System and method for forming and maintaining high energy and temperature FRC plasma via spheromak merging and neutral beam injection

Abstract

To provide systems and methods for forming and maintaining high energy and temperature FRC plasma via spheromak merging and neutral beam injection.SOLUTION: There is provided a system and a method for forming and maintaining high energy and temperature FRC plasma via spheromak merging and neutral beam injection. A high performance field reversed configuration (FRC) system includes a central confinement chamber, two divertor chambers coupled to the chamber, and two diametrically opposed spheromak injectors coupled to the divertor chambers. A magnetic system includes quasi-dc coils axially positioned along the FRC system components.SELECTED DRAWING: Figure 31B

Description

[Technical Field]

[0001] Embodiments described herein relate generally to magnetic plasma confinement systems, and more particularly to systems and methods that facilitate the formation and maintenance of high-energy, high-temperature Field Reversed Configuration (FRC) plasmas with excellent stability as well as particle, energy, and magnetic flux confinement. [Background technology]

[0002] Background information Field-reversed configurations (FRCs) belong to a class of magnetic plasma confinement topologies known as compact toroids. They exhibit a predominantly poloidal magnetic field, with zero or small self-generated toroidal fields (see M. Tuszewski, Nucl. Fusion 28, 2033 (1988)). The appeal of such configurations is their simple geometry for ease of construction and maintenance, unlimited natural divertors to facilitate energy extraction and ash removal, and very high β (β is the ratio of the mean plasma pressure inside the FRC to the mean magnetic field pressure), i.e., high power density. The essence of a high β is for economical operation and for D-He 3 and pB 11 It is advantageous for the use of advanced non-neutron fuels such as

[0003] The traditional method of forming FRCs uses the field-reversed theta-pinch technique to generate a high-temperature, high-density plasma (see A.L. Hoffman and J.T. Slough, Nucl. Fusion 33, 27 (1993)). A variation on this is the transfer-trap method, in which the plasma created in a theta-pinch "source" is almost immediately ejected at one end into a confinement chamber. The transferring plasmoid is then trapped between two strong mirrors at the end of the chamber (see, e.g., H. Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191 (1995)). Once inside the confinement chamber, various heating and current drive methods may be applied, such as (neutral or neutralized) beam injection, rotating magnetic fields, RF or ohmic heating, etc. This separation of source and confinement functions offers important engineering advantages for potential future fusion reactors. FRCs have proven to be highly robust and resistant to dynamic formation, transfer, and violent capture events. Furthermore, they tend to support favorable plasma states (see, e.g., H.Y. Guo, A.L. Hoffman, K.E. Miller, and L.C. Steinhauer, Phys. Rev. Lett. 92, 245001 (2004)). In the past decade, significant progress has been made by developing other methods for forming FRCs, namely, by fusing spheromaks with reverse helicity (see, e.g., Y. Ono, M. Inomoto, Y. Ueda, T. Matsuyama, and T. Okazaki, Nucl. Fusion 39, 2001 (1999)), as well as by driving current with a rotating magnetic field (RMF), which also provides additional stability (see, e.g., I.R. Jones, Phys. Plasmas 6, 1950 (1999)).

[0004] The collisional fusion technique, proposed long ago (see, e.g., D.R. Wells, Phys. Fluids 9, 1010 (1966)), has been significantly further developed. That is, two separate theta pinches at opposite ends of a confinement chamber simultaneously generate two plasmoids, accelerate them toward each other at high velocities, and then collide in the center of the confinement chamber and fuse to form a composite FRC. In the construction and successful operation of one of the largest FRC experiments to date, the conventional collisional fusion method has been shown to produce stable, long-lasting, high-flux, high-temperature FRCs (see, e.g., M. Binderbauer, et al., Phys. Rev. Lett. 105, 045003 (2010)). More recently, major advances have been made using the collisional fusion technique in beam-driven FRC experiments to produce relatively high-temperature FRCs for extended periods of time (typical plasma parameters are Te ≈ 250 eV, Ti ≈ 1 keV, <ne>Approximately 2-3×10 13 cm 3 This has been achieved using high-power neutral beam (NBI) injection (with a Be of approximately 1 kG and a plasma lifetime of approximately 30 ms) and effective edge biasing (Gota, H. et al., Nucl. Fusion 57, 116021 (2017); Gota, H. et al., Nucl. Fusion 59, 112009 (2019), and Gota, H. et al., Bull. Am. Phys. Soc. 64, UP10.00123 (2019)). In such experiments, the target plasma for NBI is produced by the collision and fusion of two FRC plasmas using the field-reversed theta-pinch (FRTP) dynamic formation technique (Binderbauer, Phys. Rev. Lett. 105), in which the trapped magnetic flux of the fused FRC is initially approximately 5 mWb based on a rigid rotor model with an external magnetic field of approximately 1 kG within the confinement section. By injecting high powers of over 13 MW (increased by up to about 21 MW during the shot by adjusting the beam energy) into the target plasma, the injected fast particles are trapped and travel inside and outside the dividing line with large trajectories, primarily for electron heating but also for current drive, in which fast ions are nearly classically confined. This high-power NBI has not been achieved in any other CT experiment and was a very important demonstration of the validity of the beam-driven FRC concept and its technical readiness. (Gota, Nucl. Fusion 59; Gota, Bull. Am. Phys. Soc. 64)

[0005] Improved systems, devices, and methods for generating high magnetic flux target FRC plasmas and axial feed are desirable. Summary of the Invention [Means for solving the problem]

[0006] Exemplary embodiments of systems, devices, and methods are provided herein for generating a high-flux target FRC plasma and axially replenishing the FRC plasma. To generate an optimal initial high-flux target FRC plasma, two medium-sized Spheromak injectors (also called CT injectors) are coupled opposite the ends of a centrally located plasma confinement chamber. The Spheromak injectors inject spheromaks toward the midplane of the confinement chamber, where the spheromaks fuse and form an FRC plasma within the confinement chamber. The counterhelicity fusion of the two spheromaks tends to generate an FRC plasma with elevated and trapped magnetic flux. Multiple neutral beam injectors are also coupled to the confinement chamber to drive and sustain the FRC plasma.

[0007] In an exemplary embodiment, the Neutral Beam Injector is adjustable from an initial power level to an increased power level.

[0008] In a further exemplary embodiment, the Spheromak injector is capable of injecting multi-pulsed Spheromak into the FRC plasma along the geometric axis of the confinement chamber for effective replenishment and reflux.

[0009] Other systems, devices, methods, features, and advantages of the subject matter described herein will be, or will become, apparent to one of ordinary skill in the art upon examination of the following figures and detailed description. All such additional systems, methods, features, and advantages are intended to be included within this specification, be within the scope of the subject matter described herein, and be protected by the accompanying claims. No feature of the exemplary embodiments should be construed in any way as limiting the appended claims, even without explicit recitation of those features in the claims. The present invention provides, for example, the following items. (Item 1) 1. A method for generating and maintaining a magnetic field using a field-reversed configuration (FRC), comprising: Merging the first and second spheromak plasmas and forming an FRC around the merged plasma in a confinement chamber; maintaining the FRC at a constant or nearly constant value without decay by injecting a beam of fast neutral atoms from a neutral beam injector into the FRC plasma at an angle toward the midplane of the confinement chamber; A method comprising: (Item 2) 2. The method of claim 1, wherein the step of forming the FRC includes the steps of injecting spheromak plasma from first and second spheromak injectors facing each other toward a midplane of the chamber, and merging the spheromak plasma to form the FRC. (Item 3) 3. The method according to claim 2, wherein the step of fusing the spheromak plasma and forming the FRC plasma includes reverse helicity spheromak fusion of the spheromak plasma injected into the confinement chamber from the first and second spheromak injectors. (Item 4) 4. The method of claim 2, wherein the first and second spheromak injectors comprise magnetized coaxial plasma guns (MCPGs). (Item 5) 5. The method of claim 2, wherein the first and second Spheromak injectors include an iron-core bias coil system. (Item 6) 6. The method of claim 5, wherein the iron core of the iron core bias coil system is cast iron with a magnetic permeability of about 250. (Item 7) 6. The method of claim 5, wherein the iron core of the iron core bias coil system is about 99.9% Fe with a magnetic permeability equal to or greater than about 200,000. (Item 8) 8. The method of claim 2, further comprising the step of separately controlling the first and second Spheromak injectors. (Item 9) 9. The method of claim 8, wherein the spheromak plasma ejected from the first spheromak injector is different from the spheromak plasma ejected from the second spheromak injector. (Item 10) 10. The method of claim 2, further comprising the step of replenishing the FRC plasma with one or more spheromak plasmas from one or more of the first and second spheromak injectors along the geometric axis of the confinement chamber. (Item 11) Item 11. The method of item 10, wherein the replenishment step further comprises multi-pulse injecting one or more spheromak plasmas into the FRC plasma from one or more of the first and second spheromak injectors. (Item 12) 10. The method of claim 2, further comprising forming the multi-pulse spheromak and injecting it into the FRC plasma. (Item 13) The method of any one of items 1-12, wherein the step of implanting a beam of fast neutral atoms includes one of the following steps: adjusting the beam energies of the multiple neutral beams between a first beam energy and a second beam energy, where the second beam energy is different from the first beam energy; or adjusting the beam energies of the multiple neutral beams between a first beam energy and a second beam energy, where the second beam energy is different from the first beam energy and the second beam energy is higher than the first beam energy; or adjusting the beam energies of the multiple neutral beams between a first beam energy and a second beam energy, where the second beam energy is different from the first beam energy and the multiple neutral beams switch between the first beam energy and the second beam energy for the duration of an implantation shot. (Item 14) 14. The method of claim 1, further comprising generating a magnetic field in the chamber using a quasi-DC coil extending around the chamber. (Item 15) Item 15. The method of item 14, further comprising the step of inducing a magnetic flux surface of the FRC into a diverter coupled to an end of the containment chamber. (Item 16) Item 16. The method of item 15, comprising generating a magnetic field in the divertor using a quasi-DC coil extending around the forming section and the divertor. (Item 17) 17. The method of claim 16, further comprising generating mirror magnetic fields in opposing ends of the chamber using quasi-DC mirror coils extending about opposing ends of the chamber. (Item 18) 18. The method of claim 14, further comprising generating one of a magnetic dipole field and a magnetic quadrupole field within the chamber using a saddle coil coupled to the chamber. (Item 19) 19. The method of claim 15, further comprising conditioning the interior surfaces of the chamber and diverter with a gettering system. (Item 20) 20. The method of claim 19, wherein the gettering system comprises one of a titanium deposition system and a lithium deposition system. (Item 21) 21. The method of claim 1, further comprising controlling a radial electric field profile within an edge layer of the FRC plasma. (Item 22) 22. The method of claim 21, wherein controlling the radial electric field profile in the edge layer of the FRC comprises applying a potential distribution to open flux planes of the FRC using bias electrodes. (Item 23) The method according to item 2-22, further comprising one of the steps of injecting a spheromak plasma having a magnetic flux greater than 20 mWb from the first and second spheromak injectors, or injecting a spheromak plasma having a magnetic flux greater than about 25 to 30 mWb from the first and second spheromak injectors. (Item 24) 1. A system for generating and maintaining a magnetic field using a field-reversed configuration (FRC), comprising: a containment chamber; and first and second diverters coupled to the containment chamber; first and second diametrically opposed Spheromak injectors coupled to the first and second diverters for generating a Spheromak plasma and translating the Spheromak plasma toward a midplane of the confinement chamber; a plurality of neutral atom beam injectors coupled to the confinement chamber and oriented to inject neutral atom beams toward a midplane of the confinement chamber at an angle less than normal to a longitudinal axis of the confinement chamber; a magnetic system comprising: a plurality of quasi-DC coils positioned around the confinement chamber and the first and second diverters; first and second sets of quasi-DC mirror coils positioned between the confinement chamber and the first and second forming sections; and first and second mirror plugs positioned between the confinement chamber and the first and second diverters; a gettering system coupled to the confinement chamber and the first and second divertors; one or more bias electrodes for electrically biasing the open flux planes of the generated FRC, the one or more bias electrodes being positioned in the confinement chamber and one or more of the first and second divertors; two or more saddle coils coupled to the containment chamber; A system comprising: (Item 25) 1. A system for generating and maintaining a magnetic field with a field-reversed configuration (FRC), comprising: a containment chamber; and first and second diverters coupled to the containment chamber; first and second diametrically opposed Spheromak injectors coupled to the first and second diverters; one or more of a plurality of bias electrodes and first and second mirror plugs, wherein the one or more bias electrodes are positioned within the confinement chamber and one or more of the first and second diverters, and the first and second mirror plugs are positioned between the confinement chamber and the first and second diverters; a gettering system coupled to the confinement chamber and the first and second divertors; a plurality of neutral atom beam injectors coupled to the confinement chamber and oriented at an angle toward a midplane of the confinement chamber; a magnetic system comprising a plurality of quasi-DC coils positioned around the confinement chamber and the first and second divertors, and first and second sets of quasi-DC mirror coils positioned between the confinement chambers; Equipped with the system is configured to generate an FRC and maintain the FRC without decay while the neutral beam is injected into the plasma; system. (Item 26) 26. The system of items 24 and 25, wherein the first and second spheromak injectors are configured to inject spheromak plasma toward a midplane of the chamber to fuse and form an FRC plasma. (Item 27) Item 27. The system of item 26, wherein the first and second spheromak injectors are configured to form and inject first and second spheromak plasmas having reverse helicity into the confinement chamber. (Item 28) 28. The system of claim 24, wherein the first and second spheromak injectors comprise magnetized coaxial plasma guns (MCPGs). (Item 29) 28. The system of claim 24-27, wherein the first and second Spheromak injectors include iron-core bias coil systems. (Item 30) 30. The system of claim 29, wherein the iron core of the iron core bias coil system is cast iron with a magnetic permeability of about 250. (Item 31) 30. The system of claim 29, wherein the iron core of the iron core bias coil system is about 99.9% Fe with a magnetic permeability equal to or greater than about 200,000. (Item 32) 28. The system of claim 24, wherein the first and second Spheromak injectors are independently controllable. (Item 33) Item 33. The system of item 32, wherein the first and second spheromak injectors are configured to multi-pulse inject more than one spheromak plasma into the confinement chamber. (Item 34) The system described in items 24-33, wherein the multiple neutral beams are adjustable between a first beam energy and a second beam energy, the second beam energy being different from the first beam energy, and the beam energies of the multiple neutral beams are switched between the first beam energy and the second beam energy for the duration of an implant shot. (Item 35) 35. The system of claim 24, further comprising first and second diametrically opposed reversed field theta-pinch forming sections interposed between the first and second divertors and the containment chamber. (Item 36) Item 37. The system of item 36, further comprising third and fourth diverters interposed between the first and second diametrically opposed reversed field theta-pinch forming sections and the containment chamber. [Brief explanation of the drawings]

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

[0011] [Figure 1] FIG. 1 illustrates particle confinement in the present FRC system under high performance FRC regime (HPF) compared to conventional FRC regime (CR) and compared to other conventional FRC experiments.

