HK1237115B - Systems and methods for forming and maintaining a high performance frc - Google Patents

Description

Systems and methods for forming and maintaining high performance FRCs

This application is a divisional application of patent application with application number 201280055842.6, application date November 14, 2012, and name “System and method for forming and maintaining high performance FRC”.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No. 61/559,154, filed November 4, 2011, and claims the benefit of U.S. Provisional Application No. 61/559,721, filed November 15, 2011, both of which are incorporated herein by reference.

Technical Field

[0014] The embodiments described herein relate generally to magnetic plasma confinement systems, and more particularly to systems and methods that facilitate forming and maintaining field reversal configurations with excellent stability and particle, energy, and flux confinement.

Background Art

The field-reversed configuration (FRC) belongs to a class of magnetic plasma confinement topologies known as compact plasma torus/compact toroid (CT). It exhibits a dominant poloidal magnetic field and has zero or small self-generated plasma toroidal fields (see M. Tuszewski, Nucl. Fusion 28, 2033 (1988)). The appeal of this configuration lies in its simple geometry, ease of construction and maintenance, a naturally unrestricted divertor for energy extraction and ash removal, and very high β (β is the ratio of the average plasma pressure to the average magnetic field pressure within the FRC), i.e., high power density. This high β property facilitates economic operation and the use of advanced anneutronic fuels such as D- ^He₃ and ^pB₁₁₁ .

The traditional method of forming FRC uses the field-reversed θ -pinch technique to generate a hot, high-density plasma (see A.L. Hoffman and J.T. Slough, Nucl. Fusion 33, 27 (1993)). A variation is the translation-trapping method, in which the plasma formed in the θ -pinch "source" is almost immediately ejected from one end into a confinement chamber. The translated plasma particles are then trapped between two powerful mirrors at the ends of the chamber (see, for example, H. Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191 (1995)). Once in the confinement chamber, various heating and current drive methods can be used, such as beam injection (neutral or neutralized), rotating magnetic fields, RF or ohmic heating, etc. This source separation and confinement function provides key engineering advantages for possible future fusion reactors. FRC has proven to be extremely robust and resilient to dynamic formation, translation, and violent capture events. In addition, they show a tendency to exhibit a preferred plasma state (see, for example, HY Guo, AL Hoffman, KE Miller and LC Steinhauer, Phys. Rev. Lett. 92, 245001 (2004)). Significant progress has been made in the past few decades in developing other FRC formation methods: incorporating spheromacranes with oppositely directed helicities (see, for example, Y. Ono, M. Inomoto, Y. Ueda, T. Matsuyama and T. Okazaki, Nucl. Fusion 39, 2001 (1999)) and by driving the current with a rotating magnetic field (RMF) (see, for example, IR Jones, Phys. Plasmas 6, 1950 (1999)), which also provides additional stability.

Recently, the long-proposed collision-merger technique has been significantly further developed (see, e.g., D. R. Wells, Phys. Fluids 9, 1010 (1966)): two separate theta pinches at opposite ends of a confinement chamber simultaneously generate two plasmoids and accelerate the plasmoids toward each other at high speeds; they then collide and merge at the center of the confinement chamber to form a composite FRC. The conventional collision-merger method was demonstrated to produce stable, long-lived, high-flux, high-temperature FRCs in the construction and successful operation of one of the largest FRC experiments to date (see, e.g., M. Binderbauer, H. Y. Guo, M. Tuszewski et al., Phys. Rev. Lett. 105, 045003 (2010)).

The FRC consists of a torus of closed field lines inside the interface and an annular edge layer on the open field lines near the outside of the interface. The edge layers coalesce into a jet that exceeds the length of the FRC, providing a natural divertor. The FRC topology matches that of field-reversing mirror plasmas. However, a significant difference is that FRC plasmas have a β of about 10. The inherently low internal magnetic field provides a certain population of intrinsically moving particles, i.e., particles with large Larmor radii compared to the small radius of the FRC. It is these strong dynamical effects that appear to be at least partially responsible for/contribute to the overall stability of past and current FRCs, such as those produced in collision-merger experiments.

Typical FRC experiments in the past have been subject to convection losses, in which energy constraints are determined by particle transport to a great extent. Particles mainly diffuse out from the interface volume in the radial direction and are then lost in the edge layer axially. Therefore, FRC constraints depend on the characteristics of both closed field lines and open field line regions. The particle diffusion time out from the interface is calibrated to (a~ _rs /4, where _rs is the central interface radius), and is a characteristic FRC diffusion rate, such as, where _ρ represents the ion gyration radius, evaluated with an externally applied magnetic field. The edge layer particle confinement time is basically the axial passage time in past FRC experiments. In steady state, the balance between radial particle loss and axial particle loss obtains the interface density gradient length. For past FRCs with significant density at the interface, the FRC particle confinement time is calibrated to (see, for example, M. TUSZEWSKI, "Field Reversed Configurations," Nucl. Fusion 28, 2033 (1988)).

Another drawback of existing FRC system designs is the need to use external multipoles to control rotational instabilities, such as the rapidly growing n=2 exchange instability. In this way, a typical externally applied quadrupole field provides the required magnetic restoring pressure to damp/suppress the development of these unstable modes. While this technique is sufficient for stability control of thermal bulk plasmas, it poses a serious problem for more kinetic FRCs or advanced hybrid FRCs, where a population of high kinetic energy, large orbital particles is combined with the usual thermal plasma. In these systems, the distortion of the axisymmetric magnetic field due to such multipoles leads to significant rapid particle loss via collisionless random diffusion, with the result that canonical angular momentum conservation is lost. Therefore, novel solutions to provide stability control without promoting any particle diffusion are important to exploit the higher performance potential of these previously unexplored advanced FRC concepts.

In view of the foregoing, it is therefore desirable to improve the confinement and stability of FRCs in order to use steady-state FRCs as a pathway to a wide variety of applications, ranging from compact neutron sources (for medical isotope production and nuclear waste remediation) to bulk separation and enrichment systems, and reactor cores for focusing light nuclei for future energy generation.

Summary of the Invention

Embodiments of the invention provided herein are directed to systems and methods for facilitating the formation and maintenance of novel high-performance field-reversal configurations (FRCs). Based on this novel high-performance FRC paradigm, the systems of the invention combine a number of novel concepts and approaches to significantly improve the particle, energy, and flux confinement of FRCs, as well as provide stability control without undesirable side effects.

A FRC system is provided herein comprising a central confinement vessel surrounded by two diametrically opposed, reverse-field-θ-pinch forming sections and two divertor chambers beyond the two forming sections to control neutral particle density and impurity contamination. A magnetic system comprises: a series of quasi-DC coils located axially along the components of the FRC system; quasi-DC mirror coils between either end of the confinement chamber and the adjacent forming sections; and a mirror plug comprising a compact quasi-DC mirror coil between each of the forming sections and the divertor, the compact quasi-DC mirror coil generating an additional guide field to focus the magnetic flux surface toward the divertor. The forming section comprises a modular pulsed power forming system that enables the FRC to be formed in situ and then accelerated and ejected (static formation) or simultaneously formed and accelerated (dynamic formation).

The FRC system includes a neutral atom beam injector and a pellet injector. It may also include a gettering system and an axial plasma gun. A bias electrode is also provided for electrically biasing the open flux surface.

The systems, methods, features, and advantages of the present invention will become apparent to those skilled in the art upon review of the following drawings and detailed description. All such additional methods, features, and advantages are intended to be included within this description, be within the scope of the present invention, and be protected by the appended claims. It is also intended that the present invention is not limited to the details of the exemplary embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate presently preferred embodiments of the invention, and together with the general description given above and the detailed description of the preferred embodiments given below, serve to explain and teach the principles of the invention.

FIG1 shows particle confinement in the FRC system of the present invention in the case of a high performance FRC scheme (HPC) compared to in the case of a conventional FRC scheme (CR) and compared to in the case of other conventional FRC experiments.

FIG. 2 shows components of the FRC system of the present invention and the magnetic topology of FRC that may be produced in the FRC system of the present invention.

FIG3 shows the basic layout of the FRC system of the present invention as viewed from the top, including the preferred arrangement of the neutral beam, electrodes, plasma gun, mirror plug and pellet injector.

FIG4 shows a schematic diagram of components of a pulsed power system for forming a segment.

FIG5 shows an isometric view of an individual pulse power shaping skid.

FIG6 shows an isometric view of the formed tube assembly.

Figure 7 shows a partial cross-sectional isometric view of the neutral beam system and key components.

FIG8 shows an isometric view of a neutral beam arrangement on a confinement chamber.

FIG9 shows a partial cross-sectional isometric view of a preferred arrangement of a Ti and Li gettering system.

Figure 10 shows a partial cross-sectional isometric view of a plasma gun mounted in a divertor chamber. Also shown are the associated magnetic mirror plug and divertor electrode assembly.

