System for forming and maintaining a high performance frc

(56) References cited:

WO-A2-02/062112 • COHEN ET AL.: Formation of collisionless high-[beta] plasmas by odd-parity rotating magnetic fields, PHYSICAL REVIEW LETTERS, vol. 98, no. 14, 6 April 2007 (2007-04-06), pages 145002-1-145002-4, XP002695902, USA ISSN: 0031-9007, DÓI: 10.1103/PhysRevLett.98.145002 • SMIRNOV ET AL.: Neutral beam dump utilizing cathodic ARC titanium evaporation, FUSION SCIENCE AND TECHNOLOGY, vol. 59, no. 1T, July 2010 (2010-07), pages 271-273, XP002695903, USA ISSN: 1536-1055 • ASAI ET AL.: End loss measurement of neutral-beam-injected Field-Reversed Configuration plasma, JOURNAL OF PLASMA AND FUSION RESEARCH SERIES, vol. 5, 2002, pages 220-224, XP002695904, Japan ISSN: 1883-9630 • COHEN ET AL.: RMFo-formed collisionless high-[beta] plasmas: yesterday, today and tomorrow, AIP CONFERENCE PROCEEDINGS, vol. 1154, 2007, pages 165-166, XP002695907, USA ISSN: 0094-243X

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Description

CROSS-REFERENCE ΤΟ RELATED APPLICATIONS [0001] This application claims the benefit of U.S. Provisional Application No. 61/559,154, filed November 14, 2011, and claims the benefit of U.S. Provisional Application No. 61/559,721, filed November 15, 2011.

FIELD [0002] The embodiments described herein relate generally to magnetic plasma confinement systems and, more particularly, to systems and methods that facilitate forming and maintaining Field Reversed Configurations with superior stability as well as partiele, energy and flux confinement.

BACKGROUND INFORMATION [0003] The Field Reversed Configuration (FRC) belongs to the eláss of magnetic plasma confinement topologies known as compacttoroids (CT). It exhibits predominantly poloidal magnetic fields and possesses zero or small self-generated toroidal fields (see M. Tuszewski, Nucl. Fusion 28, 2033 (1988)). The attractions of such a configuration are its simple geometry fór ease of construction and maintenance, a natural unrestricted divertorforfacilitating energy extraction and ash removal, and very high β(β\$ the ratio ofthe average plasma pressure to the average magnetic field pressure inside the FRC), i.e., high power density. The high //natúré is advantageous fór economic operation and fór the use of advanced, aneutronic fuels such as D-He³ and p-B¹¹. [0004] The traditional method of forming an FRC uses the field-reversed //-pinch technology, producing hot, high-density plasmas (see A. L. Hoffman and J. T. Slough, Nucl. Fusion 33, 27 (1993)). A variation on this is the translation-trapping method in which the plasma created in a theta-pinch source is more-or-less immediately ejected out one end intő a confinement chamber. The translating plasmoid is then trapped between two strong mirrors at the ends of the chamber (see, fór instance, H. Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191 (1995)). Once in the confinement chamber, various heating and currentdrive methods may be applied such as beam injection (neutral or neutralized), rotating magnetic fields, RF or ohmic heating, etc. This separation of source and confinement functions offers key engineering advantages fór potential future fusion reactors. FRCs have proved to be extremely robust, resilient to dynamic formation, translation, and violent capture events. Moreover, they show a tendency to assume a preferred plasma state (see e.g. Η. Y. Guo, A. L. Hoffman, K. E. Miller, and L. C. Steinhauer, Phys. Rév. Lett. 92, 245001 (2004)). Significant progress has been made in the last decade developing other FRC formation methods: merging spheromaks with oppositely-directed helicities (see e.g. Y. Ono, M. Inomoto, Y. Ueda, T. Matsuyama, and T. Okazaki, Nucl. Fusion 39, 2001 (1999)) and by driving currentwith rotating magneticfields (RMF) (see e.g. I. R. Jones, Phys. Plasmas 6, 1950 (1999)) which alsó provides additional stability.

[0005] Recently, the collision-merging technique, proposed long ago (see e.g. D. R. Wells, Phys. Fluids 9, 1010 (1966)) has been significantly developed further: two separate theta-pinches at opposite ends of a confinement chamber simultaneously generate two plasmoids and accelerate the plasmoids toward each other at high speed; they then collide at the center ofthe confinement chamber and merge to form a compound FRC. In the construction and successful operation of one of the largest FRC experiments to date, the conventional collision-merging method was shown to produce stable, long-lived, high-flux, high temperature FRCs (see e.g. M. Binderbauer, H.Y. Guo, M. Tuszewski et al., Phys. Rév. Lett. 105, 045003 (2010)).

[0006] FRCs consist of a torus of closed field lines inside a separatrix, and of an annular edge layer on the open field lines justoutside the separatrix. The edge layer coalesces intő jets beyond the FRC length, providing a natural divertor. The FRC topology coincides with that of a Field-Reversed-Mirror plasma. However, a significant difference is that the FRC plasma has a //of about 10. The inherent low internál magnetic field provides fór a certain indigenous kinetic partiele population, i.e. particles with large larmorradii, comparabletothe FRC minor radius. It is these strong kinetic effects that appearto at least partially contribute to the gross stability of pást and present FRCs, such as those produced in the collisionmerging experiment.

[0007] Typical pást FRC experiments have been dominated by convective losses with energy confinement largely determined by partiele transport. Particles diffuse primarily radially out of the separatrix volume, and are then lost axially in the edge layer. Accordingly, FRC confinement depends on the properties of both closed and open field line regions. The partiele diffusion time out of the separatrix scales as τ_± ~ a²/D± (a ~ rs/4, where rs is the Central separatrix radius), and D± is a characteristic FRC diffusivity, such as D± ~ 12.5 pie, with pie representing the ion gyroradius, evaluated at an externally applied magnetic field. The edge layer partiele confinement time τ|| is essentially an axial transit time in pást FRC experiments. In steady-state, the balance between radial and axial partiele losses yields a separatrix density gradient length δ ~ (D±t||)^1/2. The FRC partiele confinement time scales as (τ±τ||)^1/2 fór pást FRCs that have substantial density at the separatrix (see e.g. M. TUSZEWSKI, Field Reversed Configurations, Nucl. Fusion 28, 2033 (1988)).

[0008] A FRC with rotating magnetic fields applied to mirror-configuration plasmas is disclosed by S.A. Cohen et al. Formation of Collisionless High-Beta Plasmas by Odd-Parity Rotating Magnetic Fields, Physical Review Letters 98, 145002 (2007).