[0012] [Figure 2] FIG. 2 illustrates the components of the present FRC system and the magnetic topology of the FRCs that can be produced in the present FRC system.

[0013] [Figure 3A] FIG. 3A illustrates the basic layout of the present FRC system from a top view, including a preferred arrangement of the central containment vessel, formation section, neutral beam, electrodes, plasma guns, mirror plugs, and pellet injector.

[0014] [Figure 3B] FIG. 3B illustrates the central confinement vessel from a top view, showing the neutral beam aligned at an angle normal to the long axis of symmetry within the central confinement vessel.

[0015] [Figure 3C] FIG. 3C illustrates the central confinement vessel from above, showing the neutral beam aligned at an angle that is less than normal to the long axis of symmetry within the central confinement vessel and directed to inject particles toward the midplane of the central confinement vessel.

[0016] [Figure 3D] Figures 3D and 3E illustrate top and perspective views, respectively, of the basic layout of an alternative embodiment of the present FRC system, including a central confinement vessel, forming sections, inner and outer divertors, and a preferred arrangement of neutral beams, electrodes, plasma guns, and mirror plugs arranged at angles less than normal to the long axis of symmetry within the central confinement vessel. [Figure 3E] Figures 3D and 3E illustrate top and perspective views, respectively, of the basic layout of an alternative embodiment of the present FRC system, including a central confinement vessel, forming sections, inner and outer divertors, and a preferred arrangement of neutral beams, electrodes, plasma guns, and mirror plugs arranged at angles less than normal to the long axis of symmetry within the central confinement vessel.

[0017] [Figure 4] FIG. 4 illustrates a schematic of the components of a pulsed power system for the forming section.

[0018] [Figure 5] FIG. 5 illustrates an isometric view of an individual pulsed power forming skid.

[0019] [Figure 6] FIG. 6 illustrates an isometric view of the forming tube assembly.

[0020] [Figure 7] FIG. 7 illustrates a partial cross-sectional isometric view of the Neutral Beam system and key components.

[0021] [Figure 8] FIG. 8 illustrates an isometric view of the Neutral Beam array on the containment chamber.

[0022] [Figure 9] FIG. 9 illustrates a partial cross-sectional isometric view of a preferred arrangement of a Ti and Li gettering system.

[0023] [Figure 10] 10 illustrates a partial cross-sectional isometric view of a plasma gun disposed within a diverter chamber. The associated magnetic mirror plug and diverter electrode assembly are also shown.

[0024] [Figure 11] FIG. 11 illustrates a preferred layout of annular bias electrodes at the axial ends of the containment chamber.

[0025] [Figure 12] Figure 12 illustrates the evolution of the excluded magnetic flux radius in the FRC system, obtained from a series of outer diamagnetic loops in two field-reversed theta-pinch forming sections and from magnetic probes embedded inside the central metallic confinement chamber. The time is measured from the moment of synchronous field reversal in the forming source, and the distance z is given relative to the axial mid-plane of the machine.

[0026] [Figure 13] Figures 13A, 13B, 13C, and 13D illustrate data from a representative non-HPF non-sustained discharge on the present FRC system. Shown as a function of time are the excluded magnetic flux radius at the mid-plane (Figure 13A), the six-code line-integrated density from the mid-plane CO2 interferometer (Figure 13B), the Abel-transformed density radial profile from the CO2 interferometer data (Figure 13C), and the total plasma temperature from pressure equilibrium (Figure 13D).

[0027] [Figure 14] FIG. 14 illustrates the excluded magnetic flux axial profile at selected times for the same discharge of the present FRC system shown in FIGS. 13A, 13B, 13C, and 13D.

[0028] [Figure 15] FIG. 15 illustrates an isometric view of a saddle coil mounted outside the containment chamber.

[0029] [Figure 16] 16A, 16B, 16C, and 16D illustrate the correlation between injected neutral beam FRC lifetime and pulse length. As shown, longer beam pulses produce longer-lived FRCs.

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

[0031] [Figure 18] Figures 18A, 18B, 18C, and 18D illustrate data from a representative HPF unsustained discharge on the FRC system. Shown as a function of time are the excluded magnetic flux radius at the mid-plane (Figure 18A), the six-code line-integrated density from the mid-plane CO2 interferometer (Figure 18B), the Abel-transform density radial profile from the CO2 interferometer data (Figure 18C), and the total plasma temperature from pressure equilibrium (Figure 18D).

[0032] [Figure 19] Figure 19 illustrates the magnetic flux confinement as a function of electron temperature (Te), which represents a graphical representation of the newly established superior scaling scheme for HPF discharges.

[0033] [Figure 20] FIG. 20 illustrates the FRC lifetime as a function of pulse length for non-angled and angled injected neutral beams.

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

[0035] [Figure 22] 22A and 22B illustrate the basic layout of a compact toroid (CT) injector.

[0036] [Figure 23] 23A and 23B illustrate the central containment vessel and show the CT injector mounted therein.

[0037] [Figure 24] 24A and 24B illustrate the basic layout of an alternative embodiment of a CT injector having a drift tube coupled thereto.

[0038] [Figure 25] FIG. 25 illustrates a cross-sectional isometric view of the Neutral Beam System and key components for tunable energy beam output.

[0039] [Figure 26] FIG. 26 is a schematic diagram illustrating a Neutral Beam system with adjustable energy beam output.

[0040] [Figure 27] FIG. 27 is a schematic diagram illustrating the axial position control mechanism of the FRC plasma within the containment vessel (CV).

[0041] [Figure 28] FIG. 28 is a flow diagram of a general sliding mode control scheme.

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

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

[0044] [Figure 31A] 31A and 31B are schematic diagrams depicting an exemplary embodiment of an FRC confinement system with opposing Spheromak injectors. [Figure 31B] 31A and 31B are schematic diagrams depicting an exemplary embodiment of an FRC confinement system with opposing Spheromak injectors.

[0045] [Figure 32] 32A, 32B, 32C, and 32D illustrate steps in the FRC formation process via reverse helicity spheromak fusion.

[0046] [Figure 33] FIG. 33 is a schematic diagram depicting an exemplary embodiment of a Spheromac injector.

[0047] It should be noted that the figures are not necessarily to scale, and that elements of similar structure or function are generally represented by like reference numerals throughout the figures for illustrative purposes. It should also be noted that the figures are intended only to facilitate explanation of the various embodiments described herein. The figures do not necessarily illustrate every aspect of the teachings disclosed herein, nor do they limit the scope of the claims. DETAILED DESCRIPTION OF THE INVENTION

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

[0049] Representative examples of embodiments described herein that utilize many of these additional features and teachings, both separately and in combination, will now be described with reference to the accompanying drawings. This detailed description is intended merely to teach those skilled in the art further details for practicing preferred aspects of the present teachings and is not intended to limit the scope of the invention. Thus, combinations of features and steps disclosed in the following detailed description may not be necessary to practice the invention in its broadest sense, but instead are taught only to specifically illustrate representative examples of the present teachings.

[0050] Furthermore, various features of the representative examples and dependent claims may be combined in ways not specifically and explicitly recited to provide additional useful embodiments of the present teachings. Additionally, it is expressly noted that all features disclosed in the description and / or claims are intended to be disclosed separately and independently from one another, not only for purposes of original disclosure, but also for purposes of limiting the claimed subject matter, independent of any combination of features in the embodiments and / or claims. It is also expressly noted that the designation of any range of values ​​or group of entities discloses all possible intermediate values ​​or intermediate entities, not only for purposes of original disclosure, but also for purposes of limiting the claimed subject matter.

[0051] The present embodiments provided herein are directed to systems and methods that promote the formation and maintenance of FRCs with particle, energy, and magnetic flux confinement as well as superior stability. Some of the present embodiments are directed to systems and methods that promote the formation and maintenance of FRCs with increased system energy and improved durability while utilizing a neutral beam injector with adjustable beam energy capability. Some of the present embodiments are also directed to systems and methods that promote both radial and axial FRC plasma stability and axial position control of the FRC plasma along the axis of symmetry of the FRC plasma confinement chamber, independent of the axial stability properties of the FRC plasma equilibrium.

[0052] Before turning to systems and methods that utilize a pair of medium-scale spheromak injectors (or magnetized coaxial plasma guns (MCPGs)) to facilitate the creation and maintenance of high-flux target FRC plasmas and axial replenishment of FRC plasmas, a discussion of systems and methods for forming and maintaining high-performance FRCs with superior particle, energy, and flux containment as well as superior stability over conventional FRCs is provided. Such high-performance FRCs offer a pathway to a variety of applications, including compact neutron sources (for medical isotope production, nuclear waste cleanup, materials research, neutron radiography, and tomography), compact photon sources (for chemical production and processing), mass separation and enrichment systems, and light fusion cores for future energy generation.

[0053] Various auxiliary systems and modes of operation have been explored to evaluate whether a superior confinement regime within an FRC exists. These efforts have led to the breakthrough discovery and development of the high-performance FRC paradigm described herein. According to this new paradigm, the present system and method combine numerous novel ideas and tools to not only significantly improve FRC confinement but also provide stability control without negative side effects, as illustrated in FIG. 1. As discussed in more detail below, FIG. 1 depicts particle confinement within an FRC system 10, described below, operating according to a high-performance FRC regime (HPF) for forming and maintaining an FRC, as opposed to operating according to a conventional regime (CR) for forming and maintaining an FRC, and as opposed to particle confinement according to conventional regimes for forming and maintaining an FRC used in other experiments (see FIGS. 2 and 3). This disclosure will provide an overview and details of the innovative individual components of the FRC system 10 and method, as well as their collective effects. FRC system Vacuum System

[0054] 2 and 3 depict schematic diagrams of the present FRC system 10. The FRC system 10 includes a central containment vessel 100 surrounded by two diametrically opposed reversed-field theta-pinch forming sections 200, and a divertor chamber 300 beyond the forming sections 200 for controlling neutral density and impurity contamination. The present FRC system 10 contains an ultra-high vacuum and is 10 -8 It was constructed to operate at a typical base pressure of 1000 psi (2000 psi) at 250°C. Such vacuum pressures require careful initial surface preparation of all parts prior to assembly, including a 24-hour 250°C vacuum bake and hydrogen glow discharge clean, as well as the use of dual pump mating flanges, metal O-rings, and high-purity inner walls between mating parts, as well as physical and chemical cleaning.

[0055] The reversed-field theta-pinch forming sections 200 are standard field-reversed theta-pinch (FRTP) but with an advanced pulsed-power forming system (see Figures 4-6), discussed in detail below. Each forming section 200 is fabricated from standard opaque industrial-grade quartz tubing, featuring a 2-millimeter inner lining of ultra-high-purity quartz. The containment chamber 100 is fabricated from stainless steel and allows for multiple radial and tangential ports, which also serve as flux conservers on the timescale of the experiments described below, limiting fast magnetic transients. Vacuum is created and maintained within the FRC system 10 using a set of dry scroll roughing pumps, turbomolecular pumps, and cryogenic pumps. Magnetic System

[0056] Magnetic system 400 is illustrated in FIGS. 2 and 3. FIG. 2 illustrates, among other features, FRC magnetic flux and density contours (as a function of radial and axial coordinates) associated with an FRC 450 producible by FRC system 10. These contours were obtained through 2D resistive Hall MHD numerical simulations using code developed to simulate systems and methods corresponding to FRC system 10 and are in close agreement with measured experimental data. As seen in FIG. 2, FRC 450 consists of a torus of closed field lines in the interior 453 of FRC 450 inside section line 451 and an annular edge layer 456 on open field line 452 just outside section line 451. Edge layer 456 coalesces into jet 454 over the length of the FRC, providing a natural diverter.