Figure 11 shows a preferred arrangement of annular bias electrodes at the axial ends of the confinement chamber.

Figure 12 shows the evolution of the repulsive flux radius in an FRC system obtained from a series of external diamagnetic coils at two field-reversal θ-pinch formation sections and a magnetic probe embedded in a central metal confinement chamber. The time is measured from the instant of synchronous field reversal in the formation source and gives the distance z relative to the axial midplane of the machine.

Figures 13(a) to 13(d) show data from a representative non-HPF, non-persistent discharge on the FRC system of the present invention. (a) The repulsive flux radius at the midplane; (b) the 6 chords of line-integrated density from the midplane _CO2 interferometer; (c) the radial distribution of density from the inverse Abel transform of the _CO2 interferometer data; and (d) the total plasma temperature from the pressure balance are shown as a function of time.

FIG. 14 shows the repulsive flux axial distribution at selected times for the same discharge as for the FRC system of the present invention shown in FIG. 13 .

FIG15 shows an isometric view of a saddle coil mounted outside a confinement chamber.

The relationship between the FRC lifetime and the pulse length of the ejected neutral beam is shown in Figure 16. As shown, longer beam pulses produce longer-lived FRCs.

FIG17 illustrates the individual and combined effects of the different components of the FRC system on the FRC performance and the achievement of the HPF solution.

Figures 18(a) to 18(d) show data from a representative HPF, non-sustained discharge on an FRC system of the present invention. (a) The repulsive flux radius at the midplane is shown as a function of time; (b) the density from the 6-chord integral of the midplane _CO2 interferometer; (c) the radial distribution of the density from the inverse Abel transform of the _CO2 interferometer data; and (d) the total plasma temperature from the pressure balance.

Figure 19 shows the flux confinement as a function of the electron temperature ( _Te ). This represents a graphical representation of the newly established superior scaling scheme for HPF discharges.

It should be noted that the drawings are not necessarily drawn to scale, and that, for illustrative purposes, elements of similar structure or function are generally represented by similar reference numerals throughout the drawings. It should also be noted that the drawings are only intended to facilitate describing the various embodiments described herein. The drawings do not necessarily depict every aspect of the teachings disclosed herein and do not limit the scope of the claims.

DETAILED DESCRIPTION

The embodiments of the present invention provided herein are directed to systems and methods for facilitating the formation and maintenance of high-performance field-reversed configurations (FRCs) having excellent stability and excellent particle, energy, and flux confinement compared to conventional FRCs. Various auxiliary systems and operating modes have been studied to assess whether excellent confinement conditions exist in FRCs. These efforts have resulted in breakthrough discoveries and the development of the high-performance FRC paradigm described herein. Based on this new paradigm, the systems and methods of the present invention combine a number of novel concepts and approaches to significantly improve FRC confinement (as shown in FIG1 ) and provide stability control without adverse side effects. As discussed in more detail below, FIG1 depicts a comparison of operating according to a high-performance FRC scheme (HPF) for forming and maintaining FRC in an FRC system 10 described below (see FIG2 and FIG3 ) with operating according to a conventional scheme CR for forming and maintaining particle confinement of the FRC, as well as with operating according to a conventional scheme used in other experiments for forming and maintaining particle confinement of the FRC. This disclosure will summarize and describe in detail the innovative individual components and methods of the FRC system 10 and their collective effects.

Description of the FRC system

Vacuum system

Figures 2 and 3 depict schematic diagrams of the FRC system 10 of the present invention. The FRC system 100 comprises a central confinement vessel 100 surrounded by two diametrically opposed reverse field theta pinch forming sections 200 and two divertor chambers 300 extending beyond the forming sections 200 to control neutral particle density and impurity contamination. The FRC system 10 of the present invention is constructed to accommodate ultra-high vacuum and operates at a typical base pressure of 10-8 Torr. Such vacuum pressures require the use of double pumping of mating flanges, metal O-rings, high purity inner walls between mating components, and careful initial surface conditioning of all parts prior to assembly, such as physical and chemical cleaning, followed by a 24-hour 250°C vacuum bake and hydrogen glow discharge cleaning.

The reversed field theta pinch forming sections 200 are standard field reversed theta pinch (FRTP), but with an advanced pulse power forming system discussed in detail below (see Figures 4 to 6). Each forming section 200 is formed from standard opaque industrial grade quartz tubing, which features a 2 mm ultrapure quartz liner. The confinement chamber 100 is made of stainless steel to allow for numerous radial and tangential ports; it also serves as a flux conservator for the experimental timescales described below and to limit rapid magnetic transients. A combination of dry scroll roughing pumps, turbomolecular pumps, and cryopumps is used to create and maintain vacuum within the FRC system 10.

Magnetic system

Magnetic system 400 is shown in Figures 2 and 3. FIG2 shows the FRC magnetic flux and iso-density lines (as a function of radial and axial coordinates), as well as other characteristics, associated with FRC 450 that can be generated by FRC system 10. These iso-density lines were obtained through 2-D resistive Hall-MHD numerical simulations using code developed to simulate systems and methods corresponding to FRC system 10 and are consistent with measured experimental data. As seen in FIG2 , FRC 450 includes a ring of closed field lines at the interior 453 of FRC 450, inside interface 451, and a ring of annular edge layer 456, located on the open field lines 452, slightly outside interface 451. Edge layer 456 combines with jet 454, which extends beyond the length of the FRC, to provide a natural divertor.

The main magnetic system 410 includes a series of quasi-DC coils 412, 414, and 416 located at specific axial positions along the components of the FRC system 10, namely, along the confinement chamber 100, the forming section 200, and the divertor 300. The quasi-DC coils 412, 414, and 416 are powered by a quasi-DC switching power supply and generate a base magnetic bias field of approximately 0.1 T in the confinement chamber 100, the forming section 200, and the divertor 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 a switching power supply) located between either end of the confinement chamber 100 and the adjacent forming section 200. The quasi-DC mirror coils 420 provide a magnetic mirror ratio of up to 5 and can be independently energized for balanced shaping control. Furthermore, a mirror plug 440 is positioned between each of the forming section 200 and the divertor 300. Mirror plug 440 comprises a compact quasi-DC mirror coil 430 and a mirror plug coil 444. Quasi-DC mirror coil 430 comprises three coils 432, 434, and 436 (powered by a switching power supply) that generate an additional guide field to focus the magnetic flux surface 455 toward the small-diameter passage 442 passing through mirror plug coil 444. Mirror plug coil 444, wrapped around small-diameter passage 442 and powered by an LC pulse power circuit, generates a strong magnetic mirror field of up to 4 T. The purpose of this entire coil arrangement is to tightly focus and guide the magnetic flux surface 455 and the end-flowing plasma jet 454 into the remote chamber 310 of the divertor 300. Finally, a set of saddle coil "antennas" 460 (see FIG. 15 ) are located outside confinement chamber 100, two on each side of the midplane, and are fed with a DC power supply. The saddle coil antenna 460 can be configured to provide a quasi-static magnetic dipole or quadrupole field of approximately 0.01 T for controlling rotational instability and/or electronic current control. The saddle coil antenna 460 can flexibly provide a magnetic field that is symmetrical or asymmetrical about the machine's midplane, depending on the direction of the applied current.

Pulse power forming system

The pulsed power forming system 210 operates according to a modified theta-pinch principle. There are two systems, each supplying power to one of the forming sections 200. Figures 4 to 6 illustrate the main building blocks and layout of the forming system 210. The forming system 210 comprises a modular pulsed power arrangement, comprising individual units (pryers) 220, each energizing a subset of coils 232 of a ribbon assembly 230 (ribbon) wrapped around a forming quartz tube 240. Each pryer 220 comprises a capacitor 221, an inductor 223, a fast, high-current switch 225, an associated trigger 222, and a dump circuit 224. In total, each forming system 210 stores between 350-400 kJ of capacitive energy, providing up to 35 GW of power to form and accelerate FRC. Coordinated operation of these components is achieved via prior art triggers and control systems 222 and 224, which allow synchronized timing between the forming systems 210 on each forming section 200 and minimize switch jitter to tens of nanoseconds. The advantage of this modular design is its flexible operation: FRCs can be formed in situ and then accelerated and ejected (=static forming) or formed and accelerated simultaneously (=dynamic forming).