ΕΡ 2 780 913 Β1 [0009] Anotherdrawbackof priorFRC system designs was the need to use external multipoles to control rotational instabilities such as the fást growing n=2 interchange instabilities. In this way the typical externally applied quadrupole fields provided the required magnetic restoring pressure to dampen the growth of these unstable modes. While this technique is adequate fór stability control of the thermal bulkplasma, it poses asevere problem fór more kinetic FRCs or advanced hybrid FRCs, where a highly kinetic large orbit partiele population is combined with the usual thermal plasma. In these Systems, the distortions of the axisymmetric magnetic field due to such multipole fields leads to dramatic fást partiele losses via collisionless stochastic diffusion, a consequence of the loss of conservation of canonical angular momentum. A növel solution to provide stability control without enhancing diffusion of any particles is, thus, important to take advantage of the higher performance potential of these never-before explored advanced FRC concepts.

[0010] In lightoftheforegoing, itis,therefore,desirable to improve the confinement and stability of FRCs in order to use steady state FRCs as a pathway to a whole variety of applications from compact neutron sources (fór medical isotope production and nuclear waste remediation), to mass separation and enrichment systems, and to a reactor core fór fusion of light nuclei fór the future generation of energy.

SUMMARY [0011] The present embodiments provided herein are directed to systems and methods that facilitate the formation and maintenance of new High Performance Field Reversed Configurations (FRCs). In accordance with this new High Performance FRC paradigm, the present System combines a hőst of növel ideas and means to dramatically improve FRC confinement of particles, energy and flux as well as provide stability control without negative side-effects.

[0012] An FRC system provided herein includes a Central confinement véssél surrounded by two diametrically opposed reversed-field-theta-pinch formation sections and, beyond the formation sections, two divertor chambers to control neutral density and impurity contamination. A magnetic system includes a series of quasi-dc coils that are situated at axial positions along the components of the FRC system, quasi-dc mirror coils between either end of the confinement chamber and the adjacentformation sections, and mirror plugs comprising compact quasi-dc mirror coils between each of the formation sections and divertors that produce additional guide fields to focus the magnetic flux surfaces towards the divertor. The formation sections include modular pulsed power formation systems that enable FRCs to be formed in-situ and then accelerated and injected (=static formation) or formed and accelerated simultaneously (=dynamic formation).

[0013] The FRC system includes neutral atom beam injectors and a pellet injector. Gettering systems are alsó included aswell as axial plasma guns. Biasing eleetrodes are alsó provided fór electrical biasing of open flux surfaces.

[0014] The systems, methods, features and advantages of the invention will be or will become apparent to one with skill in the art upon examination of the following figures and detailed deseription. It is intended that all such additional methods, features and advantages be included within this deseription, be within the scope of the invention, and be protected by the accompanying claims. It is alsó intended that the invention is nőt limited to require the details of the example embodiments.

BRIEF DESCRIPTION OF THE FIGURES [0015] The accompanying drawings, which are included as part of the present specification, illustrate the presently preferred embodiment and, together with the generál deseription given above and the detailed deseription of the preferred embodiment given below, serve to explain and teach the principles of the present invention.

Figure 1 illustrates partiele confinement in the present FRC system under a high performance FRC régimé (HPF) versus under a conventional FRC régimé (CR), and versus other conventional FRC experiments.

Figure 2 illustrates the components of the present FRC system and the magnetic topology of an FRC producible in the present FRC system.

Figure 3 illustrates the basic layout of the present FRC system as viewed from the top, including the preferred arrangementof neutral beams, eleetrodes, plasma guns, mirror plugs and pellet injector. Figure 4 illustrates a schematic of the components ofa pulsed power system fór the formation sections. Figure 5 illustrates an isometricview ofan individual pulsed power formation skid.

Figure 6 illustrates an isometric view of a formation tűbe assembly.

Figure 7 illustrates a partial sectional isometricview of neutral beam system and key components. Figure 8 illustrates an isometric view of the neutral beam arrangement on confinement chamber. Figure 9 illustrates a partial sectional isometric view of a preferred arrangement of the Ti and Li gettering systems.

Figure 10 illustrates a partial sectional isometric view of a plasma gun installed in the divertor chamber. Alsó shown are the associated magnetic mirror plug and a divertor eleetrode assembly.

Figure 11 illustrates a preferred layout ofan annular bias eleetrode at the axial end of the confinement chamber.

Figure 12 illustrates the evolution of the excluded flux radius in the FRC system obtained from a series

ΕΡ 2 780 913 Β1 of external diamagnetic loops at the two field reversed theta pinch formation sections and magnetic probes embedded inside the Central metál confinement chamber. Time is measured from the instant of synchronized field reversal in the formation sources, and distance z is given relatíve to the axial midplane ofthe machine.

Figures 13 (a) through (d) illustrate data from a representative non-HPF, un-sustained discharge on the present FRC system. Shown asfunctionsof time are (a) excluded flux radius at the midplane, (b) 6 chords of line-integrated density from the midplane CO2 interferometer, (c) Abel-inverted density radial profiles from the CO2 interferometer data, and (d) totál plasma temperature from pressure balance. Figure 14 illustrates the excluded flux axial profiles at selected times fór the same discharge of the present FRC system shown in Figure 13.

Figure 15 illustrates an isometricview ofthe saddle coils mounted outside ofthe confinement chamber. Figure 16 illustrates the correlations of FRC lifetime and pulse length of injected neutral beams. As shown, longer beam pulses produce longer lived FRCs.

Figure 17 illustrate the individual and combined effects of different components ofthe FRC system on FRC performance and the attainmentofthe HPF régimé.

Figures 18(a) through (d) illustrate data from a representative HPF, un-sustained discharge on the present FRC system. Shown asfunctions oftime are (a) excluded flux radius at the midplane, (b) 6 chords of line-integrated density from the midplane CO2 interferometer, (c) Abel-inverted density radial profiles from the CO2 interferometer data, and (d) totál plasma temperature from pressure balance.

Figure 19 illustrates flux confinement as a function of electron temperature (T_e). It represents a graphical representation of a newly established superior scaling régimé fór HPF discharges.

[0016] It should be noted that the figures are nőt necessarily drawn to scale and that elements of similar structures orfunctions are generally represented by like reference numerals fór illustrative purposes throughout the figures. It alsó should be noted that the figures are only intended to facilitate the description of the various embodiments described herein. The figures do nőt necessarily describe every aspect of the teachings disclosed herein and do nőt limit the scope of the claims.

DETAILED DESCRIPTION [0017] The present embodiments provided herein are directed to systems and methods that facilitate forming and maintaining High Performance Field Reversed Configurations (FRCs) with superior stability as well as superior partiele, energy and flux confinement overconventional FRCs. Various ancillary systems and operating modes have been explored to assess whether there is a superiorconfinementregime in FRCs. These efforts have led to breakthrough discoveries and the development of a High Performance FRC paradigm described herein. In accordance with this new paradigm, the present systems and methods combine a hőst of növel ideas and means to dramatically improve FRC confinement as illustrated in Figure 1 as well as provide stability control without negative side-effects. As discussed in greater detail below, Figure 1 depicts partiele confinement in an FRC system 10 described below (see Figures 2 and 3), operating in accordance a High Performance FRC régimé (HPF) fór forming and maintaining an FRC versus operating in accordance with a conventional régimé CR fór forming and maintaining an FRC, and versus partiele confinement in accordance with conventional regimes fór forming and maintaining an FRC used in other experiments. The present disclosure will outline and detail the innovative individual components of the FRC system 10 and methods as well as their collective effects.

