfaces of the first and second generating portions, the inner surfaces of the first and second divertors sandwiched between the constraint chamber and the first and second generating portions, and the inner surfaces of the first and second external divertors connected to the first and second generating portions.

13. The method according to claim 12, wherein, The air intake system includes either a titanium deposition system or a lithium deposition system.

14. The method of claim 7, further comprising the step of: axially injecting plasma from an axially mounted plasma gun into the FRC plasma.

15. The method according to claim 7, further comprising the step of controlling the radial electric field distribution in the edge layer of the FRC plasma.

16. The method according to claim 15, wherein, The step of controlling the radial electric field distribution in the edge layer of the FRC plasma includes applying a potential distribution to a set of open flux surfaces of the FRC plasma using a bias electrode.

17. The method according to claim 1, further comprising: Compact ring (CT) plasma is injected into the FRC plasma at an angle from the first and second CT injectors toward the mid-plane of the confinement chamber, wherein the first and second CT injectors are exactly opposite each other on opposite sides of the mid-plane of the confinement chamber.

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