Neutral beam ejector

Neutral atom beams are deployed on the FRC system 10 to provide heating and current drive and to form fast particle pressure. As shown in Figures 3 and 8, individual beam lines comprising neutral atom beam injector systems 610 and 640 are located around the central confinement chamber 100 and eject fast particles tangentially to the FRC plasma (and perpendicular to the axis of the confinement chamber 100), with certain impact parameters such that the target capture region is located within the interface 451 (see Figure 2). Each injector system 610 and 640 is capable of projecting up to 1MW of neutral beam power into the FRC plasma, with particle energies between 20KeV and 40KeV. Systems 610 and 640 are based on positive ion multi-aperture extraction sources and utilize geometric focusing, inertial cooling, and different pumping of ion extraction grids. In addition to using different plasma sources, the main difference between systems 610 and 640 is their physical design that meets their respective mounting locations, resulting in side and top injection capabilities. For the side injector system 610, the typical components of these neutral beam injectors are specifically shown in Figure 7. As shown in FIG7 , each individual neutral beam system 610 includes an RF plasma source 612 at the input end (this is replaced by an arc source in system 640 ), and a magnetic shield 614 covering this end. An ion light source and acceleration grid 616 are coupled to the plasma source 612, and a gate valve 620 is positioned between the ion light source and acceleration grid 616 and the neutralizer 622. A deflection magnet 624 and an ion eater 628 are located between the neutralizer 622 and the aiming device 630 at the outlet end. The cooling system includes two cryogenic refrigerators 634, two cryopanels 636, and an LN2 shield 638. This flexible design allows operation over a wide range of FRC parameters.

Pellet ejector

To provide a means of injecting new particles and better control the FRC particle inventory, a 12-barrel pellet injector 700 is utilized on the FRC system 10 (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)). FIG3 shows the layout of the pellet injector 700 on the FRC system 10. Cylindrical pellets (D ~ 1 mm, L ~ 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, which is comparable to the FRC particle inventory.

Impurity absorption system

It is well known that neutral halo gas is a serious problem in all confinement systems. Charge exchange and recycling (release of cold impurity material from the walls) processes can have a devastating effect on energy and particle confinement. In addition, any significant density of neutral gas at or near the edge will result in a loss of lifetime or at least a severe reduction in the lifetime of the ejected 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 much larger than the characteristic magnetic field gradient length) that promote the ejection, a fact that is detrimental to all high-energy plasma applications, including focusing via auxiliary beam heating.

Surface conditioning is a means of controlling or mitigating the adverse effects of neutral gases and impurities in confinement systems. To this end, the FRC system 10 provided herein employs titanium and lithium deposition systems 810 and 820, which apply thin films of Ti and/or Li (tens of microns thick) to the plasma-facing surfaces of the diverter 300 and confinement chamber (or vessel 100). The coating is achieved via a vapor deposition technique. Solid Li and/or Ti is evaporated and/or sublimated and sprayed onto nearby surfaces to form the coating. The source is a nuclear furnace with a guide nozzle (in the case of Li) 822 or a heated solid sphere 812 with a guide shield (in the case of Ti). The Li evaporator system typically operates in continuous mode, while the Ti sublimator is primarily operated intermittently between plasma operations. These systems operate at temperatures above 600°C to achieve rapid deposition rates. To achieve good wall coverage, multiple strategically positioned evaporator/sublimator systems are required. FIG9 details the preferred arrangement of getter deposition systems 810 and 820 in the FRC system 10. The coating acts as a gettering surface and effectively pumps hydrogen-based atomic and molecular species (H and D). The coating can also reduce other typical impurities, such as carbon and oxygen, to insignificant levels.

Mirror plug

As described above, the FRC system 10 employs a set of mirror coils 420, 430, and 444, as shown in Figures 2 and 3. The first mirror coil set 420 is located at both axial ends of the confinement chamber 100 and is independently excited by the confinement coils 412, 414, and 416 of the main magnetic system 410. The first mirror coil set 420 primarily assists in steering and axially accommodating the FRC 450 during merging, and provides balanced shaping control during this period. The first mirror coil set 420 generates a nominally higher magnetic field (approximately 0.4 to 0.5 T) than the central confinement field generated by the central confinement coil 412. The second mirror coil set 430, comprising three compact quasi-DC mirror coils 432, 434, and 436, is located between the forming section 200 and the divertor 300 and is driven by a common switching power supply. Mirror coils 432, 434, and 436, along with a more compact pulsed mirror plug coil 444 (powered by a capacitive power supply) and a physical constriction 442, form mirror plug 440, which provides a narrow, low gas conduction path with a very high magnetic field (between 2 and 4 T, with a rise time between about 10 and 20 ms). The most compact pulsed mirror coil 444 has a compact radial size, a 20 cm bore and a similar length, compared to the meter-plus-scale bore and pancake-shaped design of confinement coils 412, 414, and 416. The purpose of mirror plug 440 is multifaceted: (1) Coils 432, 434, 436, and 444 tightly bunch and guide the magnetic flux surface 452 and end-flowing plasma jet 454 into the remote divertor chamber 300. This ensures that the discharged particles properly reach the divertor 300 and that there is a continuous flux surface 455 that traces from the open field line 452 region of the central FRC 450 all the way to the divertor 300. (2) The physical constriction 442 in the FRC system 10 provides an impediment to the flow of neutral gas from the plasma gun 350 located in the divertor 300, and the coils 432, 434, 436 and 444 can transmit the magnetic flux surface 452 and plasma jet 454 through the constriction 442. Similarly, the constriction 442 prevents gas from the forming section 200 from flowing back into the divertor 300, thereby reducing the number of neutral particles introduced into the entire FRC system 10 when the FRC is initially started. (3) The strong axial mirror created by the coils 432, 434, 436 and 444 reduces axial particle losses and therefore reduces the parallel particle diffusion rate on the open field line.

Axial plasma gun

The plasma flow from the gun 350, mounted in the divertor chamber 310 of the divertor 300, is designed to improve stability and neutral beam performance. The gun 350 is mounted on an axis inside the chamber 310 of the divertor 300, as shown in Figures 3 and 10, and generates a plasma that flows along open flux lines 452 within the divertor 300 and toward the center of the confinement chamber 100. The gun 350 operates with a high-density gas discharge in the gasket-stack channel and is designed to generate several thousand amperes of fully ionized plasma for 5 to 10 milliseconds. The gun 350 includes pulsed magnetic coils that match the output plasma flow to the desired plasma size within the confinement chamber 100. The technical parameters of the gun 350 are characterized by a channel with an outer diameter of 5 to 13 cm and an inner diameter of up to approximately 10 cm, and a discharge current of 10 to 15 kA at 400 to 600 V with an internal gun magnetic field between 0.5 and 2.3 T.

The gun plasma 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 transfer through the mirror plug 440 increases as the distance between the gun 350 and the plug 440 is reduced and the plug 440 is made wider and shorter. Under reasonable conditions, the gun 350 can each deliver approximately 10 ²² protons through the 2 to 4 T mirror plug 440, with high ion and electron temperatures of approximately 150 to 300 eV and approximately 40 to 50 eV, respectively. The gun 350 provides a large amount of fuel supply to the FRC edge layer 456 and improves the overall FRC particle confinement.

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

Knowing all the adjustment parameters discussed above and also taking into account the possibility of operating with only one or with two guns, it is clear that a wider range of operating modes can be provided.

Bias electrode

The electrical biasing of the open flux surface can provide a radial potential that causes an azimuthal E×B motion that provides a control mechanism similar to turning a knob to control the rotation of the open field line plasma and the actual FRC core 450 via velocity shear. To achieve this control, the FRC system 10 employs various electrodes strategically placed on various parts of the machine. FIG3 depicts the bias electrodes positioned at preferred locations within the FRC system 10.

In principle, there are four types of electrodes: (1) point electrodes 905 in the confinement chamber 100, which contact specific open field lines 452 in the edge of the FRC 450 to provide local charging; (2) ring electrodes 900, which charge the far edge flux layer 456 in an azimuthally symmetrical manner between the confinement chamber 100 and the forming section 200; (3) a stack of concentric electrodes 910 in the divertor 300, which charge multiple concentric flux layers 455 (thus, the selection of layers can be controlled by adjusting the coils 416 to adjust the divertor magnetic field so as to terminate the desired flux layer 456 on the appropriate electrode 910); and finally (4) the anode 920 of the plasma gun 350 itself (see Figure 10) (which intercepts the inner open flux surface 455 near the interface of the FRC 450). For some of these electrodes, Figures 10 and 11 show some typical designs.

In all cases, the electrodes are driven by a pulsed or DC power supply at voltages up to about 800 V. Depending on the electrode size and what the flux surface intersects, currents in the kiloampere range may be drawn.

