Apparatus and method for harvesting energy from an axially expanding plasma confined by a magnetic field - Patent Application 20070122999

Abstract

Magnetic field systems can generate dynamically varying strong magnetic fields to confine and control particles, objects, or plasmas. Coils in the magnetic field systems used to control the plasma can be used to collect energy from the expanding plasma.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of priority under 35 U.S.C. § 119(e) of U.S. patent application Ser. No. 63 / 386,364, filed December 7, 2022, which is incorporated herein by reference in its entirety for all purposes. [Background technology]

[0002] Strong magnetic fields can be generated by multiple current-carrying coils driven by large currents and high voltages. Such magnetic fields can be used to confine high-energy particles and / or accelerate particles or objects to high velocities. In some cases, strong magnetic fields can be used to confine plasma. Summary of the Invention

[0003] The described implementations relate to methods and apparatus for dynamically controlling plasma confined by a strong magnetic field. The relevant plasmas include (i) coherent structures (plasmoids) of plasma and magnetic fields and / or (ii) mirror-confined plasmas. The magnetic field may be generated using an assembly of electromagnetic coils (more simply referred to as "magnetic coils" or "coils") controlled to confine and / or impart energy to the confined plasma. In some cases, the magnetic coils may be used to directly and repeatedly collect energy from the expanding plasma. For repeated energy exchange with the plasma (e.g., delivering energy to and collecting energy from the plasma), at least a portion of the magnetic field generated by the magnetic coils may be spatially and temporally controlled to pulse the plasma.

[0004] More specifically, current flowing through the magnetic coil generates a magnetic field that drives adiabatic compression of the plasma, acting on the plasma by compressing it in radius and length, increasing its temperature. As the temperature of the plasma increases, fusion of constituent ions within the plasma occurs, producing energetic charged particles that can remain trapped within the plasma and increase its energy. This increases the temperature of the plasma and causes the plasma to expand axially relative to the magnetic field applied by the magnetic coil. This plasma expansion cycle results in an increasing magnetic field around the magnetic coil, which in turn generates an electromotive force via Lenz's law that drives a current in an energy storage element coupled to the magnetic coil. In some implementations, this harvested energy can be diverted to a load, including an energy storage system.

[0005] In some aspects, the technology described herein relates to harvesting energy from a plasma (e.g., a field-reversed configuration (FRC) plasma). A magnetic coil applies a magnetic field to the plasma. This magnetic field adiabatically compresses the plasma, causing it to undergo compression, heating, and fusion. The compression, heating, and fusion cause the plasma to expand axially, which transfers energy to the magnetic coil. This energy is directed from the magnetic coil to an energy storage device, such as a capacitor.

[0006] Adiabatically compressing the plasma can include increasing the current through the magnetic coil to increase the amplitude of the magnetic field.

[0007] Directing energy from the magnetic coil to the energy storage unit may include resonantly transferring energy from the magnetic coil to the energy storage unit.

[0008] In some cases, the current in at least one of the magnetic coils is crowbarred (voltage suppressed) to further resist radial expansion of the plasma and promote axial expansion of the plasma while the plasma undergoes compression, heating, and fusion. Alternatively, to promote axial expansion of the plasma, the magnetic field can be adjusted to radially overpressure the plasma (center) while the plasma undergoes compression, heating, and fusion.

[0009] The compression, heating, and fusion can cause a radial expansion of the plasma that generates additional current in the magnetic coil, which can then be stored as additional energy in the energy storage unit.

[0010] The energy from the energy store can be converted into an electrical current, for example, a direct current or an alternating current.

[0011] Some implementations relate to a method for collecting energy from an expanding plasma, the method including: injecting a plasma into a vessel; sequentially applying a plurality of currents to a plurality of magnetic coils arranged to generate a magnetic field within the vessel and sequentially vary the magnetic field applied to the plasma, such that the plasma begins to expand volumetrically within the vessel and transitions to a stage where the magnetic field resists radial expansion of the expanding plasma; and generating a collectable current in at least one of the plurality of magnetic coils based on the expanding plasma.