[0057] The main magnetic system 410 includes a series of quasi-DC coils 412, 414, and 416 located at specific axial positions along the components, i.e., along the confinement chamber 100, the forming section 200, and the diverter 300 of the FRC system 10. The quasi-DC coils 412, 414, and 416 are powered by quasi-DC switched power supplies and produce a basic magnetic bias field of approximately 0.1 T within the confinement chamber 100, the forming section 200, and the diverter 300. In addition to the quasi-DC coils 412, 414, and 416, the main magnetic system 410 includes quasi-DC mirror coils 420 (powered by switched power supplies) between either end of the confinement chamber 100 and its adjacent forming section 200. The quasi-DC mirror coils 420 provide a magnetic mirror ratio of up to 5 and can be independently excited for balanced shaping control. Additionally, a mirror plug 440 is positioned between each forming section 200 and each divertor 300. The mirror plug 440 comprises a compact quasi-DC mirror coil 430 and a mirror plug coil 444. The quasi-DC mirror coil 430 includes three coils 432, 434, and 436 (powered by a switched source) that provide an additional induction field and focus a magnetic flux surface 455 toward a small-diameter passage 442 that passes through the mirror plug coil 444. The mirror plug coil 444, which is deposited around the small-diameter passage 442 and powered by an LC pulsed power circuit, produces a strong magnetic mirror field of up to 4 T. The purpose of this entire coil arrangement is to tightly bundle and guide the magnetic flux surface 455 and the end-charged plasma jet 454 into the remote chamber 310 of the divertor 300. Finally, a set of saddle coil "antennas" 460 (see FIG. 15) are located outside the containment chamber 100, two on either side of the midplane, fed by DC power supplies. The saddle coil antennas 460 can be configured to provide a quasi-static magnetic dipole or quadrupole field of approximately 0.01 T for rotational instability control and / or electron current control. The saddle coil antennas 460 can flexibly provide magnetic fields that are symmetric or asymmetric about the machine's midplane, depending on the direction of the applied current. Pulse-type power generation system

[0058] The pulsed power shaping system 210 operates on a modified theta-pinch principle. There are two systems, each supplying power to one of the shaping sections 200. Figures 4-6 illustrate the main building blocks and arrangement of the shaping system 210. The shaping system 210 consists of a modular pulsed power arrangement of individual units (=skids) 220, each of which energizes a subset of the coils 232 of a strap assembly 230 (=strap) wrapped around the shaping quartz tube 240. Each skid 220 consists of a capacitor 221, an inductor 223, a high-speed, high-current switch 225 and associated trigger 222, and a dump circuit 224. Overall, each shaping system 210 stores 350-400 kJ of capacitive energy and provides up to 35 GW of power for shaping and accelerating FRCs. The coordinated operation of the components is achieved via state-of-the-art trigger and control systems 222 and 224, allowing synchronized timing between the formation systems 210 on each formation section 200 and minimizing switching jitter down to tens of nanoseconds. An advantage of this modular design is its flexible operation: FRCs can be formed in situ, then accelerated and injected (static formation), or simultaneously formed and accelerated (dynamic formation). Neutral Beam Injector

[0059] A neutral atomic beam 600 is deployed on the FRC system 10, providing heating and current drive as well as generating fast particle pressure. As shown in Figures 3A, 3B, and 8, the individual beam lines comprising the neutral atomic beam injector systems 610 and 640 are positioned around the periphery of the central confinement chamber 100 and use collision parameters to inject fast particles tangentially into the FRC plasma (and perpendicular or normal to the longitudinal axis of symmetry within the central confinement chamber 100) so that the target capture zone is well within the demarcation line 451 (see Figure 2). Each injector system 610 and 640 is capable of injecting up to 1 MW of neutral beam power into the FRC plasma, using particle energies between 20 and 40 keV. Systems 610 and 640 are based on a positive ion multi-aperture extraction source and utilize geometric focusing, inertial cooling of the ion extraction grid, and differential pumping. Aside from the use of different plasma sources, systems 610 and 640 are distinguished primarily by their physical designs, which accommodate their separate mounting locations, providing side and top injection capabilities. Typical components of these neutral beam injectors are specifically illustrated in FIG. 7 for side injector system 610. As shown in FIG. 7, each individual neutral beam system 610 includes an RF plasma source 612 at the input end (which is replaced by an arc source in system 640) with a magnetic shield 614 covering the end. An ion optics source and acceleration grid 616 is coupled to the plasma source 612, and a gate valve 620 is positioned between the ion optics source and acceleration grid 616 and a neutralizer 622. A bending magnet 624 and an ion dump 628 are located between the neutralizer 622 and an aiming device 630 at the exit end. The cooling system includes two cryocoolers 634, two cryopanels 636, and an LN2 shroud 638. The flexible design allows operation over a wide range of FRC parameters.

[0060] An alternative configuration for the neutral atom beam injector 600 injects fast particles tangentially to the FRC plasma, but at an angle A less than 90° relative to the longitudinal axis of symmetry within the central confinement vessel 100. These types of beam injector 615 orientations are shown in FIG. 3C. Additionally, the beam injectors 615 may be oriented such that the beam injectors 615 on either side of the central confinement vessel's midplane inject their particles toward the midplane. Finally, the axial positions of these beam systems 600 may be selected closer to the midplane. These alternative injection embodiments facilitate more central refueling options, which provide better beam coupling and higher capture efficiency of injected fast particles. Furthermore, depending on the angle and axial position, this arrangement of beam injectors 615 allows for more direct and independent control of the axial elongation and other properties of the FRC 450. For example, injecting the beam at a shallow angle A relative to the vessel's longitudinal axis of symmetry will create an FRC plasma with a longer axial extension and lower temperature, while picking it up at a more perpendicular angle A will lead to a shorter axial but hotter plasma. In this manner, the injection angle A and location of the beam injector 615 can be optimized for different purposes. In addition, such angling and positioning of the beam injector 615 allows higher energy beams (generally more favorable for depositing more power with less beam divergence) to be injected into a lower magnetic field than would otherwise be required to capture such beams. This is due to the fact that it is the azimuthal component of energy that determines the fast ion trajectory scale (which becomes progressively smaller as the injection angle relative to the vessel's longitudinal axis of symmetry is reduced at a constant beam energy). Furthermore, injection angled toward the midplane and an axial beam position close to the midplane improve beam-plasma coupling, even if the FRC plasma contracts or otherwise shrinks axially during the injection period.

[0061] 3D and 3E , another alternative configuration of FRC system 10 includes an inner diverter 302 in addition to angled beam injector 615. The inner diverter 302 is positioned between the formation section 200 and the confinement chamber 100 and is configured and operates substantially similarly to the outer diverter 300. The inner diverter 302, which includes fast-switching magnetic coils therein, is effectively inactive during the formation process, allowing the forming FRCs to pass through the inner diverter 302 as they translate toward the midplane of the confinement chamber 100. Once the forming FRCs have passed through the inner diverter 302 and into the confinement chamber 100, the inner diverter is activated and operates substantially similarly to the outer diverter, isolating the confinement chamber 100 from the formation section 200. Pellet Injector

[0062] To provide a means for injecting new particles and better control the particle loading of the FRC, a 12-barrel pellet injector 700 (see, e.g., I. Vinyar et al., "Pellet Injectors Developed at PELIN for JET, TAE, and HL-2A," Proceedings of the 26th Fusion Science and Technology Symposium, 09 / 27 to 10 / 01 (2010)) is utilized on the FRC system 10. FIG. 3 illustrates the layout of the pellet injector 700 on the FRC system 10. Cylindrical pellets (D approximately 1 mm, L approximately 1-2 mm) are injected into the FRC at velocities in the range of 150-250 km / s. Each individual pellet contains approximately 5×10 19 hydrogen atoms, comparable to the FRC particle loading. Gettering System

[0063] It is well known that neutral halo gas is a significant problem in all confinement systems. Charge exchange and recycling (release of cold impurity material from the walls) processes can have devastating effects on energy and particle confinement. In addition, any significant density of neutral gas at or near the edge would lead to an immediate loss or at least a significant reduction in the lifetime of injected large-orbit (high-energy) particles (large orbits refer to particles with orbits on the scale of the FRC topology or at least with orbital radii significantly larger than the characteristic magnetic field gradient length), a fact that is detrimental to all energetic plasma applications, including fusion via auxiliary beam heating.

[0064] Surface conditioning is a means by which the deleterious effects of neutral gases and impurities can be controlled or reduced within a confinement system. To this end, the FRC system 10 provided herein employs titanium and lithium deposition systems 810 and 820 to coat the plasma-facing surfaces of the confinement chamber (or vessel) 100 and divertors 300 and 302 with Ti and / or Li films (tens of microns thick). The coating is achieved via vapor deposition techniques. Solid Li and / or Ti are evaporated and / or sublimated and sprayed onto nearby surfaces to form the coating. The source is either an atomic oven (for Li) 822 with an induction nozzle or a solid heated sphere with an induction shroud (for Ti) 812. The Li evaporator system typically operates in continuous mode, while the Ti sublimator is often operated intermittently between plasma operations. The operating temperatures of these systems exceed 600°C to obtain high deposition rates. To achieve sufficient wall coverage, multiple strategically positioned evaporator / sublimator systems are required. Figure 9 details a preferred arrangement of gettering deposition systems 810 and 820 within the FRC system 10. The coating acts as a gettering surface, effectively pumping atomic and molecular hydrogen species (H and D). The coating also reduces other typical impurities, such as carbon and oxygen, to insignificant levels. Mirror plug

[0065] As previously mentioned, the FRC system 10 employs sets of mirror coils 420, 430, and 444, as shown in Figures 2 and 3. The first set of mirror coils 420 are located at the two axial ends of the confinement chamber 100 and are excited independently of the DC confinement, shaping, and diverter coils 412, 414, and 416 of the main magnetic system 410. The first set of mirror coils 420 primarily serve to steer and axially contain the FRC 450 during fusion and provide balanced shaping control during sustainment. The first mirror coil set 420 produces a nominally higher magnetic field (approximately 0.4-0.5 T) than the central confinement field produced by the central confinement coil 412. The second set of mirror coils 430, including three compact quasi-DC mirror coils 432, 434, and 436, is located between the forming section 200 and the divertor 300 and is driven by a common switched power supply. The mirror coils 432, 434, and 436, along with a more compact pulsed mirror plug coil 444 (powered by a capacitive power supply) and a physical constriction 442, form a mirror plug 440 that provides a narrow, low-gas-conductivity path with very high magnetic fields (2-4 T, with a rise time of approximately 10-20 ms). The most compact pulsed mirror coil 444 has compact radial dimensions, with a bore of 20 cm and similar length, compared to the meter-plus-scale bore and pancake design of the confinement coils 412, 414, and 416. The purposes of the mirror plug 440 are diverse. That is, (1) coils 432, 434, 436, and 444 tightly bundle and guide magnetic flux surface 452 and end-charged plasma jet 454 into remote diverter chamber 300. This ensures that exhaust particles properly reach diverter 300 and that there is a continuous magnetic flux surface 455 that traces from the open field line 452 region of central FRC 450 to diverter 300. (2) Physical constriction 442 within FRC system 10, through which coils 432, 434, 436, and 444 allow passage of magnetic flux surface 452 and plasma jet 454, provides an obstruction to neutral gas flow from plasma gun 350, which is seated within diverter 300.Similarly, constriction 442 prevents the backflow of gas from formation section 200 to divertor 300, thereby reducing the number of neutral particles that need to be introduced into the entire FRC system 10 when beginning FRC start-up. (3) The strong axial mirror produced by coils 432, 434, 436, and 444 reduces axial particle losses, thereby reducing the diffusivity of collimated particles on the open field line.

[0066] In an alternative configuration shown in FIGS. 3D and 3E, a set of thin, reduced diameter coils 421 are positioned between the inner diverter 302 and the forming section 200. Axial Plasma Gun

[0067] The plasma flow from the gun 350, mounted within the divertor chamber 310 of the divertor 300, is intended to improve stability and neutral beam performance. The gun 350 is mounted axially inside the chamber 310 of the divertor 300, as shown in Figures 3 and 10, and produces plasma that flows along a field line 452 within the divertor 300 toward the center of the confinement chamber 100. The gun 350 operates with a high-density gas discharge within the washer stack channel and is designed to generate a fully ionized plasma of several kiloamperes for 5 to 10 ms. The gun 350 includes a pulsed magnetic coil that matches the output plasma flow with the desired size of the plasma within the confinement chamber 100. The technical parameters of the Gun 350 are characterized by a channel with an outer diameter of 5-13 cm and an inner diameter of up to approximately 10 cm, providing a discharge current of 10-15 kA at 400-600 V, with an internal magnetic field of 0.5-2.3 T.

[0068] The gun plasma flow can penetrate the magnetic field of the mirror plug 440 and flow into the formation section 200 and the confinement chamber 100. The efficiency of plasma transmission through the mirror plug 440 increases with decreasing distance between the gun 350 and the plug 440, and by making the plug 440 wider and shorter. Under reasonable conditions, the gun 350 can transmit plasma at a rate of about 100 keV through the mirror plug 440 at 2-4 T, with high ion and electron temperatures of about 150-300 eV and about 40-50 eV, respectively. 22 The gun 350 is capable of delivering protons / second, providing significant replenishment of the FRC edge layer 456 and overall improvement in FRC particle containment.

[0069] To further increase the plasma density, a gas box could be utilized to inject additional gas from the gun 350 into the plasma stream. This technique can increase the density of the injected plasma several times. In the FRC system 10, the gas box, located on the divertor 300 side of the mirror plug 440, improves the replenishment of the FRC edge layer 456, the formation of the FRC 450, and plasma line coupling.

[0070] Given all of the adjustment parameters discussed above, and taking into account the possibility of operation with only one or both guns, it is readily apparent that a wide range of operating modes is available. bias electrode

[0071] Electrically biasing the open flux planes provides a control mechanism, providing a radial potential that induces azimuthal E×B motion, and similar to turning a knob, can control not only the rotation of the open field line plasma but also the actual FRC core 450 via velocity shear. To accomplish this control, FRC system 10 employs various electrodes strategically placed in various parts of the machine. Figure 3 depicts bias electrodes positioned at preferred locations within FRC system 10.