Description of the FRC System

Vacuum System [0018] Figures 2 and 3 depict a schematic of the present FRC system 10. The FRC system 10 includes a Central confinement véssél 100 surrounded by two diametrically opposed reversed-field-theta-pinch formation sections 200 and, beyond the formation sections 200, two divertor chambers 300 to control neutral density and impurity contamination. The present FRC system 10 was built to accommodate ultrahigh vacuum and operates at typical base pressures of 10-8 torr. Such vacuum pressures require the use of double-pumped mating flanges between mating components, metál O-rings, high purity interiorwalls, as well as careful initial surface conditioning of all parts prior to assembly, such as physical and Chemical cleaning followed by 24 hour 250 °C vacuum baking and Hydrogen glow discharge cleaning.

[0019] The reversed-field-theta-pinch formation sections 200 are standard field-reversed-theta-pinches (FRTPs), albeit with an advanced pulsed power formation system discussed in detail below (see Figures 4 through 6). Each formation section 200 is made of standard opaque industrial grade quartz tubes that feature a 2 milliméter inner lining of ultrapure quartz. The confinement chamber 100 is made of stainless steel to allow a multitude of radial and tangential ports; it alsó serves as a flux conserver on the timescale of the experiments described below and limits fást magnetic transients. Vacuums are created and maintained within the FRC system 10 with a set of dry scroll roughing pumps, turbó molecular pumps and cryo pumps.

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Magnetic System [0020] The magnetic system 400 is illustrated in Figures2 and 3. Figure 2, amongstotherfeatures, illustrates an FRC magnetic fiux and density contours (as functions ofthe radial and axial coordinates) pertaining to an FRC 450 producible by the FRC system 10. These contours were obtained by a 2-D resistive Hall-MHD numerical simulation using code developed to simulate systems and methods corresponding to the FRC system 10, and agree well with measured experimental data. As seen in Figure 2, the FRC 450 consists of a torus of closed field lines atthe interior453 ofthe FRC 450 inside aseparatrix 451, and of an annular edge layer 456 on the open field lines 452 just outside the separatrix 451. The edge layer 456 coalesces intő jets 454 beyond the FRC length, providing a natural divertor.

[0021] The main magnetic system 410 includes a series of quasi-dc coils 412, 414, and 416 that are situated at particular axial positions along the components, i.e., along the confinement chamber 100, the formation sections 200 and the divertors 300, ofthe FRC system 10. The quasi-dc coils 412, 414 and 416 are fed by quasi-dc switching power supplies and produce basic magnetic bias fields of about 0.1 T in the confinement chamber 100, the formation sections 200 and the divertors 300. In addition to the quasi-dc coils 412, 414 and 416, the main magnetic system 410 includes quasi-dc mirror coils 420 (fed by switching supplies) between eitherend ofthe confinement chamber 100 and the adjacent formation sections 200. The quasi-dc mirror coils 420 provide magnetic mirror ratios of up to 5 and can be independently energized fór equilibrium shaping control. In addition, mirror plugs 440, are positioned between each of the formation sections 200 and divertors 300. The mirror plugs 440 comprise compact quasi-dc mirror coils 430 and mirror plug coils 444. The quasi-dc mirror coils 430 include three coils 432, 434 and 436 (fed by switching supplies) that produce additional guide fields to focus the magnetic flux surfaces 455 towards the small diameter passage 442 passing through the mirror plug coils 444. The mirror plug coils 444, which wrap around the small diameter passage 442 and are fed by LC pulsed power circuitry, produce strong magnetic mirror fields of up to 4 T. The purpose of this entire coil arrangement is to tightly bundle and guide the magnetic flux surfaces 455 and end-streaming plasma jets 454 intő the remote chambers 310 ofthe divertors 300. Finally, a set of saddle-coil antennas 460 (see Figure 15) are located outside the confinement chamber 100, two on each side of the mid-plane, and are fed by de power supplies. The saddle-coil antennas 460 can be configured to provide a quasi-static magnetic dipólé or quadrupole field of about 0.01 T fór controlling rotational instabilities and/or electron current control. The saddle-coil antennas 460 can flexibly provide magnetic fields that are either symmetric orantisymmetricaboutthe machine’s midplane, depending on the direction ofthe applied currents.

Pulsed power formation systems [0022] The pulsed power formation systems 210 operate on a modified theta-pinch principle. There are two systems that each power one of the formation sections 200. Figures 4 through 6 illustrate the main building blocks and arrangement ofthe formation systems 210. The formation system 210 is composed of a modular pulsed power arrangement that consists of individual units (=skids) 220 that each energize a sub-set of coils 232 of a strap assembly 230 (=straps) that wrap around the formation quartz tubes 240. Each skid 220 is composed of capacitors 221, inductors 223, fást high current switches 225 and associated trigger 222 and dump circuitry 224. In totál, each formation system 210 Stores between 350-400 kJ of capacitive energy, which provides up to 35 GW of power to form and accelerate the FRCs. Coordinated operation of these components is achieved via a state-of-the-art trigger and control system 222 and 224 that allows synchronized timing between the formation systems 210 on each formation section 200 and minimizes switching jitter to tens of nanoseconds. The advantage of this modular design is its flexible operation: FRCs can be formed in-situ and then accelerated and injected (=static formation) or formed and accelerated at the same time (=dynamic formation).

Neutral Beám Injectors [0023] Neutral atom beams are deployed on the FRC system 10 to provide heating and current drive as well as to develop fást partiele pressure. As shown in Figures 3 and 8, the individual beam lines comprising neutral atom beam injector systems 610 and 640 are located around the Central confinement chamber 100 and inject fást particles tangentially to the FRC plasma (and perpendicular to the axis of the confinement chamber 100) with an impact paraméter such that the target trapping zone lies well within the separatrix 451 (see Figure 2). Each injector system 610 and 640 is capableof projecting up to 1 MW of neutral beam power intő the FRC plasma with partiele energies between 20 and 40 keV. The systems 610 and 640 are based on positive ion multi-aperture extraction sources and utilize geometric focusing, inertial cooling ofthe ion extraction grids and differential pumping. Apartfrom using different plasma sources, the systems 610 and 640 are primarily differentiated by their physical design to meet their respective mounting locations, yielding side and top injection capabilities. Typical components of these neutral beam injectors are specifically illustrated in Figure 7 fór the side injector systems 610. As shown in Figure 7, each individual neutral beam system 610 includes an RF plasma source 612 at an inputend (this issubstituted with an arc source in systems 640) with a magnetic sereen 614 covering the end. An ion optical source and acceleration grids 616 is coupled to the plasma source 612 and a gate valve 620 is positioned between the ion optical source and acceleration

ΕΡ 2 780 913 Β1 grids 616 and a neutralizer 622. Adeflection magnet 624 and an ion dump 628 are located between the neutralizer 622 and an aiming device 630 at the exit end. A cooling system comprises two cryo-refrigerators 634, two cryopanels 636 and a LN2 shroud 638. This flexible design allows fór operation over a broad rangé of FRC parameters.