[0012] Some implementations relate to a method of collecting energy from a plasma as it expands within a vessel, the method including: applying a plurality of currents to a plurality of magnetic coils arranged along a length of the vessel to create a magnetic field within the vessel, the magnetic field maintaining the plasma in a field-reversed configuration, resisting radial expansion of the plasma and allowing axial expansion of the plasma along the length of the vessel; and receiving a collectable current from at least one magnetic coil of the plurality of magnetic coils during the axial expansion of the plasma, the collectable current being generated in the at least one magnetic coil by the plasma as it expands axially.

[0013] Some implementations relate to a method of confining a plasma and collecting energy from the plasma as it expands, the method including: injecting the plasma into a vessel; applying first currents to a plurality of magnetic coils disposed to generate a magnetic field within the vessel, the magnetic field preparing the plasma in a first state, wherein when the plasma is in the first state, a radius of a separatrix of the plasma in the first state has a first radial value and a length of the separatrix has a first length value; and applying second currents to the plurality of magnetic coils to change the magnetic field to transition the plasma from the first state to a second state, wherein the radius of the separatrix in the second state has a second radial value that is smaller than the first radial value and the separatrix has a second length value in the second state; applying a third plurality of currents to the plurality of magnetic coils to vary the magnetic field when the plasma transitions from the second state to a third state in which the plasma has more energy than the second state and begins to expand beyond at least a second length, the third plurality of currents being selected to generate a magnetic field that resists radial expansion of the separatrix from the second radial value over at least a portion of the length of the separatrix while the length of the separatrix increases beyond the second length value; and receiving a collectable current from at least one magnetic coil of the plurality of magnetic coils while the length of the separatrix increases beyond the second length value, the collectable current being generated by the plasma as it expands beyond the second length.

[0014] Some implementations relate to a supply circuit for a magnetic field system, the supply circuit including: a first energy storage unit (C1); a first circuit branch coupled to a node of the first energy storage unit, the first circuit branch including a first switch (SW2) arranged to conduct current between the first energy storage unit and at least one magnetic coil (130-1) of the magnetic field system when the first switch is in a conductive state; a second circuit branch coupled to a node of the first energy storage unit, the second circuit branch including a second switch (SW4) arranged to conduct current between the first energy storage unit and an external load (210) when the second switch is in a conductive state and the first switch is in a non-conductive state; and a third circuit branch coupled to the node of the first energy storage unit, the second circuit branch including a second switch (SW4) arranged to conduct current between the first energy storage unit and a second energy storage unit (L R a third circuit branch including a third switch (SW3) arranged to pass current between the first energy store and the second energy store to reverse the polarity of the voltage across the first energy store.

[0015] All combinations of the foregoing concepts, and additional concepts discussed in more detail below, are considered to be part of the inventive subject matter disclosed herein (provided such concepts are not mutually inconsistent). In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the inventive subject matter disclosed herein. Terms explicitly used herein that may also appear in any disclosure incorporated by reference herein should be given the meaning most consistent with the specific concepts disclosed herein.

[0016] Those skilled in the art will understand that the drawings are primarily for illustrative purposes and are not intended to limit the scope of the inventive subject matter described herein. The drawings are not necessarily to scale, and in some instances, various aspects of the inventive subject matter disclosed herein may be shown exaggerated or enlarged in the drawings to facilitate an understanding of different features. In the drawings, like reference characters generally refer to like features (e.g., functionally similar and / or structurally similar components). [Brief explanation of the drawings]