[0072] In principle, there are four classes of electrodes: (1) point electrodes 905 in the confinement chamber 100 that contact specific open field lines 452 in the edge of the FRC 450 to provide localized charging; (2) annular electrodes 900 between the confinement chamber 100 and the forming section 200 to charge the far-edge magnetic flux layers 456 in an azimuthally symmetric manner; (3) a stack of concentric electrodes 910 in the divertor 300 to charge multiple concentric magnetic flux layers 455 (selection of each layer is controllable by adjusting the coils 416 for adjusting the divertor magnetic field to terminate the desired magnetic flux layers 456 on the appropriate electrode 910); and finally, (4) the anodes 920 of the plasma gun 350 itself (see FIG. 10 ), which capture the inner open flux surface 455 near the section line of the FRC 450. FIGS. 10 and 11 show some typical designs for some of these.

[0073] In all cases, the electrodes are driven by a pulsed or DC power supply at voltages up to about 800 V. Depending on the size of the electrodes and the magnetic flux surface being traversed, currents can be drawn in the kiloampere range. Non-sustained operation of FRC systems - conventional systems

[0074] Standard plasma formation on the FRC system 10 follows the well-developed reversed-field theta-pinch technique. A typical process for starting an FRC begins by driving the quasi-DC coils 412, 414, 416, 420, 432, 434, and 436 to steady-state operation. The RFTP pulsed power circuit of the pulsed power formation system 210 then drives the pulsed rapid reversed-field coil 232, creating a temporary reverse bias of approximately 0.05 T within the formation section 200. At this point, a predetermined amount of neutral gas at 9-20 psi is injected into the two formation volumes defined by the quartz tube chambers 240 of the formation section 200 (north and south) through a set of azimuthally oriented discharge troughs in a flange located on the outer end of the formation section 200. A small-scale RF (approximately several hundred kilohertz) field is then generated from a set of antennas on the surface of the quartz tube 240, creating pre-ionization within the neutral gas column in the form of a localized seed ionization region. This is followed by applying a theta resonance modulation on the current driving the pulsed fast reversed field coil 232, which leads to further comprehensive pre-ionization of the gas column. Finally, the main pulsed power bank of the pulsed power shaping system 210 is activated to drive the pulsed fast reversed field coil 232, creating a forward bias field of up to 0.4 T. This step can be time-sequenced, with the forward bias field being generated uniformly throughout the length of the shaping tube 240 (static shaping), or a continuous peristaltic field modulation being achieved along the axis of the shaping tube 240 (dynamic shaping).

[0075] During this entire formation process, the actual magnetic field reversal within the plasma occurs rapidly within approximately 5 μs. Multi-gigawatt pulsed power delivered to the forming plasma readily produces high-temperature FRCs, which are then ejected from the forming section 200 via either time-sequential modulation of the forward magnetic field (magnetic peristalsis) or application of a transiently increased current in the last coil of coil set 232 near the axially outer end of the forming tube 210 (forming an axial magnetic field gradient oriented axially toward the confinement chamber 100). The two (northern and southern) forming FRCs thus formed and accelerated then expand into the larger diameter confinement chamber 100, with the quasi-DC coil 412 producing a forward bias field to control the radial expansion and provide a balanced external magnetic flux.

[0076] Once the north and south forming FRCs arrive near the midplane of the confinement chamber 100, the FRCs collide. During the collision, the axial kinetic energy of the north and south forming FRCs is largely thermalized as the FRCs eventually merge into a single FRC 450. A large set of plasma diagnostics is available within the confinement chamber 100 to study the equilibrium of the FRCs 450. Typical operating conditions in the FRC system 10 produce a composite FRC with a section radius of about 0.4 m and an axial extension of about 3 m. Further characterization is performed using an external magnetic field of about 0.1 T, a magnetic field of about 5 x 10 19 m 3 and a total plasma temperature of up to 1 keV. Without any sustainment, i.e., heating and / or current drive via neutral beam injection or other auxiliary means, the lifetime of these FRCs is limited to approximately 1 ms, i.e., the intrinsic characteristic configuration decay time. Experimental data on non-sustained movements - conventional system

[0077] Figure 12 shows the radius of the dividing line r s The excluded flux radius r is approximately ΔΦ The typical time evolution of plasmoids is shown to illustrate the dynamics of the theta-pinch fusion process in FRC450. Two individual plasmoids (northern and southern) are produced simultaneously and then merged together at supersonic speeds of about 250 km / s. Z At z = 0, the plasmoids are accelerated outward from the individual forming segments 200 and collide near the midplane. During the collision, the plasmoids compress axially and then rapidly expand radially and axially before finally merging to form FRC450. Both the radial and axial dynamics of the merging FRC450 are evidenced by detailed density profile measurements and bolometer-based tomography.

[0078] Data from a representative unsustained discharge of the FRC system 10 is shown as a function of time in Figures 13A, 13B, 13C, and 13D. The FRC is initiated at t=0. The excluded flux radius at the axial midplane of the machine is shown in Figure 13A. The data was obtained from an array of magnetic probes located just inside the stainless steel wall of the containment chamber, which measures the axial magnetic field. The steel wall is an excellent flux conserver on the time scale of this discharge.

[0079] The line-integrated density from a six-cord CO2 / He-Ne interferometer located at z=0 is shown in Figure 13B. Taking into account the vertical (y) FRC displacement, as measured by bolometric tomography, the Abel transformation yields the density counter in Figure 13C. After some axial and radial oscillations during the first 0.1 ms, the FRC settles with a white density profile. This profile is quite flat, with substantial density on the axis, as required by typical 2D FRC equilibration.

[0080] The total plasma temperature, derived from pressure balance and in perfect agreement with the Thomson scattering spectroscopy measurements, is shown in FIG. 13D.

[0081] Analysis of the entire excluded flux array shows that the shape of the FRC section line (approximated by the excluded flux axial profile) gradually evolves from a racetrack to an elliptical shape. This evolution, shown in Figure 14, is consistent with a gradual magnetic reconnection from two to a single FRC. In fact, rough estimates suggest that at this particular moment, about 10% of the two initial FRC fluxes reconnect during the collision.

[0082] The length of the FRC shrinks steadily during the FRC lifetime, from 3 to about 1 m. This shrinkage suggests that convective energy losses primarily govern the FRC confinement, as visualized in Figure 14. Because the plasma pressure inside the dividing line decreases faster than the external magnetic pressure, the magnetic field line tension in the end regions compresses the FRC axially, restoring axial and radial equilibrium. For the discharges discussed in Figures 13 and 14, the FRC magnetic flux, particle loading, and thermal energy (about 10 mWb and 7 × 10 , respectively) decrease. 19 particles, and 7 kJ) decreases by roughly an order of magnitude within the first millisecond as the FRC equilibrium appears to decline. Sustained operation - HPF system

[0083] The examples in Figures 12-14 are decaying FRC characteristics without any sustainment. However, several techniques can be deployed on the FRC system 10 to further improve the FRC confinement (inner core and edge layers) for HPF systems and sustain configurations. Neutral Beam

[0084] First, fast (H) neutrons are injected into the beam from eight neutral beam injectors 600, and then injected into the B z The beam of fast neutrons is injected perpendicular to the inner FRC 450. The fast ions, primarily created by charge exchange, have betatron orbits (with a primary radius much larger than the FRC topology or at least the characteristic magnetic field gradient length), which add to the azimuthal current of the FRC 450. After a certain fraction of the discharge (0.5–0.8 ms into the shot), a sufficiently large fast ion population significantly improves the stability and confinement properties of the inner FRC (see, e.g., M.W. Binderbauer and N. Rostoker, Plasma Phys. 56, part 3, 451 (1996)). Furthermore, from a sustainability perspective, the beam from the neutral beam injector 600 is also the primary means for driving the current and heating the FRC plasma.

[0085] In the plasma regime of the FRC system 10, fast ions are primarily decelerated by plasma electrons. During the early stages of the discharge, the typical orbit-averaged deceleration time of fast ions is 0.3-0.5 ms, which primarily results in significant FRC heating of electrons. Fast ions experience large radial deviations outside the separatrix due to the inherently low inner FRC magnetic field (average of approximately 0.03 T compared to an external axial field of 0.1 T). Fast ions may be susceptible to charge exchange losses if the neutral gas density is very high outside the separatrix. Therefore, wall gettering and other techniques deployed on the FRC system 10 (such as the plasma gun 350 and mirror plug 440, which contribute to gas control, among other things) tend to minimize edge neutrons and allow the desired buildup of fast ion current. Pellet injection

[0086] Once a significant fast ion population builds within the FRC 450, with higher electron temperatures and longer FRC lifetimes, frozen H or D pellets are injected into the FRC 450 from the pellet injector 700, sustaining the FRC particle load of the FRC 450. The expected ablation timescale is short enough to provide a significant FRC particle source. This rate can also be increased by increasing the surface area of ​​the injected piece by breaking individual pellets into smaller fragments while in the barrel or injector tube of the pellet injector 700 and before entering the confinement chamber 100, a step that can be achieved by increasing the friction between the pellet and the wall of the injector tube by tightening the bend radius of the final section of the injector tube just before entering the confinement chamber 100. By varying the fragmentation as well as the firing sequence and rate of the 12 barrels (injector tubes), the pellet injection system 700 can be tuned to provide just the desired level of sustained particle load. This in turn helps maintain the internal dynamic pressure in the FRC450 and its sustained operation and lifespan.

[0087] Once the ablated atoms encounter significant plasma within the FRC 450, they become fully ionized. The resulting cold plasma components are then collisionally heated by the intrinsic FRC plasma. The energy required to maintain the desired FRC temperature is ultimately provided by the beam injector 600. In this sense, the pellet injector 700, together with the neutral beam injector 600, form a system that maintains stable conditions and sustains the FRC 4504. CT injector

[0088] As an alternative to pellet injectors, compact toroid (CT) injectors are provided primarily for refueling field-reversed configuration (FRC) plasmas. The CT injector 720 comprises a magnetized coaxial plasma gun (MCPG) and includes coaxial cylindrical inner and outer electrodes 722 and 724, a bias coil positioned inside the inner electrode 726, and an electrical breaker 728 on the end of the CT injector 720 opposite the discharge, as shown in FIGS. 22A and 22B. Gas is injected through a gas injection port 730 into the space between the inner and outer electrodes 722 and 724, from which a spheromak-shaped plasma is generated by the discharge and pushed out of the gun by the Lorentz force. As shown in FIGS. 23A and 23B, a pair of CT injectors 720 are coupled to the containment vessel 100 near and on opposite sides of the vessel's midplane to inject CT into the central FRC plasma within the containment vessel 100. The discharge end of the CT injector 720 is directed toward the midplane of the containment vessel 100 at an angle to the longitudinal axis of the containment vessel 100 , similar to the Neutral Beam injector 615 .

[0089] In an alternative embodiment, the CT injector 720 includes a drift tube 740 comprising an elongated cylindrical tube coupled to the discharge end of the CT injector 720, as shown in Figures 24 and 24B. As depicted, the drift tube 740 includes drift tube coils 742 positioned about the tube and spaced axially therealong. A plurality of diagnostic ports 744 are depicted along the length of the tube.

[0090] Advantages of the CT injector 720 include (1) control and adjustability of particle loading per injected CT, (2) high-temperature plasma is deposited (instead of cryogenic pellets), (3) the system can be operated in a repetition rate mode to allow for continuous refueling, and (4) the system can also restore some magnetic flux as the injected CT carries the embedded magnetic field. In an embodiment for experimental use, the inner diameter of the outer electrode is 83.1 mm and the outer diameter of the inner electrode is 54.0 mm. The surface of the inner electrode 722 is preferably coated with tungsten to reduce impurities originating from the electrode 722. As depicted, a bias coil 726 is mounted inside the inner electrode 722.

[0091] In recent experiments, ultrasonic CT translation velocities of up to about 100 km / s have been achieved. Other typical plasma parameters are: electron density about 5 x 1,021 m- 3 , electron temperature about 30-50 eV, and particle load about 0.5-1.0 x 1,019. The high dynamic pressure of the CT allows the injected plasma to penetrate deep into the FRC and deposit particles inside the dividing line. In recent experiments, FRC particle refueling has resulted in about 10-20% of the FRC particle load being successfully delivered by the CT injector, demonstrating that refueling can be easily performed without disrupting the FRC plasma. Saddle coil

[0092] To achieve steady-state current drive and maintain the required ion current, it is desirable to prevent or significantly reduce electron spin-up due to electron-ion frictional forces (resulting from collisional ion-electron momentum transfer). The FRC system 10 utilizes an innovative technique to provide electron splitting via an externally applied stable magnetic dipole or quadrupole field. This is accomplished via an external saddle coil 460, depicted in FIG. 15. A transversely applied radial magnetic field from the saddle coil 460 induces an axial electric field within the rotating FRC plasma. The resulting axial electron current interacts with the radial magnetic field, exerting an azimuthal splitting force on the electrons.

number

[0093] The design of the pulsed coils 444 within the mirror plug 440 allows for the local generation of high magnetic fields (2-4 T) using moderate (approximately 100 kJ) volumetric energy. Due to the magnetic field formation inherent in the present operation of the FRC system 10, all field lines within the formation volume pass through the constriction 442 in the mirror plug 440, and no plasma wall contact occurs, as suggested by the magnetic field lines in FIG. 2. Furthermore, the mirror plug 440, in conjunction with the quasi-DC divertor magnets 416, can be adjusted to direct the field lines onto the divertor electrode 910 or to widen the field lines in an end-tip configuration (not shown). The latter improves stability and suppresses thermal conduction of parallel electrons.