Pellet Injector [0024] To provide a means to inject new particles and better control FRC partiele inventory, a 12-barrel pellet injector 700 (see e.g. I. Vinyar et al., Pellet Injectors Developed atPELINfor JET, TAE, and HL-2A, Proceedings of the 26th Fusion Science and Technology Symposium, 09/27 to 10/01 (2010)) is utilized on FRC system 10. Figure 3 illustrates the layoutof the pellet injector 700 on the FRC system 10. The cylindrical pellets (D ~ 1 mm, L ~ 1 - 2 mm) are injected intő the FRC with a velocity in the rangé of 150 - 250 km/s. Each individual pellet contains about 5X10¹⁹ hydrogen atoms, which is comparable to the FRC partiele inventory.

Gettering Systems [0025] It is well known that neutral haló gas is a serious problem in all confinement systems. The charge exchange and recycling (release of cold impurity matéria! from the wall) processes can have a devastating effect on energy and partiele confinement. In addition, any significantdensity of neutral gas ator nearthe edge will lead to prompt losses of or at least severely curtail the lifetime of injected large orbit (high energy) particles (large orbit refers to particles having orbits on the scale of the FRC topology or at least orbit radii much larger than the characteristic magnetic field gradient length scale) - a fact that is detrimental to all energetic plasma applications, including fusion via auxiliary beam heating.

[0026] Surface conditioning is a means by which the detrimental effects of neutral gas and impurities can be controlled or reduced in a confinement system. To this end the FRC system 10 provided herein employs Titanium and Lithium deposition systems 810 and 820 that coat the plasma facing surfaces of the confinement cham bér (or véssél) 100 and diverters 300 with films (tens of micrometers thick) of Ti and/or Li. The coatings are achieved via vapor deposition techniques. Solid Li and/or Ti are evaporated and/or sublimated and sprayed onto nearby surfaces to form the coatings. The sources are atomic ovens with guide nozzles (in case of Li) 822 or heated spheres of solid with guide shrouding (in case of Ti) 812. Li evaporator systems typicallyoperate in a continuous mode while Ti sublimators are mostly operated intermittently in between plasma operation. Operating temperatures of these systems are above 600 °C to obtain fást deposition rates. To achieve good wall coverage, multiple strategically located evaporator/sublimator systems are necessary. Figure 9 details a preferred arrangement of the gettering deposition systems 810 and 820 in the FRC system 10. The coatings act as gettering surfaces and effectively pump atomic and molecular hydrogenic species (H and D). The coatings alsó reduce other typical impurities such as Carbon and Oxygen to insignificant levels.

Mirror Plugs [0027] As stated above, the FRC system 10 employs sets of mirror coils 420,430, and 444 asshown in Figures 2 and 3. A first set of mirror coils 420 is located at the two axial ends of the confinement chamber 100 and is independently energ ized from the confinement coils 412, 414 and 416 of the main magnetic system 410. The first set of mirror coils 420 primarily helps to steer and axially contain the FRC 450during merging and provides equilibrium shaping control during sustainment. The first mirror coil set 420 produces nominally higher magnetic fields (around 0.4 to 0.5 T) than the Central confinement field produced by the Central confinement coils 412. The second set of mirror coils 430, which includes three compact quasi-dc mirror coils 432, 434 and 436, is located between the formation sections 200 and the divertors 300 and are driven by a common switching power supply. The mirror coils 432,434 and 436, togetherwith the more compact pulsed mirror plug coils 444 (fed by a capacitive power supply) and the physical constriction 442 form the mirror plugs 440 that provide a narrow low gas conductance path with very high magnetic fields (between 2 to 4 T with risetimes of about 10 to 20 ms). The most compact pulsed mirror coils 444 are of compact radial dimensions, boré of 20 cm and similar length, compared to the meter-plus-scale boré and pancake design of the confinement coils 412, 414 and 416. The purpose of the mirror plugs 440 is multifold: (1) The coils 432, 434, 436 and 444 tightly bundle and guide the magnetic flux surfaces 452 and end-streaming plasma jets 454 intő the remote divertor chambers 300. This assures that the exhaust particles reach the divertors 300 appropriately and that there are continuous flux surfaces 455 that trace from the open field line 452 region of the Central FRC 450 all the way to the divertors 300. (2) The physical constrictions 442 in the FRC system 10, through which that the coils 432, 434, 436 and 444 enable passage of the magnetic flux surfaces 452 and plasma jets 454, provide an impedimentto neutral gas flow from the plasma guns 350 that sít in the divertors 300. In the same vein, the constrictions 442 prevent back-streaming of gas from the formation sections 200 to the divertors 300 thereby reducing the number of neutral particles that has to be introduced intő the entire FRC system 10 when commencing the start up of an FRC. (3) The strong axial mirrors produced by the coils 432,434,436 and 444 reduce axial partiele losses and thereby reduce the parallel partiele diffusivity on open field lines.

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Axial Plasma Guns [0028] Plasma streams from guns 350 mounted in the divertor chambers 310 of the divertors 300 are intended to improve stability and neutral beam performance. The guns 350 are mounted on axis inside the chamber 310 of the divertors 300 as illustrated in Figures 3 and 10 and produce plasma flowing along the open flux lines 452 in the divertor 300 and towards the center of the confinement chamber 100. The guns 350 operate at a high density gas discharge in a washer-stack channel and are designed to generate several kiloamperes offully ionized plasma fór 5 to 10 ms. The guns 350 include a pulsed magnetic coil that matches the output plasma stream with the desired size of the plasma in the confinement chamber 100. The technical parameters of the guns 350are characterized by a channel having a 5 to 13 cm outer diameter and up to about 10 cm inner diameter and provide a discharge current of 10-15 kA at 400-600 V with a gun-internal magnetic field of between 0.5 to 2.3 T. [0029] The gun plasma streams can penetrate the magnetic fields of the mirror plugs 440 and flow intő the formation section 200 and confinement chamber 100. The efficiency of plasma transfer 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 guns 350 can each deliver approximately 10²² protons/s through the 2 to 4 T mirror plugs 440 with high ion and electron temperatures of about 150 to 300 eV and about 40 to 50 eV, respectively. The guns 350 provide significant refueling of the FRC edge Iayer456, and an improved overall FRC partiele confinement.

[0030] To further increase the plasma density, a gas box could be utilized to puff additional gas intő the plasma stream from the guns 350. This technique allows a several-fold increase in the injected plasma density. In the FRC system 10, a gas box installed on the divertor 300 side of the mirror plugs 440 improves the refueling of the FRC edge Iayer456, formation of the FRC 450, and plasma line-tying.