[0017] [Figure 1] FIG. 1 shows an embodiment of a magnetic field system for generating a strong magnetic field. [Figure 2] FIG. 2 shows an example of a supply circuit for supplying and withdrawing current to and harvesting energy from at least one magnetic coil in the system of FIG. [Figure 3A] FIG. 3A shows the magnetic field and plasma injection during an operating cycle of the system of FIG. [Figure 3B] FIG. 3B shows the magnetic field and plasma configuration at a first time during an operating cycle of the system of FIG. [Figure 3C] FIG. 3C shows the magnetic field and plasma configuration at a second time during the operating cycle of the system of FIG. [Figure 3D] FIG. 3D shows the magnetic field and plasma configurations at a third time during the operating cycle of the system of FIG. [Figure 3E] FIG. 3E shows the magnetic field and plasma configurations at a fourth time during the operating cycle of the system of FIG. [Figure 4A] FIG. 4A shows an example of the separatrix radius of the plasma as a function of time during an operating cycle of the magnetic field system of FIG. [Figure 4B] FIG. 4B shows an example of the length of the separatrix as a function of time during an operating cycle of the magnetic field system of FIG. [Figure 4C] FIG. 4C shows an example of current flow in the end coil 130-1 of the magnetic coil system of FIG. [Figure 4D] FIG. 4D shows an example of current flow in the middle coil 130-2 of the magnetic coil system of FIG. [Figure 4E] FIG. 4E shows an example of current flow in the central coil 130-3 of the magnetic coil system of FIG. [Figure 5] FIG. 5 shows further details of the energy collection circuitry for the magnetic field system of FIG. [Figure 6A] FIG. 6A shows voltage waveforms associated with the energy harvesting circuit of FIG. 5 and the supply circuit of FIG. [Figure 6B] FIG. 6B shows current waveforms associated with the energy harvesting circuit of FIG. 5 and the supply circuit of FIG. DETAILED DESCRIPTION OF THE INVENTION

[0018] FIG. 1 illustrates an example of a magnetic field system 100 that can be used to generate a dynamic, strong magnetic field (e.g., peak magnetic field values ​​between 0.01 Tesla (T) and 50 T). The system 100 includes multiple magnetic coils 130-1, 130-2, and 130-3 configured to cooperatively generate a magnetic field within a vessel 150. To cooperatively generate the magnetic field, the multiple magnetic coils 130 are spaced sufficiently close to one another that the magnetic field generated by any one coil is added to the magnetic field generated within the vessel 150 by at least one other coil in the system. For example, the space between adjacent coils 130-2 and 130-3 may be equal to or less than the inner diameter D of the coil. The magnetic coil 130 can generate a strong magnetic field within a vessel 150 located adjacent to the magnetic coil 130. In the figure, the vessel 150 and the magnetic coil 130 are shown in cross section.

[0019] In some applications (acceleration of particles or objects), the vessel 150 may be a tube with at least one open end or formed into a loop. In other applications (plasma physics), the vessel 150 may be part of a larger vacuum chamber, for example, with at least one inlet port for introducing plasma. In such cases, the vessel may be made of a dielectric material such as quartz and / or other relevant vacuum-compatible materials. In some cases, the vessel 150 may be a linear tube with an inlet port at each end of the tube, with the plasma injected from one or both ends. Related implementations of plasmas include (i) coherent structures of plasma and magnetic fields (plasmoids) and / or (ii) mirror-confined plasmas. In some implementations, two plasmas are injected at each end of the vessel, accelerated toward each other, and collide at the center of the vessel. The collision may involve controlled coalescence of the injected plasmas so that the resulting merged plasmas maintain the same general structure as the injected plasmas. The collision can result in fully merged plasmas, partial coalescence of plasmas, or no coalescence, with the two plasmas maintaining separate morphologies. In other implementations, a single plasma may already exist within the vessel or may be injected from one side.

[0020] The magnetic coil may, in some cases, comprise multi-turn windings. In other cases, the magnetic coil may be formed as a single-turn or multi-feed, fractional-turn magnetic coil. The single-turn or fractional-turn coil may comprise a solid core, a conductive core, or a superconducting core. The inner diameter of the coil (enclosing the space in which the high magnetic field is generated) can be between 1 centimeter (cm) and 300 cm. Examples of such coils are described in International Patent Application PCT / US2022 / 033424, filed June 14, 2022, entitled "Inertially-Damped Segmented Coils for Generating High Magnetic Fields," which is incorporated herein by reference in its entirety.

[0021] Each of the magnetic coils 130 may be supplied with current from one or more supply circuits 120-1, 120-2, 120-3 (for simplicity of illustration, only one supply circuit is shown for each magnetic coil). Current may be provided over one or more supply lines 125 connected to each coil. The peak amount of current delivered to each coil may be, for example, 100,000 amperes (A) to 200,000,000 A.