FRC System - Non-Continuous Operation of Conventional Scheme

Standard plasma formation on the FRC system 10 follows the well-established reverse-field theta pinch technique. A typical process for initiating the FRC begins by driving the quasi-DC coils 412, 414, 416, 420, 432, 434, and 436 to steady-state operation. The RFTP pulse power circuit of the pulse power forming system 210 then drives the pulsed fast reverse magnetic field coil 232 to create a temporary reverse bias voltage of approximately -0.05 T in the forming section 200. At this point, a predetermined amount of neutral gas at 9-20 psi is injected into the two forming volumes defined by the (north and south) quartz tube chamber 240 of the forming section 200 via an azimuthally oriented puff-vale set located at the flanges at the outer ends of the forming section 200. A small RF (~hundreds of kilohertz) field is then generated from a set of antennas on the surface of the quartz tube 240 to induce pre-ionization within the neutral gas column in the form of a localized seed ionization region. This is followed by theta-ringing modulation of the current driving the pulsed rapid field reversal coil 232, which results in a more comprehensive pre-ionization of the gas column. Finally, the main pulse power group of the pulsed power forming system 210 is emitted to drive the pulsed rapid field reversal coil 232 to form a forward bias field of up to 0.4 T. This step can be timed to generate a uniform forward bias field along the entire length of the forming tube 240 (static formation) or to achieve continuous peristaltic field modulation along the axis of the forming tube 240 (dynamic formation).

During this entire formation process, the actual field reversal in the plasma occurs rapidly, within approximately 5 μs. The multi-gigawatt pulse power delivered to the forming plasma tends to generate thermal FRCs, which are then ejected from the formation section 200 via timed modulation of the forward magnetic field (magnetic creep) or the application of a temporary increase in current in the last coil of the coil set 232 near the axially outer end of the formation tube 210 (creating an axial magnetic field gradient axially directed toward the confinement chamber 100). The two (north and south) formation FRCs thus formed and accelerated then expand into the larger diameter confinement chamber 100, where the quasi-DC coil 412 generates a forward bias field to control radial expansion and provide a balanced external magnetic flux.

Once the north and south forming FRCs reach the vicinity of 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 when the FRCs finally merge into a single FRC 450. A large collection of plasma diagnostics can be provided in the confinement chamber 100 to study the equilibrium of the FRCs 450. Typical operating conditions in the FRC system 10 produce composite FRCs with an interface radius of about 0.4 m and an axial extension of about 3 m. Other characteristics are an external magnetic field of about 0.1 T, a plasma density of about 5×10 ¹⁹ m ^-3 and a total plasma temperature of up to 1 keV. Without any persistence, that is, without heating and/or without current drive via neutral beam injection or other auxiliary devices, the lifetime of these FRCs is limited to about 1 ms, which is the decay time of the characteristic configuration of the source.

Experimental Data for Non-Continuous Operations - Conventional Protocol

FIG12 shows a typical temporal evolution of the repulsive flux radius, which approximates the interface radius r _s , to illustrate the dynamics of the θ-pinch merging process of FRC 450. Two (north and south) individual plasmoids are generated simultaneously and accelerated out of their respective formation segments 200 at supersonic velocities V _z ~250 km/s and collide near the midplane at z = 0. During the collision, the plasmoids compress axially, followed by rapid radial and axial expansion, before finally merging to form FRC 450. Both the radial and axial dynamics of the merging FRC 450 are confirmed by detailed density profile measurements and radiometer-based tomography.

Figure 13 shows data from a representative discontinuous discharge from the FRC system 10 as a function of time. The FRC starts at t = 0. The repulsive flux radius at the machine's axial midplane is shown in Figure 13(a). This data was obtained from an array of magnetic probes located slightly inside the stainless steel wall of the confinement chamber, which measured the axial magnetic field. The steel wall was a good flux conservator for this discharge timescale.

The line-integrated density from a 6-chord _CO₂ /He-Ne interferometer at z = 0 is shown in Figure 13(b). Taking into account the vertical (y) FRC displacement as measured by bolometric tomography, an inverse Abel transform yields the isodensity contours of Figure 13(c). After some axial and radial sloshing during the first 0.1 ms, the FRC stabilizes with a hollow density profile. This profile is quite flat, with significant density along the axis, as required by typical 2-D FRC equilibrium.

The total plasma temperature is shown in Fig. 13(d), obtained from the pressure balance and in good agreement with Thomson scattering and spectroscopy measurements.

Analysis of the entire repulsive flux array shows that the shape of the FRC interface (approximated by the axial distribution of the repulsive flux) gradually evolves from a racetrack shape to an elliptical shape. This evolution, shown in Figure 14, is consistent with the gradual magnetic reconnection from two FRCs to a single FRC. In fact, a rough estimate suggests that in this particular case, about 10% of the two initial FRC magnetic fluxes reconnect during the collision.

During the FRC lifetime, the FRC length steadily shrinks from 3 m to approximately 1 m. This shrinkage, visible in Figure 4, indicates that most of the convective energy losses dominate the FRC confinement. Because the plasma pressure inside the interface decreases more rapidly than the external magnetic pressure, the magnetic field line tension in the end region compresses the FRC axially, restoring axial and radial equilibrium. For the discharges discussed in Figures 13 and 14, the FRC magnetic flux, particle inventory, and thermal energy (approximately 10 mWb, 7×10 ¹⁹ particles, and 7 kJ, respectively) decrease by roughly an order of magnitude in the first millisecond, as FRC equilibrium appears to be declining.

Ongoing Operation – HPF Program

The examples in Figures 12 to 14 are characterized without any sustained attenuation FRC. However, several techniques are deployed on the FRC system 10 to further improve the FRC confinement (core and edge layers) of the HPF scheme and to sustain this configuration.

Neutral beam

First, fast (H) neutral particles are ejected perpendicular to _BZ in the beams from eight neutral beam injectors 600. Starting from the moment when the north-south FRC is merged into one FRC 450 in the confinement chamber 100, the beam of fast neutral particles is ejected. The fast ions formed mainly by charge exchange have a betatron orbit (with a FRC topology scale or at least a major radius much larger than the characteristic magnetic field gradient length scale) that adds to the azimuthal current of the FRC 450. After some part of the discharge (after 0.5 to 0.8 ms into the shot), sufficiently large fast ions overall significantly improve the internal FRC stability and confinement characteristics (see, for example, MW Binderbauer and N. Rostoker, Plasma Phys. 56, Part 3, 451 (1996)). Moreover, from a continuous perspective, the beam from the neutral beam injector 600 is also the main means for driving current and heating the FRC plasma.

In the plasma scheme of FRC system 10, fast ions mainly slow down plasma electrons. During the early part of the discharge, the typical orbital average slowdown time of fast ions is 0.3 to 0.5 ms, which results in significant FRC heating of mainly electrons. Fast ions undergo large radial drift outside the interface because the internal FRC magnetic field is inherently low (average of about 0.03 T for an external axial field of 0.1 T). If the neutral gas density outside the interface is too high, fast ions will be susceptible to charge exchange losses. Therefore, wall gettering and other technologies deployed on FRC system 10 (such as plasma gun 350 and mirror plug 440 that help gas control, etc.) tend to minimize edge neutral particles and can allow the required fast ion current to accumulate.

Pellet injection

When a significant fast particle population accumulates within the FRC 450, frozen H or D pellets are ejected from the pellet ejector 700 into the FRC 450 to maintain the FRC particle inventory of the FRC 450 due to the higher electron temperature and longer FRC lifetime. The expected ablation timescale is short enough to provide a significant source of FRC particles. This rate can be increased by expanding the surface area of the ejector while in the barrel or jet tube of the pellet ejector 700 and before entering the confinement chamber 100 by breaking up individual pellets into smaller fragments. This can be achieved by increasing the friction between the pellets and the jet tube wall by tightening the bend radius of the final section of the jet tube just before entering the confinement chamber 100. By varying the firing sequence and rate and splitting of the twelve barrels (jet tubes), the pellet ejection system 700 can be tuned to provide a particle inventory that lasts only at the desired level. This, in turn, helps maintain the internal dynamic pressure in the FRC 450 and maintains the operation and lifetime of the FRC 450.

Once the ablated atoms encounter the bulk plasma in the FRC 450, they become fully ionized. The resulting cold plasma component is then heated by collisions of the native FRC plasma. The energy required to maintain the desired FRC temperature is ultimately supplied by the beam ejector 600. In this sense, the pellet ejector 700, together with the neutral beam ejector 600, forms a system that maintains a steady-state and continuous FRC 450.

Saddle coil

In order to achieve steady-state current drive and maintain the required ion current, it is desirable to prevent or significantly reduce the electron spin-up caused by electron-ion friction (due to the transfer of electron momentum from the impacting ions). The FRC system 10 utilizes innovative technology to provide electron breaking (electron breaking) via an externally applied static magnetic dipole or quadrupole field. This is achieved via the external saddle coil 460 depicted in FIG15. The radial magnetic field applied laterally from the saddle coil 460 induces an axial electric field in the rotating FRC plasma. The resulting axial electron current interacts with the radial magnetic field to generate an azimuthal breaking force on the electrons, _Fθ = . For typical conditions in the FRC system 10, the magnetic dipole (or quadrupole) field required to be applied inside the plasma needs to be only about 0.001T to provide sufficient electron breaking. The corresponding external field of about 0.015T is small enough not to cause significant rapid particle loss or otherwise adversely affect confinement. In fact, the applied magnetic dipole (or quadrupole) field helps to suppress instabilities. In combination with tangential neutral beam injection and axial plasma injection, the saddle coils 460 provide an additional level of control over current maintenance and stability.