[0031] Given all the adjustment parameters discussed above and alsó taking intő account that operation with just one or both guns is possible, it is readily apparent that a wide speetrum of operating modes is accessible.

Biasing Electrodes [0032] Electrical biasing ofopen flux surfaces can provide radial potentials that give rise to azimuthal ExB motion that provides a control mechanism, analogous to turning a knob, to control rotation of the open field line plasma as well as the actual FRC core 450 via velocity shear. To accomplish this control, the FRC system 10 employs various electrodes strategically placed in various parts of the machine. Figure 3 depicts biasing electrodes positioned at preferred locations within the FRC system 10.

[0033] In principle, there are 4 classes of eletrodes: (1) point electrodes 905 in the confinement chamber 100 that make contact with particular open field lines 452 in the edge of the FRC 450 to provide local charging, (2) annular electrodes 900 between the confinement chamber 100 and the formation sections 200 to charge faredgeflux Iayers456 in an azimuthally symmetricfashion, (3) stacks of concentric electrodes 910 in the divertors 300 to charge multiple concentric flux layers 455 (whereby the selection of layers is controllable by adjusting coils 416 to adjust the divertor magnetic field so as to terminate the desired flux layers 456 on the appropriate electrodes 910), and finally (4) the anodes 920 (see Figure 10) of the plasma guns 350 themselves (which intercept inner open flux surfaces 455 near the separatrix of the FRC 450). Figures 10 and 11 show somé typical designs fór somé of these.

[0034] In all cases these electrodes are driven by pulsed or de power sources at voltages up to about 800 V. Depending on eleetrode size and what flux surfaces are intersected, currents can bedrawn in the kilo-ampere rangé.

Un-Sustained Operation ofFRC System - Conventional Régimé [0035] The standard plasma formation on the FRC system 10 follows the well-developed reversed-field-thetapinch technique. A typical process fór starting up an FRC commences by driving the quasi-dc coils 412, 414, 416, 420, 432, 434 and 436 to steady state operation. The RFTP pulsed power circuits of the pulsed power formation systems 210 then drive the pulsed fást reversed magnet field coils 232 to create a temporary reversed bias of about -0.05 T in the formation sections 200. At this point a predetermined amount of neutral gas at 9-20 psi is injected intő the two formation volumes defined by the quartz-tube chambers 240 of the (north and south) formation sections 200 via a set of azim uthally-oriented puffvales at flanges located on the outer ends of the formation sections 200. Next a small RF (~ hundreds of kilohertz) field is generated from a set of antennas on the surface of the quartz tubes 240 to create pre-pre-ionization in the form of local seed ionization regions within the neutral gas columns. This is followed by applying a theta-ringing modulation on the current driving the pulsed fást reversed magnet field coils 232, which leads to more global preionization of the gas columns. Finally, the main pulsed power banks of the pulsed power formation systems 210 are fired to drive pulsed fást reversed magnet field coils 232 to create a forward-biased field of up to 0.4 T. This step can be time-sequenced such that the forward-biased field is generated uniformly throughout the length of the formation tubes 240 (static formation) or such that a consecutive peristaltic field modulation is achieved along the axis of the formation tubes 240 (dynamic formation).

[0036] In this entire formation process, the actual field

ΕΡ 2 780 913 Β1 reversal in the plasma occurs rapidly, within about 5 με. The multi-gigawatt pulsed powerdelivered to theforming plasma readily produces hot FRCs which are then ejected írom the formation sections 200 via application of either a time-sequenced modulation of the forward magneticfield (magnetic peristalsis) ortemporarily increased currents in the last coils of coil sets 232 near the axial outer ends of the formation tubes 210 (forming an axial magnetic field gradient that points axially towards the confinement chamber 100). The two (north and south) formation FRCs so formed and accelerated then expand intő the larger diameter confinement chamber 100, where the quasi-dc coils 412 produce a forward-biased field to control radial expansion and provide the equilibrium external magnetic flux.

[0037] Once the north and south formation FRCs arrive near the midplane of the confinement chamber 100, the FRCs collide. During the collision the axial kinetic energies of the north and south formation FRCs are largely thermalized as the FRCs merge ultimately intő a single FRC 450. A large set of plasma diagnostics are available in the confinement chamber 100 to study the equilibria of the FRC 450. Typical operating conditions in the FRC system 10 produce compound FRCs with separatrixradii of about 0.4 m and about 3 m axial extend. Further characteristics are external magnetic fields of about 0.1 T, plasma densities around 5X10¹⁹ m^-3 and totál plasma temperature of up to 1 keV. Without any sustainment, i.e., no heating and/or current drive via neutral beam injection or other auxiliary means, the lifetime of these FRCs is limited to about 1 ms, the indigenous characteristic configuration decay time.

Experimental Data of Unsustained Operation - Conventional Régimé [0038] Figure 12 shows a typical time evolution of the excluded flux radius, Γ_Δψ, which approximates the separatrix radius, r_s, to illustrate the dynamics of the thetapinch merging process of the FRC 450. The two (north and south) individual plasmoids are produced simultaneously and then accelerated out of the respective formation sections 200 at a supersonic speed, V_z ~ 250 km/s, and collide near the midplane at z = 0. During the collision the plasmoids compress axially, followed by a rapid radial and axial expansion, before eventually merging to form an FRC 450. Both radial and axial dynamics of the merging FRC 450 are evidenced by detailed density profile measurements and bolometer-based tomography.

[0039] Data from a representative un-sustained discharge of the FRC system 10 are shown as functions of time in Figure 13. The FRC is initiated at t = 0. The excluded flux radius at the machine’s axial mid-plane is shown in Figure 13(a). Thisdata isobtainedfrom an array of magnetic probes, located just inside the confinement chamber’s stainless steel wall, that measure the axial magnetic field. The steel wall is a good flux conserver on the time scales of this discharge.

[0040] Line-integrated densities are shown in Figure 13(b), from a 6-chord CO₂/He-Ne interferometer located at z = 0. Taking intő account vertical (y) FRC displacement, as measured by bolometric tomography, Ábel inversion yields the density contours of Figures 13(c). After somé axial and radial sloshing during thefirst 0.1 ms, the FRC settles with a hollow density profile. This profile is fairlyflat, with substantial density on axis, as required by typical 2-D FRC equilibria.

[0041] Totál plasma temperature is shown in Figure 13(d), derivedfrom pressure balance andfully consistent with Thomson scattering and spectroscopy measurements.

[0042] Analysis from the entire excluded flux array indicates that the shape of the FRC separatrix (approximated by the excluded flux axial profiles) evolves graduallyfrom racetrack to elliptical. This evolution, shown in Figure 14, is consistent with a gradual magnetic reconnection from two to a single FRC. Indeed, rough estimates suggest that in this particular instant about 10% of the two initial FRC magnetic fluxes reconnects during the collision.