[0022] Each of the supply circuits 120 (described in more detail with reference to FIG. 2 below) may include a power source (e.g., a voltage source), at least one energy storage unit (such as a battery, compressor, flywheel, or capacitor; capacitors are particularly useful in applications where fast energy discharge is desirable), and at least one switch that gates the flow of current from the at least one energy storage unit to the associated magnetic coil. The switches in each supply circuit 120 may be controlled (e.g., by the controller 110) independently of the switches in the other supply circuits 120 in the system. In this manner, the current waveform and timing of the current waveform delivered to each of the magnetic coils 130 may be controlled to a significant degree independently of the current delivered to other magnetic coils 130 in the system 100. In some cases, structural limitations of the magnetic field system 100 may limit the amount of variation in amplitude, waveform, and / or timing between two or more magnetic coils 130.

[0023] The controller 110 can communicate with at least one of the supply circuits 120 to control at least the delivery of current from the at least one supply circuit to one or more of the magnetic coils 130 (e.g., by activating a switch of the supply circuit). In some implementations, the controller 110 can additionally control the amount of current delivered by the supply circuit. In some cases, the controller 110 can further control the waveform of the delivered current (e.g., by selecting among individual capacitive and / or resistive elements in the supply circuit 120 and / or adjusting adjustable capacitive and / or resistive elements). The controller 110 can comprise a computer in some cases. In other cases, the controller can comprise a field programmable gate array, a programmable logic circuit, an application specific integrated circuit, a digital signal processor, or some combination thereof.

[0024] In some cases, control of current delivery to the magnetic coils may be distributed among the supply circuits or among trigger control circuits coupled to the supply circuits. For example, the controller 110 may issue a command signal to deliver current to the end coil 130-1. The command signal may be received by the end supply circuit 120-1, or the command signal may be received by a trigger control circuit coupled to the end supply circuit. Upon triggering of the first coil 130-1, the end supply circuit 120-1 or the trigger control circuit may issue a trigger command signal to the intermediate supply circuit 120-2 or a trigger control circuit coupled to the intermediate supply circuit 120-2. In this manner, all magnetic coils may be triggered, and the trigger cycle may be repeated.

[0025] In some implementations, there may be one or more predetermined delays between triggering of the supply circuits 120, energizing their associated magnetic coils 130 in sequential triggering order. For example, the magnetic coils 130-1 near the ends of the coil assembly may be energized first by their associated supply circuits 120-1, after which triggering of the supply circuits progresses inward such that the central coil 130-3 is energized last in the sequence. The delay timing may, in some cases, be electronically programmable by the controller 110 or trigger control circuitry. In some implementations, the delay timing may be manipulated using circuit delay elements connected to the supply circuits 120 that delay successive trigger command signals after an initial trigger command signal is provided to at least one of the supply circuits.

[0026] Regardless of how the trigger timing is determined, the magnetic field system 100 of FIG. 1 allows for (at least some) independent control of the energization of each of the magnetic coils 130. This independent control of the amplitude, waveform, and timing of the current delivered to each of the magnetic coils 130 allows for the generation of a dynamic, pulsating, strong magnetic field within the vessel 150. Trigger command signals may be provided to the magnetic coils 130 in rapid succession using fiber optic cables and high-speed switches. In some cases, adjacent coils may be triggered within 10 nanoseconds of each other. This rapid sequencing of trigger command signals allows for careful control of the plasma through the magnetic coils, allowing the plasma to be formed, maintained, and transitioned between different states. An exemplary circuit for controlling the triggering of the supply circuit is described in International Patent Application PCT / US2022 / 033319, filed June 13, 2022, entitled "High-Speed ​​Switching Apparatus for Electromagnetic Coils," which is incorporated herein by reference in its entirety.