[0094] The mirror plug 440 itself also contributes to neutral gas control. The mirror plug 440 allows for better utilization of the deuterium gas discharged into the quartz tube during FRC formation, because backflow into the divertor 300 is significantly reduced by the plug's low gas conductivity (only 500 L / s). Most of the discharged gas remaining inside the formation tube 210 is rapidly ionized. In addition, the high-density plasma flowing through the mirror plug 440 provides efficient neutral ionization and thus an effective gas barrier. As a result, most of the neutrons recycled within the divertor 300 from the FRC edge layer 456 do not return to the confinement chamber 100. Additionally, neutrons associated with the operation of the plasma gun 350 (discussed below) will be largely confined to the divertor 300.

[0095] Finally, the mirror plugs 440 tend to improve FRC edge layer confinement. With a mirror ratio (plug / confining field) in the range of 20-40 and a length of 15 m between the north and south mirror plugs 440, the edge layer particle confinement time τ ∥ increases by at most one digit. ∥ Improvements in the FRC particle containment can be easily increased.

[0096] The radial diffusion (D) particle loss from the section volume 453 is proportional to the axial loss (τ ∥ ), then (2πr s L s )(Dn s / δ)=2πr s L s δ)(n s / τ ∥ ) and from there, the segregation density gradient length is given by δ = (Dτ ∥ ) 1 / 2 where r s、 L s , and n s are the segment radius, segment length, and segment density, respectively. The FRC particle confinement time is τ N =[πr s 2 L s <n>] / [(2πr s L s )(Dn s / d)]=( <n> / n s )(τ I τ ∥ ) 1 / 2 where τ I =a 2 / D and a=r s / 4. In physics, τ ∥ The improvement in leads to an increase in δ (a decrease in the seismic density gradient and drift parameter) and therefore a reduction in FRC particle losses. The overall improvement in FRC particle confinement is s But τ ∥ Generally speaking, it is difficult to call it a quadratic equation because it increases with .

[0097] τ ∥ Significant improvement in also requires that the edge layer 456 remain extremely stable (i.e., free of n=1 flutes, firehoses, or other MHD instabilities inherent in open systems). The use of the plasma gun 350 provides this desirable edge stability. In this sense, the mirror plug 440 and plasma gun 350 form an effective edge control system. Plasma gun

[0098] The plasma gun 350 improves the stability of the FRC exhaust jet 454 through line coupling. The gun plasma from the plasma gun 350 is generated without azimuthal angular momentum, which proves useful for controlling FRC rotational instabilities. Thus, the gun 350 is an effective means of controlling FRC stability without requiring older quadrupole stabilization techniques. As a result, the plasma gun 350 makes it possible to exploit the beneficial effects of fast particles or, as outlined in this disclosure, access highly hybrid motion FRC regimes. Thus, the plasma gun 350 allows the system 10 to be operated with a saddle coil current that is just sufficient for electron splitting but below the threshold that would cause FRC instability and / or lead to dramatic fast particle diffusion.

[0099] As mentioned in the discussion of mirror plugs above, τ ∥ If it can be significantly improved, the supplied gun plasma will be comparable to the edge layer particle loss rate (about 10 22 / s). The lifetime of the gun-produced plasma in the FRC system 10 is within the range of milliseconds. In fact, consider a gun plasma with a density of about 10 e about 10 13 cm 3 confined between the end mirrors plugs 440 and an ion temperature of about 200 eV. The capture length L and the mirror ratio R are about 15 m and 20, respectively. The mean free path of the ions due to Coulomb collisions is λ ii about 6×10 3 cm, and since λ ii lnR / R < L, the ions are confined in a gas dynamic system. The plasma confinement time in this system is τ gd ~RL / 2V s ~2 ms, where V s is the ion sound speed. For comparison, the classical ion confinement time for these plasma parameters is τ c ~0.5τ ii (lnR+(lnR) 0.5 )~0.7 ms. Anomalous cross-field diffusion can, in principle, shorten the plasma confinement time. However, in the FRC system 10, assuming a Bohm diffusion rate, the estimated cross-field confinement time for the gun plasma is τ ^ >τ g about 2 ms. Thus, the gun will provide significant replenishment of the FRC edge layer 456 and improvement of the overall FRC particle confinement.

[0100] Furthermore, the gun plasma flow can be turned on within approximately 150-200 milliseconds, allowing its use in initiating, translating, and fusing FRCs into the confinement chamber 100. When turned on at approximately t~0 (FRC main bank initiation), the gun plasma helps sustain the dynamically forming and fusing FRCs 450. The combined particle load from the forming FRC and from the gun is sufficient for neutral beam trapping, plasma heating, and long-term persistence. When turned on in the range of t -1 to 0 ms, the gun plasma can fill the quartz tube 210 with plasma or ionize gases exhaled into the quartz tube, thus enabling FRC formation with reduced or perhaps even zero exhaled gas. The latter may require a sufficiently cool forming plasma to allow for fast diffusion of the reverse bias field. When turned on at t < -2 ms, the plasma flow is sufficient to allow neutral beam formation several tens of meters prior to FRC arrival. 13 cm 3 1-3 m of the formation and confinement region of the formation section 200 and confinement chamber 100, with a target plasma density of 3 The plasma gun 350 may be capable of filling a field volume of 1000 . The formed FRC may then be formed and translated into the resulting containment vessel plasma. In this manner, the plasma gun 350 allows for a wide variety of operating conditions and parameter regimes. Electrical Bias

[0101] Controlling the radial electric field profile within the edge layer 456 is beneficial to FRC stability and confinement in various ways. The innovative biasing components deployed in the FRC system 10 allow for the application of various deliberate distributions of electric potential to open magnetic flux planes throughout the machine from areas well outside the central confinement region within the confinement chamber 100. In this way, radial electric fields can be generated across the edge layer 456 just outside the FRC 450. These radial electric fields then modify the azimuthal rotation of the edge layer 456 and affect its confinement via E×B velocity shear. Any differential rotation between the edge layer 456 and the FRC core 453 can then be conducted to the interior of the FRC plasma by shear. As a result, controlling the edge layer 456 directly affects the FRC core 453. Furthermore, because free energy within the plasma rotation can also contribute to instabilities, this technique provides a direct means for controlling instability initiation and growth. In FRC system 10, appropriate edge biasing provides effective control of FRC core rotation as well as translation and rotation of open field lines. The locations and shapes of the various provided electrodes 900, 905, 910, and 920 allow control of different groups of magnetic flux surfaces 455 and at different and independent potentials. In this manner, a wide array of different electric field configurations and strengths are achieved, each of which can have different characteristic effects on plasma performance.

[0102] A key advantage of all these innovative biasing techniques is the fact that the behavior of the core and edge plasmas can be influenced from well outside the FRC plasma, i.e., without the need to bring any physical components into contact with the central hot plasma (which would have important implications for energy, magnetic flux, and particle losses). This has major beneficial impacts on the performance and all potential applications of the HPF concept. Experimental data - HPF operation

[0103] The injection of fast particles via the beam from the Neutral Beam Gun 600 plays a key role in enabling the HPF regime. Figures 16A, 16B, 16C, and 16D illustrate this fact. Depicted is a set of curves showing the correlation between FRC lifetime and beam pulse length. All other operating conditions were held constant for all discharges comprising this study. This data was averaged over many shots and therefore represents typical behavior. It is clearly evident that longer beam durations produce longer-lived FRCs. Based on this evidence as well as other diagnostics in this study, it is demonstrated that beam stability increases and losses decrease. The correlation between beam pulse length and FRC lifetime is not perfect because beam trapping becomes inefficient below a certain plasma size; that is, as the FRC 450 shrinks in physical size, not all of the injected beam is intercepted and trapped. The shrinkage of the FRC is primarily due to the fact that the net energy loss from the FRC plasma during the discharge (about 4 MW approximately midway through the discharge) is somewhat greater than the total power delivered into the FRC via the neutral beam (about 2.5 MW) for the particular experimental setup. Locating the beam closer to the midplane of vessel 100 would tend to reduce these losses and extend the FRC lifetime.

[0104] Figures 17A, 17B, 17C, and 17D illustrate the effect of different components to achieve the HPF regime. This shows a typical system of curves depicting the lifetime of the FRC 450 as a function of time. In all cases, a constant and moderate amount of beam power (approximately 2.5 MW) is injected throughout the duration of each discharge. Each curve is representative of a different combination of each component. For example, operating the FRC system 10 without any mirror plug 440, plasma gun 350, or gettering from the gettering system 800 results in the rapid onset of rotational instability and loss of the FRC topology. Adding the mirror plug 440 alone delays the onset of the instability and increases confinement. Utilizing the mirror plug 440 and plasma gun 350 in combination further reduces instability and increases the lifetime of the FRC. Finally, adding gettering (Ti in this case) to the top of the gun 350 and plug 440 produces the best results, with the resulting FRC being free of instabilities and exhibiting the longest lifetime. It is clear from this experimental demonstration that the perfect combination of each component produces the best effect and produces a beam with the best target conditions.

[0105] As shown in Figure 1, the newly discovered HPF regime exhibits significantly improved transport behavior. Figure 1 illustrates the change in particle confinement time in FRC system 10 between the conventional regime and the HPF regime. As shown, the HPF regime provides an improvement of well over five times. In addition, Figure 1 details the particle confinement time in FRC system 10 compared to that in prior conventional FRC experiments. Relative to these other machines, the HPF regime of FRC system 10 improves confinement by a factor of 5 to approximately 20. Finally, and most importantly, the nature of the confinement scaling in FRC system 10 is significantly different from all previous measurements. Prior to the establishment of the HPF regime in FRC system 10, various empirical scaling laws were derived from data in prior FRC experiments to predict confinement time. All of these scaling laws primarily depended on the ratio R 2 / ρ i where R is the radius of the magnetic field null (a rough measure of the physical scale of the machine) and ρ i is the ion Larmor radius (a rough measure of the applied magnetic field) evaluated in an externally applied field. It is clear from Figure 1 that long-term confinement in a conventional FRC is only possible with large machine sizes and / or high magnetic fields. The operation of the FRC system 10 in the conventional FRC regime CR tends to follow those scaling laws, as shown in Figure 1. However, the HPF regime is significantly superior, demonstrating that significantly better confinement can be obtained without large machine sizes or high magnetic fields. More importantly, it is also clear from Figure 1 that, compared to the CR regime, the HPF regime results in improved confinement times while reducing the plasma size. Similar trends are also evident for the flux and energy confinement times, as explained below, which also increase by more than three to eight times in the FRC system 10. The breakthrough in the HPF regime therefore enables the use of moderate beam powers, lower magnetic fields, and smaller sizes to sustain and maintain FRC equilibrium in the FRC system 10 and future high-energy machines. These improvements combined result in lower operating and construction costs as well as reduced engineering complexity.

[0106] For further comparison, FIGS. 18A, 18B, 18C, and 18D show data from a representative HPF system discharge in FRC system 10 as a function of time. FIG. 18A depicts the excluded magnetic flux radius at the midplane. For these longer timescales, the conductive iron wall is no longer a good flux conserver, and to properly account for flux diffusion through the iron, the magnetic probes inside the wall are increased along with the probes outside the wall. Compared to typical performance in conventional system CR, the HPF system operating mode exhibits over 400% longer lifetimes, as shown in FIGS. 13A, 13B, 13C, and 13D.

[0107] A representative code for the line-integrated density trace, along with its Abelian transform complement, is shown in FIG. 18B, and the density contours are shown in FIG. 18C. Compared to the conventional FRC system CR, the plasma is more quiescent throughout the pulse, demonstrating very stable operation, as shown in FIGS. 13A, 13B, 13C, and 13D. The peak density is also slightly lower in the HPF shot, which is a consequence of the higher total plasma temperature (up to two times), as shown in FIG. 18D.

[0108] For the individual discharges illustrated in Figures 18A, 18B, 18C, and 18D, the energy, particle, and magnetic flux confinement times are 0.5 ms, 1 ms, and 1 ms, respectively. At a nominal time of 1 ms into the discharge, the plasma energy stored is 2 kJ, but the losses are about 4 MW, making this target highly suitable for neutral beam sustainment.

[0109] Figure 19 summarizes the full benefits of the HPF scheme in the form of newly established experimental HPF flux confinement scaling. As can be seen from Figure 19, around t = 0.5 ms, i.e., t < Based on measurements taken at t > 0.5 ms and t > 0.5 ms, the flux confinement (and similarly particle confinement and energy confinement) is s ) versus electron temperature (T e ) varies approximately as the square of T e This strong scaling, with a positive exponent (but not a negative one) in , is completely opposite to that exhibited by conventional tokamaks, where confinement is typically inversely proportional to some exponent of the electron temperature. The appearance of this scaling is a direct consequence of the HPF regime and large-orbit (i.e., orbits on the scale of the FRC topology and / or at least the characteristic magnetic field gradient length scale) ion population. Essentially, this new scaling substantially favors high operating temperatures, enabling reactors of relatively moderate size.

[0110] The advantages offered by the HPF system mean that neutral beam-driven FRC sustainment, or steady state, is achievable, meaning that global plasma parameters such as plasma thermal energy, total particle number, plasma radius and length, as well as magnetic flux, can be sustained at reasonable levels without substantial decay. For comparison, Figure 20 shows data from a representative HPF system discharge in FRC system 10 as a function of time in plot A, and projected data from a representative HPF system discharge in FRC system 10 as a function of time in plot B, where the FRC 450 is sustained without decay throughout the duration of the neutral beam pulse. For plot A, a neutral beam with a total power in the range of approximately 2.5 to 2.9 MW was injected into the FRC 450 for an active beam pulse length of approximately 6 ms. The plasma diamagnetic lifetime depicted in plot A was approximately 5.2 ms. More recent data indicates that a plasma diamagnetic lifetime of approximately 7.2 ms is achievable using an active beam pulse length of approximately 7 ms.