Mirror plug

The design of the pulsed coil 444 within the mirror plug 440 allows for the local generation of high magnetic fields (2 to 4 T) with modest (approximately 100 kJ) capacitive energy. To form the magnetic field typical of the present invention's operation of the FRC system 10, all field lines within the formation volume pass through the constriction 442 at the mirror plug 440, as indicated by the magnetic field lines in FIG2 , without plasma wall contact. Furthermore, the mirror plug 440, in series with the quasi-DC divertor magnet 416, can be adjusted to direct the field lines onto the divertor electrode 910 or to flare them outward into a cusp configuration (not shown). The cusp configuration improves stability and suppresses parallel electron heat conduction.

Mirror plug 440 itself also contributes to neutral gas control. Mirror plug 440 allows for better utilization of the deuterium gas charged to the quartz tube during FRC formation, as the relatively low gas conduction through the plug (very low, 500 L/s) significantly reduces gas backflow into divertor 300. Most of the residual charge gas inside formation tube 210 is rapidly ionized. Furthermore, the high-density plasma flowing through mirror plug 440 provides efficient neutral ionization, thereby providing an effective gas barrier. Consequently, most of the neutrals recirculating in divertor 300 from FRC edge layer 456 do not return to confinement chamber 100. Furthermore, neutrals associated with the operation of plasma gun 350 (as discussed below) will be primarily confined to divertor 300.

Finally, mirror plugs 440 tend to improve FRC edge layer confinement. With a mirror ratio (plug/confining magnetic field) in the range of 20 to 40 and a length of 15 m between the north and south mirror plugs 440, edge layer particle confinement time increases by up to an order of magnitude. This improvement tends to increase FRC particle confinement.

Assuming that radial diffusive (D) particle losses originating from the interface volume 453 are balanced by axial losses ( ) originating from the edge layer 456 , we obtain From this equation, the interface density gradient length can be rewritten as . Here, r _s , L _s , and n _s are the interface radius, interface length, and interface density, respectively. The FRC particle confinement time is , where and . Physically, the improvement results in increased δ (reduced interface density gradient and drift parameter) and, therefore, reduced FRC particle losses. The overall improvement in FRC particle confinement is generally slightly less than quadratic, as n _s increases with .

Significant improvement in the mirror plug 440 also requires that the edge layer 456 remain generally stable (i.e., without n=1 flutes, firehose, or other MHD instabilities typical of open systems). Using the plasma gun 350 provides this preferred edge stability. In this regard, the mirror plug 440 and plasma gun 350 form an effective edge control system.

Plasma gun

The plasma gun 350 improves the stability of the FRC exhaust jet 454 by line-tying. The plasma gun 350 generates a gun plasma without azimuthal momentum, which proves suitable for controlling FRC rotational instabilities. As such, the gun 350 is an effective means of controlling FRC stability without the need for older quadrupole stabilization techniques. Thus, the plasma gun 350 enables the use of the beneficial effects of fast particles or the adoption of advanced hybrid dynamics FRC schemes as outlined in this disclosure. Thus, the plasma gun 350 enables the FRC system 10 to operate with saddle coil currents sufficient for electron breakage but below a threshold that would cause FRC instability and/or result in significant fast particle diffusion.

As mentioned above in the discussion of mirror plugs, if significant improvements can be achieved, the supplied gun plasma will be comparable to the edge layer particle loss rate (~10 ²² /s). The lifetime of the plasma generated by the gun in the FRC system 10 is in the millisecond range. In practice, it is assumed that the gun plasma with a density of _ne ~10 ¹³ cm ^-3 and an ion temperature of approximately 200 eV is confined between the end mirror plugs 440. The trapping length L and mirror ratio R are approximately 15 m and 20, respectively. The mean free path of ions due to Coulomb collisions is , and due to , the ions are confined in a gas dynamic regime. The plasma confinement time in this regime is , where V _s is the ion sound velocity. For comparison, the classical ion confinement time for these plasma parameters would be . Anomalous lateral diffusion can, in principle, shorten the plasma confinement time. However, in the FRC system 10, assuming Bohm diffusivity, the estimated lateral confinement time of the gun plasma is . Therefore, the gun will provide significant fuel replenishment to the FRC edge layer 456 and improved overall FRC particle confinement.

Furthermore, the gun plasma flow can be turned on within about 150 to about 200 microseconds, which allows for FRC initiation, translation, and merging into the confinement chamber 100. If turned on at about t~0 (FRC main group initiation), the gun plasma helps sustain the currently dynamically forming and merging FRC 450. The combined particle inventory from the forming FRC and from the gun is sufficient for neutral beam capture, plasma heating, and long-term persistence. If turned on at t in the range of -1 to 0 ms, the gun plasma can fill the quartz tube 210 with plasma or ionize the gas filled into the quartz tube, thereby allowing FRC formation with reduced or even potentially zero fill gas. FRC formation with zero fill gas may require a sufficiently cool forming plasma to allow rapid diffusion of the reverse bias magnetic field. If turned on at t<-2 ms, the plasma flow can fill the approximately 1 to 3 m ³ field line volume of the formation section 200 and confinement chamber 100 formation and confinement region with a target plasma density of several 10 ¹³ cm ^-3 , sufficient to allow neutral beam accumulation before the FRC arrives. The forming FRC can then be formed and translated into the resulting confinement vessel plasma.In this manner, the plasma gun 350 can allow for a wide variety of operating conditions and parameter regimes to be achieved.

Electrical bias

Controlling the radial electric field distribution in the edge layer 456 benefits FRC stability and confinement in various ways. Thanks to the innovative biasing components deployed in the FRC system 10, a variety of carefully planned potential distributions can be applied to a set of open flux surfaces throughout the machine, starting from areas well outside the central confinement region in the confinement chamber 100. In this way, radial electric fields can be generated in the edge layer 456, slightly outside the FRC 450. These radial electric fields then modify the azimuthal rotation of the edge layer 456 and achieve its confinement via E×B velocity shear. Any differential rotation between the edge layer 456 and the FRC core 453 can then be transmitted to the inside of the FRC plasma via shear. Thus, controlling the edge layer 456 directly affects the FRC core 453. Furthermore, since free energy in plasma rotation can also cause instabilities, this technique provides a direct means of controlling the onset and growth of instabilities. In the FRC system 10, appropriate edge biasing provides effective control over open field line transport and rotation, as well as FRC core rotation. The positions and shapes of the various provided electrodes 900, 905, 910 and 920 allow different flux surface groups 455 to be controlled and placed at different and independent potentials. In this way, a large number of different electric field configurations and strengths can be achieved, each with a different characteristic effect on plasma performance.

The key advantage of all these innovative biasing techniques is that the core and edge plasma behavior can be achieved completely outside the FRC plasma, i.e., without having any physical components touching the central hot plasma (which would have potentially severe consequences for energy, flux, and particle losses). This has a significant beneficial impact on the performance and all possible applications of the HPF concept.

Test Data - HPF Operation

The ejection of fast particles from the neutral beam gun 600 via the beam plays an important role in enabling the HPF scheme to be implemented. Figure 16 illustrates this reality. A set of curves is depicted that shows how the lifetime of the FRC is related to the beam pulse length. For all discharges that constitute this study, all other operating conditions were kept constant. The data from multiple shots were averaged and therefore represent typical behavior. It is obvious that longer beam durations produce longer-lived FRCs. Considering this evidence and other diagnostics during this study, it was demonstrated that the beam increased stability and reduced losses. The relationship between beam pulse length and FRC lifetime is not ideal because beam capture becomes inefficient below a certain plasma size, that is, as the physical size of the FRC 450 shrinks, not all ejected beams are intercepted and captured. The shrinkage of the FRC is primarily due to the fact that for a particular experimental setup, the net energy loss from the FRC plasma during the discharge (~4 MW) is slightly greater than the total power (~2.5 MW) fed into the FRC via the neutral beam. Positioning the beam closer to the midplane of the container 100 will tend to reduce these losses and extend the FRC lifetime.

FIG17 illustrates the effects of different components on implementing the HPF scheme. It shows a typical series of curves depicting the lifetime of the FRC 450 as a function of time. In all cases, a constant, moderate beam power (approximately 2.5 MW) was injected for the entire duration of each discharge. Each curve represents a different combination of components. For example, operating the FRC system 10 without any mirror plug 440, plasma gun 350, or gettering from gettering system 800 resulted in rapid onset of rotational instability and loss of FRC topology. Adding only the mirror plug 440 delayed the onset of instability and increased confinement. Utilizing a combination of the mirror plug 440 and plasma gun 350 further reduced instabilities and extended FRC lifetime. Finally, adding a getter (in this case, Ti) in addition to the gun 350 and plug 440 yielded the best results, resulting in an FRC free of instabilities and exhibiting the longest lifetime. From this experimental demonstration, it is clear that the perfect combination of components produces the best results and provides a beam with optimal target conditions.