[0027] 2 illustrates an example of a supply circuit 120-1 that may be used to supply and receive current to at least one magnetic coil 130-1 of the magnetic field system 100 of FIG. 1. One or more magnetic coils 130-1 connected to the supply circuit 120-1 may be modeled as an inductor L1. During operation, the supply circuit 120-1 may store and supply energy to the magnetic coils 130-1 to generate a magnetic field that confines and controls the plasma within the vessel 150 (e.g., to compress the plasma radially and axially). The supply circuit 120-1 may include an energy collection circuit portion that collects a portion of the energy delivered to the magnetic coils for storage and subsequent use in the next operating cycle, as described further below. The energy collection circuit portion may be modeled as an inductor L1. R and directional switch SW3. The supply circuit may further include an energy harvesting circuit 245 that can receive energy from the magnetic coil 130-1 to provide the external load 210, as described further below. The energy harvesting circuit 245 may include a switch that is activated to receive current from an energy storage unit C1, which may be implemented as one or more capacitors.

[0028] The supply circuit 120-1 includes an energy storage unit (modeled as a capacitor C1), a power supply (voltage supply V supp, modeled as , switch SW1, and directional switches SW2 and SW3 having diodes D1 and D2. The directional switches may comprise, for example, silicon-controlled rectifiers (SCRs), although other switches may be used. In operation, switch SW1 may be closed to provide an initial charge to energy storage C1 (with switches SW2, SW3, and SW5 open). Switch SW1 may then open and SW2 may close to deliver a current pulse to magnetic coil 130-1. Unused energy from the pulse and / or electrical energy harvested from the magnetic coil 130-1 (which, combined with unused energy from the pulse, may exceed the amount of energy stored in capacitor C1 before the start of the pulse) may pass through capacitor C1 and accumulate charge therein. In some implementations, when a peak charge (of opposite polarity) has accumulated in capacitor C1, which may be sensed by optional sensing and control circuitry 220, switch SW2 is opened and switch SW3 is closed to charge another energy storage (inductor L in this example). R The recovered energy in the energy storage C1 may be inverted through a recovery circuit branch including a capacitor C2. The inversion can recharge the capacitor C1 to its initial polarity for the next operating cycle.

[0029] If used, the sensing and control circuit 220 may include a voltage sensor that detects the voltage on the charge node of the energy storage unit C1 and logic circuitry that outputs a control signal to one or more of the switches SW2, SW3, SW5 and / or the energy collection circuit 245. When additional energy is harvested from the magnetic coil (which may be detected by the sensing and control circuit 220 as a voltage above a threshold voltage at the energy storage unit), the energy collection circuit 245 may be activated to provide a portion of the harvested energy to the external load 210. The external load may or may not include a power conditioner to convert the output power to a waveform suitable for power applications (such as a conventional two-phase or three-phase AC waveform) or to a DC voltage. In some implementations, the load 210 may include a power grid. Other supply circuits 120-1 capable of recovering unused energy passing through the magnetic coil 130-1 are also possible, and exemplary supply circuits can be found in International Patent Application No. PCT / US2022 / 032277, filed June 3, 2022, entitled "Energy Recovery in Electrical Systems," which is incorporated herein by reference in its entirety and is included in the appendix attached to this application.

[0030] 3A, 3B, 3C, and 3D show simplified time sequence images of exemplary magnetic field lines B (dashed lines) and the configuration of the confined plasma 310 of the magnetic field system 100 of FIG.

[0031] The figure shows one example implementation in which a pulsating strong magnetic field may be used to directly and repeatedly deposit and extract energy from the plasma 310. In one embodiment, when the magnetic field system 100 collides with two or more plasmas as described above with reference to FIGS. 3A and 3B, the energy and size of the plasmas may increase as the kinetic energy of the moving plasmas is converted into plasma energy. In some cases, this increase in energy may also exert a back electromotive force (EMF) on the system's magnetic coils, generating additional current in the coils. The additional current may supplement the current provided by the energy storage unit C1 and / or may be recovered or harvested.