[0111] As discussed above with respect to Figures 16A, 16B, 16C, and 16D, the correlation between beam pulse length and FRC lifetime is not perfect because beam trapping becomes inefficient below a certain plasma size, i.e., not all injected beam is intercepted and trapped as the physical size of the FRC 450 shrinks. FRC shrinkage or decay is primarily due to the fact that the net energy loss from the FRC plasma during the discharge (approximately 4 MW at approximately the middle of the discharge) is somewhat greater than the total power delivered into the FRC via the neutral beam (approximately 2.5 MW) for the particular experimental setup. As described with respect to Figure 3C, beam injection angled from the neutral beam gun 600 toward the midplane improves beam-plasma coupling even as the FRC plasma shrinks or otherwise contracts axially during the injection period. In addition, proper pellet refueling will maintain the required plasma density.

[0112] Plot B shows the results of a simulation performed using an active beam pulse length of approximately 6 ms and a total beam power from the neutral beam gun 600 slightly above approximately 10 MW. The neutral beams are assumed to inject H (or D) neutrons with particle energies of approximately 15 keV. The equivalent current injected by each beam is approximately 110 A. For plot B, the beam injection angle relative to the device axis was approximately 20°, and the target radius was 0.19 m. The injection angle can be varied within the range 15° to 25°. The beams are assumed to be injected azimuthally cocurrently. The net axial force, as well as the net lateral force from the neutral beam momentum injection, is assumed to be minimized. Similar to plot A, fast (H) neutrons are injected from the neutral beam injector 600 into one FRC 450 from the moment the north and south forming FRCs fuse within the confinement chamber 100.

[0113] The underlying simulations for plot B use a coupled set of transport equations for all plasma species to model two-way loss processes, as well as a multidimensional Hall MHD solver for the background plasma and equilibrium and a full-kinetic Monte Carlo-based solver for the energetic beam components and all scattering processes. The transport components are experimentally calibrated and extensively benchmarked against experimental databases.

[0114] As shown by plot B, the steady-state diamagnetic lifetime of FRC450 will be the beam pulse length. However, it is important to note that the key correlation plot B shows that the plasma or FRC begins to decay at the time the beam is turned off, not before. The decay will be similar to that observed during the discharge, which is not beam-assisted (probably about 1 ms beyond the beam-off time), and is simply a reflection of the characteristic decay time of the plasma, which is driven by intrinsic loss processes.

[0115] Turning to Figures 21A, 21B, 21C, 21D, and 21E, the experimental results illustrated in the figures demonstrate the achievement of FRC persistence or steady state driven by the angled neutral beam. That is, global plasma parameters such as plasma radius, plasma density, plasma temperature, as well as magnetic flux, are sustained at a constant level without decay relative to the NB pulse duration. For example, such plasma parameters remain essentially constant for approximately 5+ ms. Such plasma performance, including persistence characteristics, has a strongly correlated NB pulse duration, and diamagnetism remains even several milliseconds after NB termination due to accumulated fast ions. As illustrated, plasma performance is limited only by pulse length constraints arising from finite stored energy in the associated power supplies of not only the NB injector but also many other critical system components. Neutral beam adjustable beam energy

[0116] 3A, 3B, 3C, 3D, 3E, and 8, a neutral atomic beam 600 is deployed on the FRC system 10 to generate high-velocity particle pressure as well as provide heating and current drive. The individual beam lines comprising the neutral atomic beam injector system 600 are positioned around the periphery of the central confinement chamber 100 and are preferably angled to inject neutral particles toward the midplane of the confinement chamber 100, as shown in FIGS. 3C, 3D, and 3E.

[0117] To further improve FRC persistence and demonstrate FRC ramp-up to high plasma temperatures and increased system energies, the present FRC system 10 includes a neutral beam injector (NBI) system 600 with increased power and extended pulse lengths, e.g., for illustrative purposes only, up to 30 ms pulse lengths, of approximately 20+ MW power with multiple positive ion-based injectors 615 (see FIGS. 3D and 3E ) and features a flexible, modular design, with a subset of the NBI injectors 615, e.g., four of the eight NBI injectors 615, having the capability to adjust the beam energy from an initial lower beam energy to an increased beam energy, e.g., from approximately 15 keV to approximately 40 keV, at a constant beam current during a shot. This capability of the NBI injectors 615 is desirable for achieving more efficient heating and resulting pressurization of the plasma core 450. In particular, this capability enables highly desirable performance improvements at peak energy operating levels compared to lower energy levels. For example, (i) up to two times the heating power, (ii) approximately one-fifth reduction in charge exchange losses, and (iii) up to two times the heating efficiency. Additionally, the continuously variable beam energy producible by the NBI injector 615 allows optimal matching of the trajectory parameters of the injected and then trapped fast ions to the instantaneous magnetic pressure profile during the ramp-up process. Finally, the fast ramp-up rate, allowing ramp-up durations of 0.1 to 10 ms, along with the fast (approximately 1 ms or less) adjustment capability of the beam energy and power of the NBI injector 615, provides an additional effective "control knob," i.e., a controllable feature for plasma shaping and active feedback control of the plasma via modulation of the beam energy and power.

[0118] Sufficient heating power is required to enable heating and pressurization of the FRC 450, both sustained and ramping up to high plasma temperatures and elevated system energy. Assuming a sufficiently low loss rate, the rate of ramp-up is primarily a function of the amount of power that can be deposited into the FRC core 450 by the NBI injector 615 at any given time. A higher primary neutral beam power through the injection port is therefore always desirable.

[0119] Furthermore, the effective heating rate resulting from the NBI injector 615 is a complex interplay between the injected beam properties and the current, sustained, instantaneous profile of the magnetic field across the FRC core 450, as well as the temperature, electron and ion densities, and neutral concentrations of all species. Of these, the magnetic field profile is carefully varied on sub-millisecond timescales by the control system during ramp-up, while the dynamic pressure-related profile evolves through turbulence in the energy as well as inherent variations derived from self-organization processes and the plasma deposited by the injection process. The beam's tunability provides a means to most optimally adapt to these fluctuating conditions.

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

[0121] Another example of a profile effect on overall heating efficiency concerns where power is deposited. Higher beam energy will typically lead to relatively higher energy deposition at the FRC periphery compared to the core. Raising the magnetic field but keeping the beam energy the same will result in tighter trapped ion trajectories and correspondingly higher power coupling to the FRC core plasma. These facts, in turn, significantly affect energy retention as well; for example, energy deposited at the periphery is much more easily transported out of the system along the open field line structure, while energy deposited in the core is lost relatively more slowly due to lower cross-field transport times. Therefore, close coordination of magnetic field ramp-up and appropriate increases in beam energy is desirable.

[0122] The beam system 600 is designed for fast voltage ramps in the range of 0.1 to 10 ms. This provides the potential to increase ion and electron temperatures by a factor of 2 and 10, respectively, on timescales shorter than typical macroscopic instability growth times. Thus, plasma stability is fundamentally increased, as are operational reliability and repeatability.

[0123] A variable voltage rise time of 0.05 to 1 ms provides a sufficiently rapid response time so that the beam can be utilized as part of an active feedback system. In this way, beam modulation can be used to control macro- and microstability. For example, temporarily shifting the radial power deposition profile by varying the beam energy (and thereby shifting the radial energy deposition pattern) can affect pressure gradients, which can oppose the generation of unstable plasma modes. The FRC system 10 shown in Figures 3D and 3E utilizes this capability in conjunction with fast magnetic feedback to control internal tilt, rotation rate, drift wave generation, and other operating scenarios.

[0124] 25 depicts an illustration of an NBI injector 615 of the present FRC system 10. The NBI injector 615, in the exemplary embodiment, is shown to include an arc driver 650, a plasma box 651, an ion optics system 652 comprising extraction and acceleration grid triodes or tetrodes, an aiming gimbal 653, an arc evaporator 655, such as a Ti arc evaporator, a cryogenic pump 656 having a surface structure, such as a ribbed surface structure, configured for increased cryogenic pumping, and a neutralizer 654 comprising a deflection magnet 656 for removing non-neutralized ions, and a collimating aperture 658 including an insertable calorimeter 659 for intermittent beam characterization, diagnostics, and recalibration.

[0125] More specifically, referring to FIG. 26, the implementation of the adjustable beam system is preferably based on a triode type ion optical system (=IOS) 660, as shown. This concept is an acceleration - deceleration scheme. As illustrated in FIG. 26, the first grid G1 is set to voltage V1, while the second grid G2 is set to voltage V2, and the final grid G3 is set to voltage V3. The extracted ions are first accelerated to energy E1 = e×(V1 - V2) while traversing the gap between G1 and G2 (where e here refers to the charge of the ion). They are then decelerated in the gap between G2 and G3 such that E2 = E1+e×(V2 - V3). The voltages are typically adjusted such that V1 > V2 < V3. Based on appropriate individual power supplies PS1, PS2, PS3, the grid voltages can be gradually adjusted during the pulse to vary the output of the emitted ions 662. For example, to initiate a beam pulse of hydrogen atoms, the operating voltages may be adjusted to V1 = 15 kV, V2 = - 25 kV, and V3 = 0 V. The initial beam ions are first accelerated to 40 keV and then will emerge from the IOS with an energy of 15 keV. In the second half of the pulse, the power supplies can be switched to provide V1 = 40 kV, V2 = - 1 kV, V3 = 0 V. The beam deceleration in the second gap will then be virtually absent, resulting in an output beam energy of approximately 40 keV. Each of the power supplies is individually controllable and provides appropriate voltage modulation. The initial beam ions are extracted from the scale of a standard arc or RF - based plasma source PS. After emerging from the IOS 660, the beam ions 662 cross a neutralizer 664, and the fast ions are converted to neutral ions via charge exchange with electrons detached from the cold neutral gas present within the neutralizer 664. Appropriate cryogenic pumping prevents the neutral gas from leaking out of the downstream orifice of the neutralizer 664. At the end of the neutralizer, there is also an appropriate bending magnet 666 that provides for the removal of non - neutralized fast ions 663, and an ion dump 668 associated with absorbing the fast ions and their energy.The emerging atomic beam 670 is then passed through a suitable aperture 6720 to reduce the beam divergence and provide a well-collimated stream of neutral atoms towards the core of the reactor.

[0126] In an alternative version, the IOS is based on a tetrode design. In this case, the IOS consists of four grids with the same acceleration-deceleration principle as described for the triode case. Those skilled in the art will readily recognize the similarities between the system components and operating principles. The introduction of the fourth grid provides further fine-tuning possibilities and overall more operating flexibility.

[0127] The exemplary embodiments provided herein are described in US Provisional Patent Application No. 62 / 414,574, which is incorporated herein by reference. Plasma stability and axial position control

[0128] Conventional solutions to FRC instabilities typically provide axial stability at the expense of radial instability, or radial stability at the expense of axial instability, but not both. Primarily, the plasma position is stable laterally or radially, with the desired property of being axisymmetric at the expense of axial instability. In view of the foregoing, embodiments provided herein are directed to systems and methods that facilitate FRC plasma stability in both the radial and axial directions, as well as axial position control of the FRC plasma along the axis of symmetry of the FRC plasma confinement chamber, independent of the axial stability properties of the FRC plasma equilibrium. However, the axial position instability is actively controlled using a set of external axisymmetric coils that control the FRC plasma axial position. The present systems and methods provide feedback control of the FRC plasma axial position, independent of the stability properties of the plasma equilibrium, by using nonlinear control techniques that affect the voltage applied to a set of external coils concentric with the plasma.

[0129] The embodiments presented herein stabilize or control axial instability while exploiting the axially unstable balance of the FRC to enhance radial stability. In this way, both axial and radial stability are obtained. The control method is designed to modify the external or equilibrium magnetic field to radially or laterally stabilize the FRC plasma at the expense of axial instability, and then act on the radial field coil current to instantly restore the position of the FRC plasma toward the midplane of the confinement chamber while minimizing overshoot and / or oscillations around the midplane. An advantage of this solution is that it reduces the complexity of the actuators required for control. Compared to conventional solutions with multiple degrees of freedom, the method of the embodiments presented herein reduces the complexity of the control problem along the FRC plasma rotation axis, which has one degree of freedom.

[0130] The combination of coil current waveform, fueling, and neutral beam power generated in an axially unstable plasma defines a plasma control scenario that places the plasma in an axially unstable regime. This scenario can be preprogrammed using prior knowledge from simulation or experiment, or controlled feedback to maintain axially unstable equilibrium. The plasma position should be controlled independently of the stability properties of the equilibrium during discharge; for example, the control scheme should function to its limits for either an axially stable or axially unstable plasma. The most axially unstable plasma that can be controlled has a growth time comparable to the vessel skin time.

[0131] Turning now to systems and methods that facilitate both radial and axial FRC plasma stability and axial position control of the FRC plasma along the axis of symmetry of the FRC plasma confinement chamber, FIG. 27 shows a simplified schematic illustrating an exemplary embodiment of an axial position control mechanism 510. A rotating FRC plasma 520, shown within the confinement chamber 100, has a plasma current 522 and an axial displacement direction 524. A balance field (not shown) is produced within the chamber 100 by symmetric current components, such as, for example, quasi-DC coils 412 (see FIGS. 2, 3A, 3D, and 3E). The balance field produces no net force in the axial displacement direction 524, but can be adjusted to produce a stable plasma in either the transverse / radial or axial direction. For purposes of the embodiments presented herein, the balance field is adjusted to produce a transverse / radial stable FRC plasma 520. As previously mentioned, this results in axial instability and, therefore, axial displacement of the FRC plasma 520 in the axial displacement direction 524. As the FRC plasma 520 moves axially, it induces currents 514 and 516 that are antisymmetric, i.e., in opposite directions, in the walls of the confinement chamber 100 on either side of the midplane of the confinement chamber 100. The FRC plasma 520 will induce these types of current components both within the vessel and also in the external coil. These antisymmetric current components 514 and 516 produce radial fields that interact with the toroidal plasma current 522 and produce forces that oppose the movement of the FRC plasma 520, the result of which is to slow down the plasma axial displacement. These currents 514 and 516 gradually dissipate over time due to the resistivity of the confinement chamber 100.