As shown in Figure 1, the newly discovered HPF scheme shows significantly improved transport behavior. Figure 1 shows the particle confinement time variation of FRC system 10 between conventional scheme and HPF scheme. As can be seen, in the HPF scheme, it is improved by a factor far exceeding 5. In addition, Figure 1 describes the particle confinement time of FRC system 10 in detail, compared with the particle confinement time in existing conventional FRC experiments. About these other machines, the HPF scheme of FRC system 10 has improved confinement by a factor between 5 and close to 20. Lastly and most importantly, the nature of the confinement calibration of FRC system 10 in the HPF scheme is significantly different from all previous measurements. Before establishing the HPF scheme in FRC system 10, in existing FRC experiments, various empirical calibration laws were drawn from data to predict confinement time. All those calibration rules roughly depend on ratio, where R is the radius of the magnetic field without FRC (a rough measurement of the physical scale of the machine) and is the ion Larmor radius (a rough measurement of applied magnetic field) evaluated in an externally applied field. As is apparent from Figure 1, the long confinement in conventional FRC is only possible at larger machine size and/or high magnetic field. The FRC system 10 in the conventional FRC scheme CR of operation tends to follow those scaling rules, as shown in Figure 1. However, the HPF scheme is extremely superior and illustrates that better confinement can be achieved without the need for larger machine size or high magnetic field. More importantly, as is also apparent from Figure 1, the HPF scheme leads to improved confinement time with reduced plasma size compared with the CR scheme. As described below, similar trends can also be seen for flux and energy confinement time, which increase in the FR system 10 by a factor of 3-8. The breakthrough of the HPF scheme can therefore allow the use of moderate beam power, lower magnetic field and smaller size to continue and maintain the FRC balance in the FRC system 10 and future higher energy machines. Coexisting with these improvements is lower operation and construction cost and reduced engineering complexity.

For further comparison, Figure 18 shows data from a representative HPF regime discharge in FRC system 10 as a function of time. Figure 18(a) depicts the repulsive flux radius at the midplane. For these longer timescales, the conductive steel wall is no longer a good flux conservator, and the magnetic probe inside the wall increases with the probe outside the wall to adequately compensate for the flux diffusion through the steel. Compared to typical performance in a conventional regime CR, as shown in Figure 13, the HPF regime operating mode exhibits over 400% longer lifetime.

A representative chord of the line-integrated density trace is shown in Figure 18(b), and its inverse Abel-transformed complement, the isopycnal lines, are shown in Figure 18(c). Compared to the conventional FRC scheme, as shown in Figure 13, the plasma is much quieter throughout the pulse, indicating very stable operation. The peak density is also slightly lower in the HPF shot, a result of the hotter overall plasma temperature (up to a factor of 2), as shown in Figure 18(d).

The energy, particle and flux confinement times are 0.5 ms, 1 ms and 1 ms respectively for the corresponding discharge shown in Figure 18. With a reference time of 1 ms into the discharge, the stored plasma energy is 2 kJ and the losses are about 4 MW, making this target very suitable for neutral beam persistence.

Figure 19 summarizes all the advantages of the HPF scheme in the form of a newly established experimental HPF flux confinement scaling. As can be seen in Figure 19, based on previously performed measurements and after t = 0.5 ms, i.e., t < 0.5 ms and t > 0.5 ms, the confinement scales with approximately the square of the electron temperature. This strong scaling with positive (and non-negative) powers of _Te is in stark contrast to the scaling exhibited by conventional tokamaks, where confinement is typically inversely proportional to some power of the electron temperature. This scaling is a direct consequence of the HPF state and the large orbital ion population (i.e., orbits scaled with the FRC topology and/or at least the characteristic magnetic field gradient length). Ultimately, this new scaling significantly favors high operating temperatures and allows for relatively modest reactor sizes.

While the invention is susceptible to various modifications and alternative forms, specific examples thereof have been shown in the drawings and herein described in detail. It should be understood that the invention is not limited to the particular forms or methods disclosed, but on the contrary, the invention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the appended claims.

In the above description, specific names are set forth for the purpose of explanation only to provide a thorough understanding of the present disclosure. However, it is apparent to those skilled in the art that these specific details are not required to practice the teachings of the present disclosure.

Various features of the representative examples and appended claims may be combined in ways not specifically and expressly recited to provide additional useful embodiments of the present teachings. It should also be expressly noted that all value ranges or indications of groups of entities disclose every possible intermediate value or intermediate entity, both for the purpose of original disclosure and for the purpose of limiting the claimed subject matter.

Disclosed are systems and methods for generating and maintaining a FRC for a HPF scheme. It should be understood that the embodiments described herein are for illustrative purposes and should not be construed as limiting the subject matter of the present disclosure. Various modifications, uses, substitutions, combinations, improvements, and production methods that do not depart from the scope or spirit of the invention will be apparent to those skilled in the art. For example, the reader will understand that the specific order and combination of process actions described herein are illustrative only, unless stated otherwise, and that different or additional process actions or different combinations or orders of process actions may be used to perform the present invention. As another example, each feature of one embodiment may be mixed and matched with other features shown in other embodiments. Features and processes known to those skilled in the art may likewise be incorporated as needed. In addition and obviously, features may be added or subtracted as needed. Therefore, the present invention is not limited except by the appended claims and their equivalents.

Claims (82)