[0032] To simplify the illustration, the vessel 150, the supply circuit 120, and the controller 110 are omitted, and only the magnetic coil assembly 300 is shown with the plasma. The magnetic field lines B are shown in rudimentary dashed lines, and the spatial extent of the plasma 310 is shown in rudimentary solid lines (e.g., the location of the plasma's separatrix). The separatrix is ​​the location of the last closed magnetic field line within the plasma 310. While the magnetic coil assembly 300 and plasma 310 are three-dimensional, a cross-sectional view of the magnetic coil assembly 300 and plasma 310 is shown. For example, the magnetic coil 130 and plasma 310 are symmetric about a central axis 305 through the vessel. While only five coils are shown, the magnetic field system 100 may have 10 to 100 or more coils. Furthermore, the illustration may only show the central portion of the magnetic field system. Additional coils may be present at each end of the system to form and inject the plasma from each end toward the center of the magnetic field system, where the plasma merges.

[0033] To initiate an operating cycle for some implementations, two or more plasmoids 310a, 310b can be injected into the magnetic coil assembly 300, as shown in FIG. 3A. As will be appreciated by those skilled in the art, a plasmoid is a coherent structure of plasma and magnetic field. The plasmoids 310a, 310b can be formed at the end regions of the magnetic coil assembly 300 and then accelerated toward each other using the magnetic coil 130. The plasmoids can merge within the vessel 150 of the magnetic coil assembly to form a single plasma 310, depicted in FIG. 3B. The merging of the plasmoids can add heat to the plasma 310. The plasma 310 can be heated until the plasma is stable and reaches a separatrix radius r. s and axial length l s (±z direction). Note that in other configurations, the plasmoids may or may not partially converge, but remain close to each other in a more confined space.

[0034] At a first time t=t1, the magnetic field system 100 may be placed in an initial or first state of its operating cycle. Currents I1, I2, and I3 may be applied to the system's magnetic coil 130 to generate a magnetic field B that confines the plasma 310 to a first spatial extent. The plasma may have a toroidal shape or may be a field-reversed configuration (FRC) plasma. For example, the plasma may be mostly or completely ionized with fully magnetized electrons and likely to further contain magnetized ions. Furthermore, the plasma may have a significant diamagnetic current and a plasma beta value β of 30% or greater. The beta value is the ratio of the pressure of the plasma given by Equation 2 to the magnetic pressure above the plasma given by Equation 1 below, averaged over the surface of the plasma. The amounts of currents I1, I2, and I3 at time t1 may be approximately equal relative to the initial state or may increase slightly with distance from the center of the vessel to confine the plasma to the center of the vessel 150 and coil assembly 300. Due to the current applied to the magnetic coil 130, an azimuthal current (indicated by the dots and Xs) circulating around the plasma can be maintained within the vessel 150. In this initial state, the plasma separatrix has an initial radius r perpendicular to the axis 305. s and half length l in the direction along axis 305 s The initial volume of plasma V o may be present.

[0035] The current delivered to the magnetic coil 130 is then increased to energize the plasma 310, transitioning it from the initial state to a second state. At a second time t=t2, when the second state occurs, the volume of the plasma can be reduced compared to the volume of the plasma in the first state. Figure 3C shows a simplified representation of this reduction in plasma volume. Increasing currents I1, I2, and I3 increase the strength of the magnetic field B, which increases the magnetic pressure on the plasma 310, pushing the plasma radially inward, reducing the plasma's volume and increasing the plasma's internal temperature and pressure. The increased magnetic pressure is shown in the diagram as wide black arrows pointing toward the top and bottom of the page. This increased pressure is primarily exerted radially around the periphery of the plasma. Pressure on the edges of the plasma can also reduce its length. The local magnetic pressure P acting on the plasma is B teeth,

[0036]

number

[0037] To further confine the plasma, the current applied to the magnetic coils 130 may be applied differently and in a time sequence to each coil. For example, the initial increase in current I3 applied to the coils at the ends of the coil assembly (also called mirror coils) may be greater than the increase in current I1 applied to the coils at the center of the coil assembly 300 to initially form magnetic field lobes 340 near the ends of the coil assembly, as shown in FIG. 3C. The dashed lines indicate contours of approximately equal magnetic field strength. The lobes 340 can exert magnetic pressure on the edges of the plasma, reducing their length.