[0043] The FRC length shrinks steadily from 3 down to about 1 m during the FRC lifetime. This shrinkage, visible in Figure 14, suggests that mostly convective energy loss dóm inates the FRC confinement. As the plasma pressure inside the separatrix decreases faster than the external magnetic pressure, the magnetic field line tension in the end regions compresses the FRC axially, restoring axial and radial equilibrium. Forthe discharge discussed in Figures 13 and 14, the FRC magnetic flux, partiele inventory, and thermal energy (about 10 mWb, 7X10¹⁹ particles, and 7 kJ, respectively) decrease by roughly an order of magnitude in the first millisecond, when the FRC equilibrium appears to subside.

Sustained Operation - HPF Régimé [0044] The examples in Figures 12 to 14 are characteristicofdecaying FRCs without any sustainment. However, several techniques are deployed on the FRC system 10 to further improve FRC confinement (inner core and edge layer) to the HPF régimé and sustain the configuration.

Neutral Beams [0045] First, fást (H) neutrals are injected perpendicular to B_z in beams from the eight neutral beam injectors 600. The beams of fást neutrals are injected from the moment the north and south formation FRCs merge in the confinement chamber 100 intő one FRC 450. The fást ions, created primarily by charge exchange, have betatron orbits (with primary radii on the scale of the FRC topology or at least much larger than the characteristic magnetic field gradient length scale) that add to the azimuthal current of the FRC 450. After somé fraction of

ΕΡ 2 780 913 Β1 the discharge (after 0.5 to 0.8 ms intő the shot), a sufficiently largefast ion populationsignificantly improvesthe inner FRC’s stability and confinement properties (see e.g. M.W. Binderbauer and N. Rostoker, Plasma Phys. 56, part 3, 451 (1996/). Furthermore, from a sustainment perspective, the beams from the neutral beam injectors 600 are alsó the primary means to drive current and heat the FRC plasma.

[0046] In the plasma régimé of the FRC system 10, the fástionsslowdown primarilyon plasmaelectrons. During the early partof a discharge, typical orbit-averaged slowing-down times of fást ions are 0.3 - 0.5 ms, which results insignificant FRC heating, primarilyofelectrons.Thefast ions make large radial excursions outside of the separatrix because the internál FRC magnetic field is inherently low (about 0.03 T on average fór a 0.1 T external axial field). The fást ions would be vulnerable to charge exchange loss, if the neutral gas density were too high outside of the separatrix. Therefore, wall gettering and othertechniques (such asthe plasma gun 350 and mirror plugs 440 that contribute, amongst other things, to gas control) deployed on the FRC system 10 tend to minim ize edge neutrals and enable the required build-up of fást ion current.

Pellet Injection [0047] When a significant fást ion population is built up within the FRC 450, with higher electron temperatures and longer FRC lifetimes, frozen H or D pellets are injected intő the FRC 450 from the pellet injector 700 to sustain the FRC partiele inventory of the FRC 450. The anticipated ablation timescales are sufficiently short to provide a significant FRC partiele source. This rate can alsó be increased by enlarging the surface area of the injected piece by breaking the individual pellet intő smallerfragments while in the barrels or injection tubes 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 walls of the injection tűbe by tightening the bend radius of the last segment of the injection tűbe right before entry intő the confinement chamber 100. By virtue of varying the firing sequence and rate ofthe 12 barrels (injection tubes) as well as the fragmentation, it is possible to tune the pellet injection system 700 to provide just the desired level of partiele inventory sustainment. In turn, this helps maintain the internál kinetic pressure in the FRC 450 and sustained operation and lifetime ofthe FRC 450.

[0048] Once the ablated atoms encounter significant plasma in the FRC 450, they become fully ionized. The resultant cold plasma component is then collisionally heated by the indigenous FRC plasma. The energy necessary to maintain a desired FRC temperature is ultimately supplied by the beam injectors 600. In this sense the pellet injectors 700 together with the neutral beam injectors 600 form the system that maintains a steady state and sustains the FRC 450.

Saddle Coils [0049] 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 the electronion frictional force (resulting from collisional ion electron momentum transfer). The FRC system 10 utilizes an innovative technique to provide electron breaking via an externally applied static magnetic dipólé or quadrupole field. This is accomplished via the external saddle coils 460 depicted in Figure 15. The transverse applied radial magnetic field from the saddle coils 460 induces an axial electric field in the rotating FRC plasma. The resultant axial electron current interacts with the radial magnetic field to produce an azimuthal breaking force on the electrons, Fg=-oV_eg<|B_r|²>. Fór typical conditions in the FRC system 10, the required applied magnetic dipólé (or quadrupole) field inside the plasma needs to be only of orderO.001 T to provide adequate electron breaking. The corresponding external field of about .015 T is small enough to nőt cause appreciable fást partiele losses or otherwise negatively impact confinement. In fact, the applied magnetic dipólé (or quadrupole) field contributes to suppress instabilities. In combination with tangential neutral beam injection and axial plasma injection, the saddle coils 460 provide an additional level of control with regards to current maintenance and stability.

Mirror Plugs [0050] The design of the pulsed coils 444 within the mirror plugs 440 permitsthe localgeneration of high magnetic fields (2 to 4 T) with modest (about 100 kJ) capacitive energy. Fór formation of magnetic fields typical of the present operation ofthe FRC system 10, all field lines within the formation volume are passing through the constrictions 442 at the mirror plugs 440, as suggested by the magnetic field lines in Figure 2 and plasma wall contact does nőt occur. Furthermore, the mirror plugs 440 in tandem with the quasi-dc divertor magnets 416 can be adjusted so to guide the field lines onto the divertor electrodes 910, orflare the field lines in an end cusp configuration (notshown). The latter improves stability and suppresses parallel electron thermal conduction.

[0051] The mirror plugs 440 by themselves alsó contribute to neutral gas control. The mirror plugs 440 permit a better utilization ofthe deutérium gas püffed in to the quartz tubes during FRC formation, as gas back-streaming intő the divertors 300 is significantly reduced by the small gas conductance of the plugs (a meager 500 L/s). Most ofthe residual püffed gas inside the formation tubes 210 is quickly ionized. In addition, the high-density plasmaflowing through the mirror plugs 440 provides efficient neutral ionization hence an effective gas barrier. As a result, most ofthe neutrals recycled in the divertors 300 from the FRC edge layer 456 do nőt return to the confinement chamber 100. In addition, the neutrals associated with the operation ofthe plasma guns 350 (as dis9

ΕΡ 2 780 913 Β1 cussed below) will be mostly confined to the divertors 300.

[0052] Finally, the mirror plugs 440 tend to improve the FRC edge layer confinement. With mirror ratios (plug/confinement magnetic fields) in the rangé 20 to 40, and with a 15 m length between the north and south mirror plugs 440, the edge layer partiele confinement time τ|| increases by up to an order of magnitude. Improving τ|| readily increases the FRC partiele confinement.