[0132] Radial field coils 530 and 531, positioned about containment chamber 100 on either side of the mid-plane, provide additional radial field components due to currents 532 and 534 induced in opposite directions in coils 530 and 531. Radial field coils 530 and 531 may comprise an axially symmetric set of coils that may be positioned inside or outside of containing vessel 100. Radial coils 530 and 531 are shown positioned outside containing vessel 100, similar to quasi-DC coils 412 (see FIGS. 2, 3A, 3D, and 3E). Each coil or set of coils 530 and 531 may carry a different current than the coils on the opposite side of the mid-plane, but the current is antisymmetric with respect to the mid-plane of containing vessel 100, such that along the mid-plane, B z ≠0, B r = 0. Radial field coils 530 and 531 generate complementary radial field components that interact with toroidal plasma current 522 and produce an axial force that, in turn, pushes the plasma backward toward the midplane of confinement chamber 100.

[0133] The control mechanism 510 includes a control system configured to act on the radial field coil currents to instantly restore the plasma position toward the machine midplane while minimizing overshoot and / or oscillations around the midplane. The control system includes a processor operably coupled to the radial field coils 530 and 531, the quasi-DC coil 412, its respective power supplies, and other components, such as magnetic sensors, to provide plasma position, plasma velocity, and active coil current measurements. The processor may be configured to perform the calculations and analyses described herein and may include or be communicatively coupled to one or more memories, including non-transitory computer-readable media. This may include processor- or microprocessor-based systems, including systems using microcontrollers, reduced instruction set computers (RISC), application-specific integrated circuits (ASICs), logic circuits, and any other circuits or processors capable of performing the functions described herein. The above is merely exemplary and thus is not intended to limit in any way the definition and / or meaning of the terms “processor” or “computer.”

[0134] The functions of the processor may be implemented using either software routines, hardware components, or a combination thereof. The hardware components may be implemented using a variety of technologies, including, for example, integrated circuits or discrete electronic components. The processor unit typically includes readable / writable memory storage devices and also typically includes hardware and / or software for writing to and / or reading the memory storage devices.

[0135] The processor may include a computing device, an input device, a display unit, and an interface, for example, for accessing the Internet. The computer or processor may include a microprocessor. The microprocessor may be connected to a communication bus. The computer or processor may also include memory. The memory may include random access memory (RAM) and read-only memory (ROM). The computer or processor may also include a storage device, which may be a hard disk drive or a removable storage drive, such as a floppy disk drive, an optical disk drive, and the like. The storage device may also be other similar means for loading computer programs or other instructions into the computer or processor.

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

[0137] The problem of controlling the position of an axially stable or unstable FRC configuration using a radial field coil actuator is solved using a branch of nonlinear control theory known as sliding mode control. A linear function of the system state (sliding surface) acts as the error signal, with the desired asymptotically stable (sliding) behavior. The sliding surface is designed using Lyapunov theory to exhibit asymptotic stability within a wide range of FRC dynamic parameters. The proposed control scheme can then be used for both axially stable and unstable plasmas without the need to retune the parameters used in the sliding surface. This property is advantageous because, as mentioned above, the equilibrium may need to transition between axially stable and axially unstable equilibrium at different phases of the FRC discharge.

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

[0139] Coil current and plasma position are required to implement position control. Plasma velocity is required to improve performance, but is optional. A nonlinear function of this error signal (relay control law) generates discrete voltage levels for each pair of power supplies connected to the mid-plane symmetric coils. The mid-plane symmetric coils are fed relay voltages of equal magnitude but opposite sign. This creates a radial field component that restores the plasma position towards the mid-plane.

[0140] To demonstrate the feasibility of the control scheme, a precise plasma model is used to simulate the plasma dynamics. The model utilizes the magnet geometry. The plasma current distribution corresponds to an axially unstable equilibrium with a growth time of 2 ms when only the plasma and vessel are considered. The power supply is assumed to operate using discrete voltage levels, typically 800 V steps.

[0141] Figure 29 shows several plasma control simulations highlighting the relationship between the voltage applied to the coils and the plasma position settling time, along with the coil peak current and ramp rate required to return the plasma, displaced axially by 20 cm, to the mid-plane. These sliding-mode axial position control simulation examples are run at 0.3 T using four pairs of outer trim coils. The four examples are shown corresponding to power supplies with discrete voltage levels of 200 V (black squares), 400 V (black circles), 800 V (black triangles), and 1600 V (white squares). For all four examples, the control bandwidth is 16 kHz and the sampling frequency is 32 kHz. The plasma position (top), current in the outermost coil pair (center), and coil current ramp rate (bottom) are shown. The plasma displacement is allowed to become unstable until it reaches 20 cm. At this point, feedback control is applied.

[0142] Simulation results show the following: 1. A coil ramp-up rate of 0.5 MA / sec is sufficient to return the plasma to the mid-plane within 5 ms (black square trace), requiring a 200V power supply. 2. A coil ramp-up rate of 1 MA / sec is sufficient to return the plasma to the mid-plane within 2.3 ms (black circular trace), requiring a 400V power supply. 3. A coil ramp-up rate of 2 MA / sec is sufficient to return the plasma to the mid-plane within 1.3 ms (black triangle trace), requiring an 800 V power supply. 4. To return the plasma to the mid-plane within 1.0 ms (white square trace), a coil ramp-up rate of 4 MA / sec is sufficient, requiring a 1600 V power supply.

[0143] The peak currents for all trim coils as a function of trim coil position for the third case studied above (2 MA / s ramp rate) are also shown in Figure 30. A sliding mode axial position control simulation example is started at 0.3 T using four pairs of external trim coils using a power supply with three levels (+800 V, 0, -800 V), a control bandwidth of 16 kHz, and a sampling rate of 32 kHz. A coil ramp-up rate of 2 MA / s is required to return the plasma to the midplane within 1.3 ms. The peak currents required in all coil pairs are less than 1.5 kA. The actual switching frequency required (approximately 2 kHz) is well below the control system bandwidth.

[0144] The control system can also be implemented with a target surface that is a function of coil current and plasma velocity only, without plasma position. In this case, the axial position control loop provides only stabilization of the axial dynamics, rather than control. This means that the plasma can drift slowly along its axis in a metastable state. Position control is then provided using an additional feedback loop that controls the plasma gap between the plasma section and the vessel, thus simultaneously performing plasma shape and position control.

[0145] Another plasma confinement device in which a similar control system is used is the tokamak. To maintain plasma confinement, the plasma current in a tokamak must be kept between lower and upper limits, which are approximately proportional to the plasma density and the toroidal field, respectively. To operate at high plasma densities, the plasma current must be increased. At the same time, the poloidal field must be kept as low as possible, thus ensuring a safety factor q greater than q = 2. This is achieved by elongating the plasma along the mechanical axis, allowing for large plasma currents (and thus high plasma densities) without increasing the boundary magnetic field above its safety limit. These elongated plasmas are unstable along the mechanical axis (known as the vertical direction in tokamak terminology) and also require a plasma stabilization mechanism. Vertical plasma position control in a tokamak is also restored using a set of radial field coils and is therefore very similar to the RFC position control problem. However, the reasons for requiring stabilization in tokamaks and FRCs are different. In tokamaks, plasma vertical instability is a cost imposed for operating at high plasma currents, requiring plasma stretching to operate with high toroidal fields. In FRCs, plasma instability is a cost imposed for obtaining transverse stability. Tokamaks have a toroidal field stabilizing configuration, and therefore they do not require transverse stabilization.

[0146] The present disclosure is directed to facilitating the generation and maintenance of high-flux target FRC plasmas and the axial refueling of FRC plasmas. In an exemplary embodiment, the process involves the formation of a high-flux FRC (up to 30 mWb) by fusing two spheromaks with opposing helicities. Fusion experiments have been performed on various devices to study magnetic reconnection by fusing two spheromak-type plasma toroids together through contact and reconnection along a toroidally symmetric line. A spheromak is a spherically or toroidally shaped plasma in which a force-free current (j × B = 0) arranges an equilibrium configuration depending on the presence of a current (flux) hole in the major axis. Two toroidal spheromaks carrying equivalent toroidal currents in the same or opposing toroidal fields are forced to fuse by controlled external coil currents; these are referred to as cohelicity or counterhelicity fusion, respectively. As explained in Yamada, M., et al., Phys. Rev. Lett. 65, 721 (1990), antihelicity fusion generates antiparallel magnetic field lines at the reconnection site, and magnetic reconnection is expected to occur very efficiently (Bhattacharjee, A., Phys. Fluids 26, 3332 (1983)). Experimental results also show that antihelicity fusion indeed reconnects comprehensively much faster than cohelicity fusion, and then forms a high-flux FRC structure (consisting of only poloidal fields) after canceling the counterdirectional toroidal fields of the spheromaks caused by the fusion.

[0147] In an exemplary embodiment, the process includes the following steps: 1. Large flux target FRC plasma (Φ) via reverse helicity spheromak fusion using MCPG D It generates approximately 25-30mWb. 2. Amplify, stabilize, and power-enhance the FRC plasma toward fusion plasma conditions by forming a target plasma with sufficient magnetic flux and injecting a high-energy neutral beam, thus further converting the beam energy into thermal energy. 3. To achieve a high flux and dense FRC system as well as to maintain and improve the FRC plasma confinement properties, additional multi-pulse spheromaks are formed and injected into the FRC plasma for particle replenishment and reflux.

[0148] 31A and 31B, an exemplary embodiment of an FRC confinement system is depicted as having a confinement chamber 100 and a pair of divertors 302 coupled to the confinement chamber 100 on opposite ends. To generate an optimal initial high-flux target FRC plasma 453, a pair of medium-sized spheromak injectors 250 (or magnetized coaxial plasma guns (MCPGs)) are coupled to opposite ends of the centrally located plasma confinement chamber 100. The spheromak injectors 250 inject high-flux (less than 20 mWb) spheromak plasma toward the midplane of the confinement chamber 100, where the spheromak fuses and forms an FRC plasma within the confinement chamber 100. The counter-helicity fusion of the two spheromaks generates a large-flux target FRC plasma (Φ ) with rising and trapped magnetic flux. D They tend to generate multiple The Neutral Beam Injector 615 is also coupled to the confinement chamber 100 at an angle toward the midplane of the confinement chamber 100 to drive and maintain the FRC plasma 453. In an exemplary embodiment, the Neutral Beam Injector 615 is adjustable from an initial power level to an increased power level. In a further exemplary embodiment, the Spheromak injector 250 is capable of injecting multi-pulsed Spheromak into the FRC plasma along the geometric axis of the confinement chamber for effective replenishment and reflux.

[0149] Previous spheromak fusion studies (see Figures 32A-32D) demonstrated the feasibility and potential for compact toroid fusion plasmas. In a series of MRX experiments at the Princeton Plasma Physics Laboratory from 2004 to 2008, reverse helicity fusion was applied to study the formation, stability, and persistence of oblate FRCs. It was demonstrated that a central ohmic heating solenoid, as used in tokamaks, can be used to amplify the toroidal current in the FRC to sustain it for times longer than the resistive decay time (Gerhardt, SP, et al., Phys. Plasmas 15, 032503 (2008)). In addition, field-shaping coils were used to control the FRC boundary shaping and elongation. This allowed for the study of the effects of these field shaping factors on stability. It has been experimentally demonstrated that tilting modes with n=1 (where n is the toroidal mode number) can be stabilized in an oblate FRC (Gerhardt, SP, et al., Phys. Rev. Lett. 99, 245003 (2007)). Also, growth rate modes with n≧2 were slowed down with favorable geometry. These results have provided a significant advance in the understanding of open-boundary FRC physics. In addition to these stability and persistence results, significant ion heating was observed in reverse helicity fusion experiments. Co-helicity fusion of two spheromaks produced a sufficiently high beta spheromak plasma (β ≈0.2-0.3) with less heating. A non-negligible ion temperature (T i >25 eV, T≒10 eV, n e >10 14 cm 3 ) the ability to produce fused plasmas allows for the study of high-beta plasma stability properties in variable toroidal magnetic field components.

[0150] In the exemplary embodiment, the Spheromac injector 250 is a relatively compact Spheromac injector having an outer electrode 254, a W-coated inner electrode 255, an outer bias coil 252 positioned around the outer electrode 254, an iron-core bias coil 253 positioned within the inner electrode 255, a gas discharge 256, and an HV power supply 258, as depicted in Figure 33. The Spheromac injector 250 produces sufficient magnetic flux by utilizing and improving a recently developed iron-core bias coil system 253 (see Edo, T., et al., Jrnl of Plasma and Fusion Res. 13, 3405062 (2018)). Recent preliminary tests have shown that an air-core bias coil with a DC power supply produces a magnetic flux in the formed Spheromak that scales with approximately 1.67 μWb / Amp, while an MCPG with an iron-core (cast iron has a magnetic permeability of approximately μ250) bias coil system can produce approximately 100 times higher magnetic flux per ampere (i.e., approximately 0.16 mWb / Amp). By holding the current density constant, the Spheromak injector can be sufficiently scaled up in size to generate much higher magnetic flux (less than 30 mWb) without causing the undesirable effects typically associated with electrode discharge. In a further exemplary embodiment, the iron core is formed using pure iron (99.9% Fe; μ>200,000), which tends to achieve higher magnetic flux with reasonable bias currents.