[0038] As shown in FIG. 3D , these lobes 340 can be increased and / or propagated inward toward the center of the coil assembly 300 by sequencing the time-integrated increase in current applied to each adjacent coil in a direction moving toward the center of the coil assembly 300 (as further described in connection with FIGS. 4C-4E ). For example, the peak increase in current I3 can reach the central magnetic coil 130-3 before the peak increase in current I2 reaches the intermediate magnetic coil 130-2. This time-sequence application of current can increase the magnetic pressure acting axially on the plasma, as indicated by the wide black arrows pointing left and right in FIGS. 3C and 3D . In response to the magnetic pressure, the plasma 310 exerts a pressure back on the magnetic field, indicated in the figures by the wide gray arrows. The counter-reaction pressure within the plasma is

[0039]

number

[0040] As shown in FIG. 3D, the plasma 310 reaches a minimum volume V min When the magnetic coil reaches , the energy of the plasma may increase or be increased so that it cannot be compressed any further. For example, an internal reaction (e.g., nuclear) may occur, or energy from another source (such as a high-power laser, particle beam, or microwave heating) may be imparted to the plasma 310. A rapid increase in plasma energy or the production of energy by the plasma may indicate another state of the plasma. Examples of nuclear reactions include fusion (e.g., DT fusion, DD fusion, and / or 3 He-D fusion).

[0041] As the energy increases, the plasma 310 may begin to expand into an elongated shape, as shown in FIG. 3E, as the plasma transitions to yet another state. Energy may be released from the plasma and collected by the magnetic coil assembly 300 during the plasma expansion. The expanding plasma increases the magnetic field around the magnetic coil, generating an electromotive force via Lenz's law. The electromotive force (resonantly) drives a current through the magnetic coil and into the energy storage element. This current recharges at least a portion of the energy storage in the supply circuit 120. In some implementations, the energy collected from the expanding plasma, along with the energy recovered from the energy recovery circuit, may exceed the energy delivered to the coil, and a portion of the excess energy is realized as usable energy by the system, either through another energy storage device or through the energy collection circuit that powers the external load 210. This energy collection represents a direct coupling of energy from the plasma.

[0042] Furthermore, regardless of plasma expansion, energy can be extracted from the plasma in other ways. For example, a working gas can pass over and around the plasma, releasing heat. In other implementations, charged particles or neutrons can be ejected from the plasma and transfer energy to a receiving material (such as a photovoltaic energy recovery system for charged particles or a molten blanket for neutrons). In some implementations, heat generated by the plasma when producing energy may be captured and converted to electrical energy (e.g., by generating steam and driving a steam turbine). Such conversion processes represent indirect coupling of energy from the plasma 310.

[0043] According to some implementations, the plasma 310 may be constrained in at least one dimension as it expands from a state at time t3 to another state at a later time t4, a plasma configuration for which is shown rudimentarily in Figure 3E. For example, currents applied to the internal magnetic coils 130-2, 130-3 may locally resist the expansion of the separatrix radius or constrain the plasma 310 to a constant separatrix radius r while it expands. s maintain or in a controlled manner s The magnetic coil 130 may be controlled (e.g., with a feedback loop or by applying a predetermined waveform to the coil) to allow the magnetic coil 130 to expand. To maintain a constant separatrix radius, an increased or decreased current may be applied to at least a portion of the magnetic coil 130 (e.g., the inner coil 130-2).

[0044] In some cases, the current in one or more of the coils may be maintained using a circuit across the coil's supply line to resist plasma expansion. In some implementations, this is achieved by a crowbar circuit. The circuit may be within the supply circuit or may be activated by the supply circuit (e.g., by closing switch SW5 via the sensing and control circuit 220). In some implementations, the sensing and control circuit 220 may control the amount of current in each coil by controlling the opening and closing of switches SW2, SW3, and SW5, as well as at least one switch in the energy collection circuit 245. For example, the sensing and control circuit 220 may crowbar one or more coils 130-3 (and possibly coil 130-2) near the center of the vessel 150 to resist radial plasma expansion at that location. As the plasma expands axially into the uncrowbarred coils (coil 130-1 and possibly coil 130-2), the current in those coils increases, generating energy for energy collection and providing energy to the respective energy storage units C1. The coil into which the plasma expands can be the coil 130 used to otherwise guide the plasma. Additionally or alternatively, the coil into which the plasma expands can be an additional auxiliary coil 135 (shown in FIG. 1 ) located between or outside the coils 130.