[0053] Assuming radial diffusive (D) partiele loss from theseparatrixvolume453 balanced byaxial loss (τ||) from the edge layer 456, one obtains (2nr_sL_s)(Dn_s/ö) = (2πΓ₅Ι_₅δ)(η₅/τ||), from which the separatrix density gradient length can be rewritten as δ = (Dt||)^1/2. Here rs, Ls and ns are separatrix radius, separatrix length and separatrix density, respectively. The FRC partiele confinement time is τΝ = [πΓ52|_5<η>]/[(2πΓ5Ι_5)(0η5/δ)] = (<η>/η5)(τ±τ||)ΐ/², where τ± = a²/D with a=r_s/4. Physically, improving τ|| leads to increased δ (reduced separatrix density gradient and drift paraméter), and, therefore, reduced FRC partiele loss. The overall improvement in FRC partiele confinement is generally somewhat less than quadratic because n_s increases with τ||.

[0054] A significant improvement in η| alsó requires that the edge layer 456 remains grossly stable (i.e., no n = 1 flute, firehose, or other MHD instability typical of open systems). Use of the plasma guns 350 provides fór this preferred edgestability. In thissense, the mirror plugs 440 and plasma gun 350 form an effective edge control system.

Plasma Guns [0055] The plasma guns 350 improve the stability of the FRC exhaust jets 454 by line-tying. The gun plasmas from the plasma guns 350 are generated without azimuthal angular momentum, which proves useful in controlling FRC rotational instabilities. As such the guns 350 are an effective means to control FRC stability without the needfortheolderquadrupole stabilization technique. As a result, the plasma guns 350 make it possible to take advantage of the beneficial effects of fást particles or access the advanced hybrid kinetic FRC régimé as outlined in this disclosure. Therefore, the plasma guns 350 enable the FRC system 10 to be operated with saddle coil currents just adequate fór eleetron breaking bút below the threshold that would cause FRC instability and/or lead to dramatic fást partiele diffusion.

[0056] As mentioned in the Mirror Plug discussion above, if η| can be significantly improved, the supplied gun plasma would be comparable to the edge layer partiele loss rate (~ 10²²/s). The lifetime of the gun-produced plasma in the FRC system 10 is in the millisecond rangé. Indeed, consider the gun plasma with density ηθ ~ 10¹³cm^-3 and ion temperature of about 200 eV, confined between the end mirror plugs 440. The trap length L and mirror ratio R are about 15 m and 20, respectively. The ion mean free path due to Coulomb collisions is λ_Η ~

6X10³ cm and, since XülnR/R < L, the ions are confined in the gas-dynamic régimé. The plasma confinement time in this régimé is rgd ~ RL/2VS ~ 2 ms, where Vs is the ion sound speed. Fór comparison, the classical ion confinement time fór these plasma parameters would be rc ~ 0.5τ,ϊ(Ι n R + (InR)⁰·⁵) ~ 0.7 ms. The anomalous transverse diffusion may, in principle, shorten the plasma confinement time. However, in the FRC system 10, ifwe assume the Bohm diffusion rate, the estimated transverse confinement time fór the gun plasma is τ± > r_gd ~ 2 ms. Hence, the guns would provide significant refueling of the FRC edge layer 456, and an improved overall FRC partiele confinement.

[0057] Furthermore, the gun plasma streams can be turnéd on in about 150 to 200 microseconds, which permits use in FRC start-up, translation, and merging intő the confinement chamber 100. If turnéd on around t ~ 0 (FRC main bank initiation), the gun plasmas help to sustain the present dynamically formed and merged FRC 450. The combined partiele inventories from the formation FRCs and from the guns is adequate fór neutral beam capture, plasma heating, and long sustainment. If turnéd on at t in the rangé -1 to 0 ms, the gun plasmas can fill the quartz tubes 210 with plasma or ionize the gas püffed intő the quartz tubes, thus permitting FRC formation with reduced oreven perhaps zero püffed gas. The latter may require sufficiently cold formation plasma to permit fást diffusion of the reversed bias magnetic field. If turnéd on at t < -2 ms, the plasma streams could fill the about 1 to 3 m³ field line volume of the formation and confinement regions of the formation sections 200 and confinement chamber 100 with a target plasma density of a few 10¹³cm^-3, sufficient to allow neutral beam build-up prior to FRC arrival. The formation FRCs could then be formed and translated intő the resulting confinement véssél plasma. In this way the plasma guns 350 enable a wide variety ofoperating conditions and paraméter regimes.

Electrical Biasing [0058] Control of the radial electric field profile in the edge layer 456 is beneficial in various ways to FRC stability and confinement. By virtue ofthe innovative biasing components deployed in the FRC system 10 it is possible to apply a variety of deliberate distributions of electric potentials to a group of open flux surfaces throughout the machine from areas well outside the Central confinement region in the confinement chamber 100. In this way radial electric fields can be generated across the edge layer 456 just outside ofthe FRC 450. These radial electric fields then modify the azimuthal rotation of the edge layer 456 and effect its confinement via EXB velocity shear. Any differential rotation between the edge layer 456 and the FRC core 453 can then be transmitted to the inside ofthe FRC plasma by shear. As a result, controlling the edge layer 456 directly impacts the FRC core 453. Furthermore, since the free energy in the plasma rotation can alsó be responsible fór instabilities, this tech10

ΕΡ 2 780 913 Β1 nique provides a direct means to control the onset and growth of instabilities. In the FRC system 10, appropriate edge biasing provides an effective control of open field line transport and rotation as well as FRC core rotation. The location and shape of the various provided electrodes 900, 905, 910 and 920 allows fór control of different groups of flux surfaces 455 and at different and independent potentials. In this way a wide array of different electric field configurations and strengths can be realized, each with different characteristic impact on plasma performance.

[0059] A key advantage of all these innovative biasing techniques is the fact that core and edge plasma behavior can be effected from well outside the FRC plasma, i.e. there is no need to bring any physical components in touch with the Central hot plasma (which would have severe implications fór energy, flux and partiele losses). This has a major beneficial impact on performance and all potential applications of the HPF concept.