[0151] 3D and 3E depict a CT fusion FRC plasma confinement system 10 comprising a confinement chamber 100, a first pair of inner diverters 302 coupled to opposing ends of the confinement chamber 100, opposing CT forming and injection systems 200 coupled on first ends relative to the inner diverters 302, and a second pair of outer diverters 300 coupled to second ends of the CT forming and injection systems 300. To achieve Spheromak fusion, as shown in FIG. 31A, the CT forming / injection sections 200 and outer diverters 300 shown in FIGS. 3D and 3E are removed and replaced by Spheromak injectors 250 coupled to the inner diverters, as illustrated in FIGS. 31A and 31B. The Spheromak injectors 250 are located just inside the diverter's concentric electrodes 310, which are used for stability control of the FRC 453 via edge biasing. The edge bias system creates a radial electric field on the open field line and therefore around the FRC section line (scrape-off layer region) which, in synergy with NBI, stabilizes the inclusive MHD mode. r ×B z The spheromak injectors 250 are individually operated and controlled to generate the initial FRC as well as various spheromak plasmas, which allows the initial plasma density and trapped magnetic flux to be varied to find the optimum target FRC for effective neutral beam injection. During the spheromak formation, translation, and fusion processes, relatively low equilibrium and mirror fields (B e A field of about 1 kG, mirror ratio of about 2) is applied by balance and mirror coils 412 and 420 until FRC plasma 453 is sufficiently formed, after which the fields should be gradually increased (B e (Maximum 3 kG, mirror ratio of about 3-3.5). The neutral beam is also injected into the confinement chamber 100 from the injector 615 through the discharge, and the beam energy is also accordingly e The power can be gradually increased from an initial elevated power level, e.g., from about 15 keV to 40 keV. Furthermore, the magnet and neutral beam injector systems can be actively controlled, and the FRC plasma should be stabilized and maintained in real time.

[0152] The Spheromak injectors 250 are powered using individually controlled power supplies 258 to not only fully replenish particles inside the confinement chamber 100 but also to recirculate already formed FRCs. When an oppositely oriented CT injector is positioned near the midplane of a confinement chamber with multi-pulse capability, the CT injector radially injects Spheromak-like plasmoids into the FRC. In other words, the injected CT must penetrate into the transverse magnetic field (Bz ≈1 kG) without fragmenting or producing strong magnetic / density perturbations. Furthermore, radial CT injection near the midplane affects fast ion confinement to some extent, and the system tends not to be scalable for high-field fusion devices. Therefore, injecting CT from the Spheromak injector 250 on the geometric axis (i.e., "axial" CT injection) is significantly more beneficial than radial CT injection from several scientific perspectives.

[0153] Alternatively, in an exemplary embodiment, the system configuration depicted in Figures 2, 3A, 3D, and 3E, including two diametrically opposed reversed field theta-pinch forming sections 200, can be modified to include diametrically opposed spheromak injectors 250 coupled to an outer divertor 300 for replenishment of the FRC plasma contained within the containing chamber.

[0154] According to an embodiment of the present disclosure, a method for generating and maintaining a magnetic field using a field-reversed configuration (FRC) includes the steps of: fusing first and second spheromak plasmas; forming an FRC around the fused plasmas in a confinement chamber; and maintaining the FRC at a constant or nearly constant value without attenuation by injecting a beam of fast neutral atoms from a neutral beam injector into the FRC plasma at an angle toward the midplane of the confinement chamber.

[0155] According to a further embodiment of the present disclosure, the method further includes injecting spheromak plasma from opposing first and second spheromak injectors toward a midplane of the chamber, and fusing the spheromak plasma to form an FRC.

[0156] According to a further embodiment of the present disclosure, the method further comprises a step of reverse helicity spheromak fusion of the spheromak plasma injected into the confinement chamber from the first and second spheromak injectors.

[0157] According to a further embodiment of the present disclosure, the first and second Spheromak injectors comprise magnetized coaxial plasma guns (MCPGs).

[0158] According to a further embodiment of the present disclosure, the first and second Spheromak injectors include an iron-core bias coil system.

[0159] According to a further embodiment of the present disclosure, the iron core of the iron core bias coil system comprises cast iron with a magnetic permeability of about 250.

[0160] According to a further embodiment of the present disclosure, the iron core of the iron core bias coil system is about 99.9% Fe with a magnetic permeability equal to or greater than about 200,000.

[0161] According to a further embodiment of the present disclosure, the method further includes separately controlling the first and second Spheromak injectors.

[0162] According to a further embodiment of the present disclosure, the spheromak plasma ejected from the first spheromak injector is different from the spheromak plasma ejected from the second spheromak injector.

[0163] According to a further embodiment of the present disclosure, the method further includes replenishing the FRC plasma with one or more Spheromak plasmas from one or more of the first and second Spheromak injectors along the geometric axis of the confinement chamber.

[0164] According to a further embodiment of the present disclosure, the method further includes multi-pulse injecting one or more spheromak plasmas into the FRC plasma from one or more of the first and second spheromak injectors.

[0165] According to a further embodiment of the present disclosure, the method further includes forming and injecting a multi-pulsed spheromak into the FRC plasma.

[0166] According to a further embodiment of the present disclosure, the method further includes a step of adjusting the beam energies of the plurality of neutral beams between a first beam energy and a second beam energy, wherein the second beam energy is a step different from the first beam energy, or a step of adjusting the beam energies of the plurality of neutral beams between the first beam energy and the second beam energy, wherein the second beam energy is different from the first beam energy and the second beam energy is a step higher than the first beam energy, or a step of adjusting the beam energies of the plurality of neutral beams between the first beam energy and the second beam energy, wherein the second beam energy is different from the first beam energy, and the plurality of neutral beams switch between the first beam energy and the second beam energy for the duration of the implant shot.

[0167] According to a further embodiment of the present disclosure, the method further includes generating a magnetic field within the chamber using a quasi-DC coil extending about the chamber.

[0168] According to a further embodiment of the present disclosure, the method further includes inducing a magnetic flux surface of the FRC into a diverter coupled to an end of the containment chamber.

[0169] According to a further embodiment of the present disclosure, the method further includes generating a magnetic field in the divertor using a quasi-DC coil extending about the forming section and the divertor.

[0170] According to a further embodiment of the present disclosure, the method further includes generating mirror magnetic fields within the opposing ends of the chamber using quasi-DC coils extending about the opposing ends of the chamber.

[0171] According to a further embodiment of the present disclosure, the method further includes generating one of a magnetic dipole field and a magnetic quadrupole field within the chamber using a saddle coil coupled to the chamber.

[0172] According to a further embodiment of the present disclosure, the method further includes conditioning the interior surfaces of the chamber and the diverter with a gettering system.

[0173] According to a further embodiment of the present disclosure, the method further comprises the gettering system including one of a titanium deposition system and a lithium deposition system.

[0174] According to a further embodiment of the present disclosure, the method further includes controlling a radial electric field profile within an edge layer of the FRC of the FRC plasma.

[0175] According to a further embodiment of the present disclosure, bias electrodes are used to apply a potential distribution to the open flux planes of the FRC.

[0176] According to further embodiments of the present disclosure, the method further includes one of the steps of injecting the spheromak plasma from the first and second spheromak injectors having a magnetic flux greater than 20 mWb, or injecting the spheromak plasma from the first and second spheromak injectors having a magnetic flux greater than about 25-30 mWb.

[0177] According to a further embodiment of the present disclosure, a system for generating and maintaining a magnetic field using a Field Reversed Configuration (FRC) includes a confinement chamber; first and second divertors coupled to the confinement chamber; first and second diametrically opposed spheromak injectors coupled to the first and second divertors for generating a spheromak plasma and translating the spheromak plasma toward a mid-plane of the confinement chamber; a plurality of neutral atomic beam injectors coupled to the confinement chamber and oriented to inject neutral atomic beams toward the mid-plane of the confinement chamber at an angle less than normal to a longitudinal axis of the confinement chamber; and a plurality of neutral atomic beam injectors positioned around the confinement chamber and the first and second divertors. the first and second mirror plugs positioned between the confinement chamber and the first and second diverters; a gettering system coupled to the confinement chamber and the first and second diverters; one or more bias electrodes for electrically biasing the open flux surfaces of the generated FRC; one or more bias electrodes positioned in the confinement chamber and one or more of the first and second diverters; and two or more saddle coils coupled to the confinement chamber.

[0178] According to a further embodiment of the present disclosure, a system for generating and maintaining a magnetic field using a Field Reversed Configuration (FRC) includes a confinement chamber, first and second divertors coupled to the confinement chamber, first and second diametrically opposed spheromak injectors coupled to the first and second divertors, one or more of a plurality of bias electrodes, and first and second mirror plugs, wherein the one or more bias electrodes are positioned within the confinement chamber and one or more of the first and second outer divertors, and the first and second mirror plugs are coupled to the confinement chamber and the first and second outer divertors. and a magnetic system including: a gettering system coupled to the confinement chamber and the first and second diverters; a plurality of neutral atom beam injectors coupled to the confinement chamber and oriented at an angle toward a midplane of the confinement chamber; a plurality of quasi-DC coils positioned around the confinement chamber and the first and second diverters; and a set of first and second quasi-DC mirror coils positioned between the confinement chambers, the system configured to generate an FRC and maintain the FRC without decay while the neutral beam is injected into the plasma.

[0179] According to a further embodiment of the present disclosure, the first and second spheromak injectors are configured to inject a spheromak plasma toward a mid-plane of the chamber to fuse and form an FRC plasma.

[0180] According to a further embodiment of the present disclosure, the first and second spheromak injectors are configured to form and inject first and second spheromak plasmas having reverse helicity into the confinement chamber.

[0181] According to a further embodiment of the present disclosure, the first and second Spheromak injectors comprise magnetized coaxial plasma guns (MCPGs).

[0182] According to a further embodiment of the present disclosure, the first and second Spheromak injectors include an iron-core bias coil system.

[0183] According to a further embodiment of the present disclosure, the iron core of the iron core bias coil system is cast iron with a magnetic permeability of about 250.

[0184] According to a further embodiment of the present disclosure, the iron core of the iron core bias coil system is about 99.9% Fe with a magnetic permeability equal to or greater than about 200,000.

[0185] According to a further embodiment of the present disclosure, the first and second Spheromak injectors are independently controllable.

[0186] According to a further embodiment of the present disclosure, the first and second spheromak injectors are configured for multi-pass injection of more than one spheromak plasma into the confinement chamber.

[0187] According to a further embodiment of the present disclosure, the multiple neutral beams are adjustable between a first beam energy and a second beam energy, the second beam energy being different from the first beam energy, and the beam energies of the multiple neutral beams are switchable between the first beam energy and the second beam energy for the duration of the implant shot.

[0188] According to further embodiments of the present disclosure, the bias electrodes include one or more point electrodes positioned within the containment chamber to contact the open magnetic field lines, a set of annular electrodes between the containment chamber and the first and second diverters, and a plurality of concentrically stacked electrodes positioned within the first and second diverters to charge the plurality of concentric magnetic flux layers.

[0189] According to a further embodiment of the present disclosure, the system further comprises first and second diametrically opposed reversed field theta-pinch forming sections interposed between the first and second divertors and the containment chamber.

[0190] According to a further embodiment of the present disclosure, the system includes third and fourth diverters interposed between the first and second diametrically opposed reversed field theta-pinch forming sections and the containment chamber.

[0191] However, the exemplary embodiments provided herein are intended merely as illustrative examples and are not limiting in any way.

[0192] All features, elements, components, functions, and steps described with respect to any embodiment provided herein are intended to be freely combinable and substituted with those from any other embodiment. If a feature, element, component, function, or step is described with respect to only one embodiment, it should be understood that that feature, element, component, function, or step can be used with all other embodiments described herein unless expressly stated otherwise. Therefore, this paragraph always serves as a leading basis and written support for the introduction of claims, which combine features, elements, components, functions, and steps from different embodiments or substitute features, elements, components, functions, and steps from one embodiment for another, even if the following description does not explicitly state that such combinations or substitutions are possible in specific cases. Explicitly listing every possible combination and substitution would be an undue burden, especially considering that, upon reading this specification, any and all such combination and substitution possibilities would be readily recognized by those skilled in the art.

[0193] In many instances, entities are described herein as being coupled to other entities. The terms "coupled" and "connected" (or any of their forms) are used interchangeably herein and should be understood to be inclusive, in both cases, of the direct coupling of two entities (without any non-negligible (e.g., parasitic) intervening entities) and the indirect coupling of two entities (with one or more non-negligible intervening entities). When entities are shown as being directly coupled together or described as being coupled together without description of any intervening entities, it should be understood that those entities can also be indirectly coupled together, unless the context clearly dictates otherwise.

[0194] While the embodiments are susceptible to various modifications and alternative forms, specific examples thereof have been shown in the drawings and described in detail herein. It should be understood, however, that these embodiments are not limited to the particular forms disclosed; on the contrary, these embodiments are intended to cover all modifications, equivalents, and alternatives falling within the spirit of the disclosure. Furthermore, negative limitations may be recited or added to the claims that define the scope of the claimed invention by any feature, function, step, or element of the embodiments, but also by any feature, function, step, or element not falling within its scope.< / n> < / n> < / ne>

Claims

[Claim 1] The invention described in this specification.

Images