1. A method for generating and maintaining a magnetic field using a field-reverse configuration (FRC), comprising: A magnetic field is generated using a magnetic system coupled to a constraint chamber. First and second diameter-opposed FRC forming sections are coupled to the constraint chamber, and first and second divertors are coupled to the first and second forming sections. The magnetic system includes first and second mirror plugs and two or more saddle-shaped coils coupled to the constraint chamber. The first and second mirror plugs are positioned between the first and second forming sections and the first and second divertors. The constraint chamber and the first and second divertors are subjected to gettering using a gettering material layer from a gettering system coupled to the constraint chamber and the first and second divertors. FRCs are generated in each of the first and second forming sections, and each FRC is translated toward the mid-plane of the constraint chamber, where the FRCs merge into a merged FRC. The first and second forming sections include a modular forming system. Neutral atomic beams are ejected from multiple neutral atomic beam ejectors into the combined FRC, the neutral atomic beam ejectors being coupled to the confinement chamber and oriented orthogonal to the axis of the confinement chamber. Plasma is ejected from first and second axial plasma guns into the merged FRC, the first and second axial plasma guns being operatively coupled to the first and second divertors, the first and second forming sections, and the confinement chamber. The open flux surface of the merged FRC is electrically biased by one or more bias electrodes, the one or more bias electrodes being positioned in one or more of the confinement chamber, the first and second forming sections, and the first and second divertors. Ion pellets are ejected into the merged FRC from an ion pellet ejector connected to the confinement chamber. 2. The method according to claim 1, wherein the particle constraint of the merged FRC is at least 2 times larger than the particle constraint of the FRC having substantially the same magnetic field radius (R) and a particle constraint calibration substantially dependent on ^R² / _ρi , wherein _ρi is the ion Larmor radius evaluated in an externally applied field. 3. The method according to claim 1, wherein the magnetic system comprises a plurality of quasi-DC coils axially spaced apart at appropriate locations along the confinement chamber, the first and second forming sections, and the first and second divertors. 4. The method according to claim 3, wherein the magnetic system further comprises a first mirror coil assembly positioned between the ends of the first and second forming sections and the constraint chamber. 5. The method according to claim 4, wherein the mirror plug comprises a second mirror coil assembly located between the first and second forming sections and each of the first and second divertors. 6. The method according to claim 5, wherein the mirror plug further comprises an assembly of mirror plug coils wound around a narrowed portion in a passage between the first and second forming sections and each of the first and second divertors. 7. The method according to claim 6, wherein the mirror plug coil is a compact pulsed mirror coil. 8. The method according to claim 1, wherein the first and second forming sections comprise elongated tubes. 9. The method according to claim 8, wherein the forming system is a pulse power forming system. 10. The method of claim 8, wherein the step of forming and translating the FRCs comprises: energizing a coil set of individual strip assemblies of a plurality of strip assemblies wound around the elongated tube of the first and second forming sections, wherein the forming system includes a plurality of power and control units coupled to the individual strip assemblies of the plurality of strip assemblies. 11. The method according to claim 10, wherein each of the plurality of power and control units includes a triggering and control system. 12. The method according to claim 11, wherein the triggering and control system of the individual power and control unit among the plurality of power and control units is capable of synchronizing to allow static FRC formation or dynamic FRC formation, in which the FRC is formed and then injected, and in which the FRC is formed and translated simultaneously. 13. The method according to claim 1, wherein the plurality of neutral atomic beam injectors comprises one or more RF plasma source neutral atomic beam injectors and one or more arc source neutral atomic beam injectors. 14. The method according to claim 1, wherein the plurality of neutral atom beam injectors are oriented to have a jetting path tangential to the FRC, and the target collection area is within the interface of the FRC. 15. The method according to claim 14, wherein the pellet ejector is a 12-tube pellet ejector connected to the confinement chamber and oriented to guide ion pellets into the FRC. 16. The method according to claim 1, wherein the getter system comprises one or more of a titanium deposition system and a lithium deposition system, the titanium deposition system and the lithium deposition system coating the plasma-facing surfaces of the confinement chamber and the first and second divertors. 17. The method according to claim 1, wherein the bias electrode comprises one or more of the following: one or more point electrodes positioned in the confinement chamber for contacting the open field line; an annular electrode assembly charging the far-edge flux layer in an azimuth-symmetrical manner between the confinement chamber and the first and second forming segments; a plurality of concentrically stacked electrodes positioned in the first and second divertors for charging the plurality of concentric flux layers; and an anode of a plasma gun for intercepting open flux. 18. A method for generating and maintaining a magnetic field using a field-reverse configuration (FRC), comprising: A magnetic field is generated using a magnetic system coupled to a confinement chamber. First and second diameter-opposed FRC forming sections are coupled to the confinement chamber, and first and second divertors are coupled to the first and second forming sections. FRCs are generated in each of the first and second forming sections, and each FRC is translated toward the mid-plane of the constraint chamber, where the FRCs merge into a merged FRC. Neutral atomic beams are ejected from multiple neutral atomic beam ejectors into the combined FRC, the neutral atomic beam ejectors being coupled to the confinement chamber and oriented orthogonal to the axis of the confinement chamber. Plasma is ejected from first and second axial plasma guns into the merged FRC, the first and second axial plasma guns being operatively coupled to the first and second divertors, the first and second forming sections, and the confinement chamber. 19. The method according to claim 18, wherein the particle constraint of the merged FRC is deviated by a coefficient at least 2 greater than that of the FRC having substantially the same magnetic field radius (R) and a particle constraint calibration substantially dependent on ^R² / _ρi , wherein _ρi is the ion Larmor radius evaluated in an externally applied field. 20. The method of claim 18, wherein the magnetic system comprises a plurality of quasi-DC coils axially spaced apart at appropriate locations along the confinement chamber, the first and second forming sections, and the first and second divertors. 21. The method of claim 20, wherein the magnetic system further comprises a first mirror coil assembly positioned between the ends of the first and second forming sections and the constraint chamber. 22. The method of claim 21, wherein the magnetic system further comprises a mirror plug, the mirror plug comprising a second set of mirror coils between the first and second forming sections and each of the first and second divertors. 23. The method of claim 22, wherein the mirror plug further comprises an assembly of mirror plug coils wound around a narrowed portion in a passage between the first and second forming sections and each of the first and second divertors. 24. The method according to claim 23, wherein the mirror plug coil is a compact pulsed mirror coil. 25. The method of claim 18, further comprising: ejecting plasma from first and second axial plasma guns into the merged FRC, the first and second axial plasma guns being operatively coupled to the first and second divertors, the first and second forming sections, and the confinement chamber. 26. The method of claim 18, further comprising: using a getter material layer from a getter system to getter the confinement chamber and the first and second divertors, the getter system being coupled to the confinement chamber and the first and second divertors. 27. The method of claim 18, further comprising: electrically biasing the open flux surface of the merged FRC using one or more bias electrodes, the one or more bias electrodes being located within one or more of the constraint chamber, the first and second forming sections, and the first and second divertors. 28. The method according to claim 18, characterized in that it further comprises two or more coils connected to the constraint chamber. 29. The method of claim 18, further comprising: ejecting ion clusters from an ion cluster ejector coupled to the confinement chamber into the merged FRC. 30. The method according to claim 18, wherein the forming segment comprises a modular forming system for generating the FRC and translating it toward the midplane of the constraint chamber. 31. A method for generating and maintaining a magnetic field using a field-reverse configuration (FRC), comprising: A magnetic field is generated using a magnetic system coupled to a confinement chamber. First and second diameter-opposed FRC forming sections are coupled to the confinement chamber, and first and second divertors are coupled to the first and second forming sections. FRCs are generated in each of the first and second forming sections, and each FRC is translated toward the mid-plane of the constraint chamber, where the FRCs merge into a merged FRC. Neutral atomic beams are ejected from multiple neutral atomic beam ejectors into the combined FRC, the neutral atomic beam ejectors being coupled to the confinement chamber and oriented orthogonal to the axis of the confinement chamber. The open flux surface of the merged FRC is electrically biased by one or more bias electrodes located in one or more of the constraint chamber, the first and second forming sections, and the first and second divertors. 32. The method according to claim 31, wherein the particle constraint of the merged FRC is deviated by a coefficient at least 2 greater than that of the FRC having substantially the same magnetic field radius (R) and a particle constraint calibration substantially dependent on ^R² / _ρi , wherein _ρi is the ion Larmor radius evaluated in an externally applied field. 33. The method of claim 31, wherein the bias electrode comprises one or more of the following: one or more point electrodes positioned within the confinement chamber to contact the open field line; an annular electrode assembly charging the far-edge flux layer in an azimuth-symmetrical manner between the confinement chamber and the first and second forming segments; a plurality of concentrically stacked electrodes positioned within the first and second divertors to charge the plurality of concentric flux layers; and an anode of a plasma gun for intercepting open flux. 34. The method of claim 31, wherein the magnetic system comprises a plurality of quasi-DC coils axially spaced apart at appropriate locations along the confinement chamber, the first and second forming sections, and the first and second divertors. 35. The method of claim 34, wherein the magnetic system further comprises a first mirror coil assembly positioned between the ends of the first and second forming sections and the constraint chamber. 36. The method of claim 35, wherein the magnetic system further comprises a first mirror plug and a second mirror plug, wherein the first mirror plug and the second mirror plug comprise a second mirror coil assembly located between the first and second forming sections and each of the first and second divertors. 37. The method of claim 36, wherein the first and second mirror plugs further comprise an assembly of mirror plug coils wound around a narrowed portion in a passage between the first and second forming sections and each of the first and second divertors. 38. The method according to claim 37, wherein the mirror plug coil is a compact pulsed mirror coil. 39. The method of claim 31, further comprising the step of energizing a coil assembly of a plurality of strip assemblies wound around an elongated tube surrounding the first and second forming sections, wherein a plurality of power and control units of the forming system are coupled to the individual strip assemblies of the plurality of strip assemblies. 40. The method of claim 39, wherein each of the plurality of power and control units includes a triggering and control system. 41. The method according to claim 40, wherein the triggering and control system of the individual power and control unit among the plurality of power and control units is capable of synchronizing to allow static FRC formation or dynamic FRC formation, in which the FRC is formed and then injected, and in which the FRC is formed and translated simultaneously. 42. The method according to claim 31, wherein the plurality of neutral atom beam injectors are oriented to have a jetting path tangential to the FRC, and the target collection area is within the interface of the FRC. 43. The method of claim 31, further comprising ejecting ion clusters from an ion cluster ejector coupled to the confinement chamber into the merged FRC. 44. The method according to claim 31, further comprising: two or more saddle-shaped coils connected to the constraint chamber. 