Experimental Data - HPF Operation [0060] Injection of fást particles via beams from the neutral beam guns 600 plays an important role in enabling the HPF régimé. Figure 16 illustrates this fact. Depicted is a set of curves showing how the FRC lifetime correlates with the length of the beam pulses. All other operating conditions are held constantforall discharges comprising this study. The data is averaged over many shots and, therefore, represents typical behavior. It is clearly evident that longer beam duration produces longer lived FRCs. Looking at this evidence as well as other diagnostics during this study, it demonstrates that beams increase stability and reduce losses. The correlation between beam pulse length and FRC lifetime is nőt perfect as beam trapping becomes inefficient below a certain plasma size, i.e., as the FRC 450 shrinks in physical size nőt all ofthe injected beams are intercepted and trapped. Shrinkage of the FRC is primarily due to the fact that net energy loss (~ 4 MW) from the FRC plasma during the discharge is somewhat larger than the totál power fed intő the FRC via the neutral beams (~2.5 MW) fór the particular experimental setup. Locating the beams at a location closer to the mid-plane of the véssél 100 would tend to reduce these losses and extend FRC lifetime. [0061] Figure 17 illustrates the effectsof different components to achieve the HPF régimé. It shows a family of typical curves depicting the lifetime ofthe FRC 450 as a function of time. In all cases a constant, modest amount of beam power (about 2.5 MW) is injected fór the full duration of each discharge. Each curve is representative of a different combination of components. Fór example, operating the FRC system 10 without any mirror plugs 440, plasma guns 350 or gettering from the gettering Systems 800 results in rapid onset of rotational instability and loss of the FRC topology. Adding only the mirror plugs 440 delays the onset of instabilities and increases confinement. Utilizing the combination of mirror plugs

440 and a plasma gun 350 further reduces instabilities and increases FRC lifetime. Finally adding gettering (Ti in this case) on top of the gun 350 and plugs 440 yields the best results - the resultant FRC is free of instabilities and exhibits the longest lifetime. It is clearfrom this experimental demonstration that the full combination of components produces the best effect and provides the beams with the best target conditions.

[0062] Asshown in Figure 1, the newly discovered HPF régimé exhibits dramatically improved transport behavior. Figure 1 illustrates the change in partiele confinement time in the FRC system 10 between the conventionally régimé and the HPF régimé. As can be seen, it has improved by well over a factor of 5 in the HPF régimé. In addition, Figure 1 details the partiele confinement time in the FRC system 10 relatíve to the partiele confinement time in prior conventional FRC experiments. With regards to these other machines, the HPF régimé of the FRC system 10 has improved confinement by a factor of between 5 and close to 20. Finally and most importantly, the natúré of the confinement sealing of the FRC system 10 in the HPF régimé is dramatically different from all prior measurements. Before the establishment of the HPF régimé in the FRC system 10, various empirical scaling laws were derived from data to predict confinement times in prior FRC experiments. All those sealing rules depend mostly on the ratio R²/pj, where R is the radius ofthe magneticfield null (a loose measure ofthe physical scale ofthe machine) and p, is the ion larmor radius evaluated in the externally applied field (a loose measure of the applied magnetic field). It is clearfrom Figure 1 that long confinement in conventional FRCs is only possible at large machine size and/or high magnetic field. Operating the FRC system 10 in the conventional FRC régimé CR tends to follow those sealing rules, as indicated in Figure 1. However, the HPF régimé is vastly superiorand shows that much better confinement is attainable without large machine size or high magnetic fields. More importantly, it is alsó clearfrom Figure 1 that the HPF régimé results in improved confinement time with reduced plasma size as compared to the CR régimé. Similar trends are alsó visible fór flux and energy confinement times, as described below, which have increased by over a factor of 3-8 in the FRC system 10 as well. The breakthrough ofthe HPF régimé, therefore, enables the useof modest beam power, lower magnetic fields and smaller size to sustain and maintain FRC equilibria in the FRC system 10 and future higher energy machines. Hand-in-hand with these improvements comes lower operating and construction costs as well as reduced engineering complexity.

[0063] Fór further comparison, Figure 18 shows data from a representative HPF régimé discharge in the FRC system 10 as a function of time. Figure 18(a) depicts the excluded flux radius at the mid-plane. Fór these longer timescales the conducting steel wall is no longer as good a flux conserver and the magnetic probes internál to the wall are augmented with probes outside the wall to prop11

EP 2 780 913 Β1 erly accountfor magneticfluxdiffusion through the steel. Compared to typical performance in the conventional régimé CR, as shown in Figure 13, the HPF régimé operating mode exhibits over400% longer lifetime.

[0064] A representative cord ofthe line integrated density trace is shown in Figure 18(b) with its Ábel inverted complement, the density contours, in Figure 18(c). Compared to the conventional FRC régimé CR, as shown in Figure 13, the plasma is more quiescent throughout the pulse, indicative of very stable operation. The peak density is alsó slightly lower in HPF shots - this is a consequence of the hotter totál plasma temperature (up to a factorof 2) as shown in Figure 18(d).

[0065] Fór the respective discharge illustrated in Figure 18, the energy, partiele and flux confinement times are 0.5 ms, 1 ms and 1 ms, respectively. At a reference time of 1 ms intő the discharge, the stored plasma energy is 2 kJ while the losses are about 4 MW, making this target very suitable fór neutral beam sustainment. [0066] Figure 19 summarizes all advantages of the HPF régimé in the form of a newly established experimental HPF flux confinement scaling. As can be seen in Figure 19, based on measurements taken before and after t = 0.5 ms, i.e., t < 0.5 ms and t > 0.5 ms, the confinement scales with roughly the square of the eleetron Temperature. This strong scaling with a positive power of T_e (and nőt a negative power) is completely opposite to that exhibited by conventional tokomaks, where confinement is typically inversely proportional to somé power of the eleetron temperature. The manifestation of this scaling is a direct consequence ofthe HPF state and the large orbit (i.e. orbits on the scale ofthe FRC topology and/or at least the characteristic magnetic field gradient length scale) ion population. Fundamentally, this new scaling substantially favors high operating temperatures and enables relatively modest sízed reactors.

[0067] While the invention is susceptible to various modifications, and alternative forms, specific examples thereof have been shown in the drawings and are herein deseribed in detail. It should be understood, however, that the invention is nőt to be limited to the particular forms or methods disclosed, bút to the contrary, the invention is to cover all modifications and alternatives faliing within the scope ofthe appended claims.

[0068] In the deseription above, fór purposes of explanation only, specific nomenclature is setforth to provide a thorough understanding of the present disclosure. However, it will be apparent to one skilled in the art that these specific details are nőt required to practice the teachings ofthe present disclosure.

[0069] The various features of the representative examples and the dependent claims may be combined in ways that are nőt specifically and explicitly enumerated in orderto provide additional useful embodiments ofthe present teachings. It is alsó expressly noted that all value ranges or indications of groups of entities disclose every possible intermediate value or intermediate entity fór the purpose ofthe original disclosure.

[0070] Systems and methods forgenerating and maintaining an HPF régimé FRC have been disclosed. It is understood that the embodiments deseribed herein are fór the purpose of elucidation and should nőt be considered limiting the subject matterofthe disclosure. Various modifications, uses, substitutions, combinations, improvements, methods of productions without departing from the scope ofthe present invention would be evident to a person skilled in the art. Fór example, the reader is to understand that the specific ordering and combination of process actions deseribed herein is merely ilIustrative, unless otherwise stated. As another example, each feature of one embodiment can be mixed and matched with otherfeaturesshown in otherembodiments. Accordingly, the invention is nőt to be restricted except in light ofthe attached claims.