45. The method according to claim 31, characterized in that a getter material layer from a getter system is used to getter the confinement chamber and the first and second divertors, the getter system being coupled to the confinement chamber and the first and second divertors. 46. The method of claim 31, further comprising: ejecting plasma from first and second axial plasma guns into the merged FRC, the first and second axial plasma guns being operatively coupled to the first and second divertors, the first and second forming sections, and the confinement chamber. 47. A method for generating and maintaining a magnetic field using a field-reverse configuration (FRC), comprising: A magnetic field is generated using a magnetic system coupled to a confinement chamber. First and second diameter-opposed FRC forming sections are coupled to the confinement chamber, and first and second divertors are coupled to the first and second forming sections. FRCs are generated in each of the first and second forming sections, and each FRC is translated toward the mid-plane of the constraint chamber, where the FRCs merge into a merged FRC. Neutral atomic beams are ejected from multiple neutral atomic beam ejectors into the combined FRC, the neutral atomic beam ejectors being coupled to the confinement chamber and oriented orthogonal to the axis of the confinement chamber. Plasma is ejected from first and second axial plasma guns into the merged FRC, the first and second axial plasma guns being operatively coupled to the first and second divertors, the first and second forming sections, and the confinement chamber. 48. The method according to claim 47, wherein the particle constraint of the merged FRC is deviated by a coefficient at least 2 greater than that of the FRC having substantially the same magnetic field radius (R) and a particle constraint calibration substantially dependent on ^R² / _ρi , wherein _ρi is the ion Larmor radius evaluated in an externally applied field. 49. The method according to claim 47, wherein each of the first and second forming sections comprises an elongated tube and a pulse power forming system connected to the elongated tube. 50. The method of claim 49, characterized in that it includes the step of energizing a coil assembly of a plurality of strip assemblies of individual strip assemblies wound around the elongated tube of the first and second forming sections, the forming system including a plurality of power and control units coupled to the individual strip assemblies of the plurality of strip assemblies. 51. The method according to claim 50, wherein each of the plurality of power and control units includes a triggering and control system. 52. The method according to claim 51, wherein the triggering and control system of the individual power and control unit among the plurality of power and control units is capable of synchronizing to allow static FRC formation or dynamic FRC formation, in which the FRC is formed and then injected, and in which the FRC is formed and translated simultaneously. 53. The method of claim 47, further comprising: electrically biasing the open flux surface of the merged FRC by one or more bias electrodes, the one or more bias electrodes being positioned in one or more of the constraint chamber, the first and second forming sections, and the first and second divertors. 54. The method of claim 53, wherein the one or more bias electrodes comprise one or more of the following: one or more point electrodes positioned within the confinement chamber to contact the open field line; an annular electrode assembly charging the far-edge flux layer in an azimuth-symmetrical manner between the confinement chamber and the first and second forming segments; a plurality of concentrically stacked electrodes positioned in the first and second divertors to charge the plurality of concentric flux layers; and an anode of a plasma gun for intercepting open flux. 55. The method of claim 47, wherein the magnetic system comprises a plurality of quasi-DC coils axially spaced apart at appropriate locations along the constraint chamber, the first and second forming sections and the first and second divertors, and a first set of mirror coils positioned between the ends of the first and second forming sections and the constraint chamber. 56. The method of claim 55, wherein the magnetic system further comprises a first mirror plug and a second mirror plug, wherein the mirror plug comprises a second mirror coil assembly located between the first and second forming sections and each of the first and second divertors. 57. The method of claim 56, wherein the mirror plug further comprises a compact pulsed mirror plug coil assembly wound around a narrowed portion in the passage between the first and second forming sections and each of the first and second divertors. 58. The method according to claim 47, wherein the plurality of neutral atom beam injectors are oriented to have a jetting path tangential to the FRC, and the target collection area is within the interface of the FRC. 59. The method according to claim 47, further comprising: ejecting ion clusters from an ion cluster ejector connected to the confinement chamber into the merged FRC. 60. The method according to claim 47, further comprising: two or more saddle-shaped coils connected to the constraint chamber. 61. The method of claim 47, further comprising: using a getter material layer from a getter system to getter the confinement chamber and the first and second divertors, the getter system being coupled to the confinement chamber and the first and second divertors. 62. A method for generating and maintaining a magnetic field using a field-reverse configuration (FRC), comprising: A magnetic field is generated using a magnetic system coupled to a confinement chamber. First and second diameter-opposed FRC forming sections are coupled to the confinement chamber, and first and second divertors are coupled to the first and second forming sections. FRCs are generated in each of the first and second forming sections, and each FRC is translated toward the mid-plane of the constraint chamber, where the FRCs merge into a merged FRC. Neutral atomic beams are ejected from multiple neutral atomic beam ejectors into the combined FRC, the neutral atomic beam ejectors being coupled to the confinement chamber and oriented orthogonal to the axis of the confinement chamber. The constraint chamber and the first and second divertors are subjected to gettering using a gettering material layer from a gettering system connected to the constraint chamber and the first and second divertors. 63. The method according to claim 62, wherein the particle constraint of the merged FRC is at least 2 times larger than the particle constraint of the FRC having substantially the same magnetic field radius (R) and a particle constraint calibration substantially dependent on ^R² / _ρi , wherein _ρi is the ion Larmor radius evaluated in an externally applied field. 64. The method according to claim 62, wherein the getter system comprises one or more of a titanium deposition system and a lithium deposition system, the titanium deposition system and the lithium deposition system coating the plasma-facing surfaces of the confinement chamber and the first and second divertors. 65. The method according to claim 64, wherein the deposition system employs vapor deposition technology. 66. The method according to claim 64, wherein the lithium deposition system comprises a plurality of atomic furnaces having guide nozzles. 67. The method according to claim 64, wherein the titanium deposition system comprises a plurality of heated solid spheres having guiding sheaths. 68. The method of claim 62, further comprising: ejecting plasma from a first axial plasma gun and a second axial plasma gun into the merging FRC, the first axial plasma gun and the second axial plasma gun being operatively coupled to the first and second divertors, the first and second forming sections and the confinement chamber. 69. The method according to claim 62, wherein each of the first and second forming sections comprises an elongated tube and a pulse power forming system connected to the elongated tube. 70. The method of claim 69, further comprising: energizing a coil assembly of individual strip assemblies of a plurality of strip assemblies wound around the elongated tube of the first and second forming sections, wherein the forming system includes a plurality of power and control units coupled to the individual strip assemblies of the plurality of strip assemblies. 71. The method of claim 62, further comprising: electrically biasing the open flux surface of the merged FRC by one or more bias electrodes, the one or more bias electrodes being positioned in one or more of the constraint chamber, the first and second forming sections, and the first and second divertors. 72. The method of claim 71, wherein the one or more bias electrodes comprise one or more of the following: one or more point electrodes positioned within the confinement chamber to contact the open field line; an annular electrode assembly charging the far-edge flux layer in an azimuth-symmetrical manner between the confinement chamber and the first and second forming segments; a plurality of concentrically stacked electrodes positioned within the first and second divertors to charge the plurality of concentric flux layers; and an anode of a plasma gun for intercepting open flux. 73. The method of claim 62, wherein the magnetic system comprises: a plurality of quasi-DC coils axially spaced apart at appropriate locations along the constraint chamber, the first and second forming sections, and the first and second divertors; a first mirror coil assembly positioned between the ends of the first and second forming sections and the constraint chamber; and a second mirror coil assembly positioned between each of the first and second forming sections and the first and second divertors. 74. The method of claim 62, further comprising: a compact pulsed mirror coil assembly wound around a narrowed portion in the passage between each of the first and second forming sections and the first and second divertors. 75. A method for generating and maintaining a magnetic field using a field-reverse configuration (FRC), comprising: A magnetic field is generated using a magnetic system coupled to a confinement chamber, with first and second diameter-opposed FRC forming sections coupled to the confinement chamber, and first and second divertors coupled to the first and second forming sections. The magnetic system includes two or more saddle-shaped coils coupled to the confinement chamber on each side of the midplane of the confinement chamber. FRCs are generated in each of the first and second forming sections, and each FRC is translated toward the mid-plane of the constraint chamber, where the FRCs merge into a merged FRC. Neutral atomic beams are ejected from multiple neutral atomic beam ejectors into the combined FRC, the neutral atomic beam ejectors being coupled to the confinement chamber and oriented orthogonal to the axis of the confinement chamber. 76. The method according to claim 75, wherein the particle constraint of the merged FRC is deviated by a coefficient at least 2 greater than that of the FRC having substantially the same magnetic field radius (R) and a particle constraint calibration substantially dependent on ^R² / _ρi , wherein _ρi is the ion Larmor radius evaluated in an externally applied field. 77. The method of claim 75, further comprising: ejecting plasma from a first axial plasma gun and a second axial plasma gun into the merging FRC, the first axial plasma gun and the second axial plasma gun being operatively coupled to first and second divertors, the first and second forming sections and the confinement chamber. 78. The method according to claim 75, wherein each of the first and second forming sections comprises an elongated tube and a pulse power forming system connected to the elongated tube. 79. The method of claim 75, wherein the open flux surface of the merged FRC is electrically biased by one or more bias electrodes, the one or more bias electrodes being located in one or more of the constraint chamber, the first and second forming sections, and the first and second divertors. 80. The method of claim 79, wherein the one or more bias electrodes comprise one or more of the following: one or more point electrodes positioned within the confinement chamber to contact the open field line; an annular electrode assembly charging the far-edge flux layer in an azimuth-symmetrical manner between the confinement chamber and the first and second forming segments; a plurality of concentrically stacked electrodes positioned in the first and second divertors to charge the plurality of concentric flux layers; and an anode of a plasma gun for intercepting open flux. 81. The method of claim 75, wherein the magnetic system comprises: a plurality of quasi-DC coils spaced apart at appropriate locations along the constraint chamber, the first and second forming sections, and the first and second divertors; a first mirror coil assembly positioned between the ends of the constraint chamber and the first and second forming sections; and a second mirror coil assembly positioned between each of the first and second forming sections and the first and second divertors. 82. The method of claim 81, further comprising: a compact pulsed mirror coil assembly wound around a narrowed portion in the passage between each of the first and second forming sections and the first and second divertors.