[0045] Crowbarring the central coil 130-3 prevents radial expansion of the plasma at the center of the vessel 150, instead causing a (greater) axial expansion of the plasma. If desired, the current through the central coil 130-3 can be increased to radially overpressure the plasma at the center of the vessel 150, resulting in increased fusion energy production and / or causing the plasma to elongate (expand axially) by an even greater amount and / or at a faster rate, potentially producing more harvestable energy than possible via axial expansion.

[0046] In one implementation, the circuit is timed so that the majority of the rear EMF component is generated after the peak current in the coil is reached. As a result, the net rear EMF contributes to current flow in the direction of the entire circuit and toward the recharging capacitor C1.

[0047] In systems with feedback control of the current applied to coil 130, the voltage may be sensed on the magnetic coil to detect changes in the separatrix radius of the plasma. (As will be understood by those skilled in the art, the separatrix radius may be determined from the voltage and the magnetic field.) Additionally or alternatively, diamagnetic probes and / or other magnetic sensors (such as a sensing coil loop around a magnetic coil) may be positioned at one or more locations along the axis of vessel 150 to measure r at one or more locations along the axis of vessel 150. s There may be multiple sensors at each position along the axis of the vessel 150. The sensed voltage and / or magnetic field may be processed in a feedback loop to determine the separatrix radius r s The amount of current applied to each magnetic coil can be determined to control

[0048] During the operating cycle between times t1 and t3, the current value of at least one of the magnetic coils may be increased by a factor having a value in the range of 1.5 to 10,000 (or any subrange therein) from the initial current value at time t1. The magnetic field magnitude at the center of the vessel 150 may be increased by a factor having a value in the range of 1.5 to 10,000 (or any subrange therein), and the plasma volume may be decreased by a factor having a value in the range of 2 to 1,000 (or any subrange therein) during the time interval t1 to t3. The radius of the plasma separatrix is ​​increased from the initial value r before the current increase. si may be decreased by a factor in the range of 1.5 to 20 (or any subrange therein, e.g., 1.5 to 5) compared to r. siThe initial value of t1 to t3 may be between 1 cm and 100 cm. The length of the separatrix may be reduced by a factor having a value in the range of 1.5 to 50 (or any subrange within this range) compared to the initial length before the current is increased to compress the plasma 310. The initial length of the separatrix may be between 5 cm and 5 m. The time interval from t1 to t3 may have a duration having a value in the range of 1 nanosecond to 100 milliseconds (or any subrange within this range).

[0049] Maintaining a constant separatrix radius (or r s By allowing the plasma 310 to controllably expand, the plasma 310 remains well coupled to the coil assembly 300. The plasma and its azimuthal current wall can then expand primarily axially along the coil assembly 300, achieving its longest length at time t4, as shown in FIG. 3E. As the plasma expands axially, the current in the magnetic coil 130 expands along at least a central portion of the coil assembly 300 with a constant and approximately equal separatrix radius r s In some cases, the sequence may be controlled to maintain a radius r s may allow the plasma to expand in a controllable manner. The axial flux of the plasma current and associated magnetic field can generate currents in one or more magnetic coils of the coil assembly 300 or in one or more auxiliary magnetic coils distributed along the vessel 150. The generated currents can be collected as usable energy. This method of energy collection represents a direct coupling of energy from the plasma. In some cases, the same coils used to control the expansion of the plasma (e.g., to maintain a nearly constant separatrix radius while the plasma expands axially) are used to collect energy from the expanding plasma.

[0050] After time t4, the plasma 310 may cool to the extent that it can no longer provide harvestable energy and / or maintain its expanded volume, imparting an amount of energy to the coil assembly. In some cases, the plasma 310 may then begin to return to the initial state shown in FIG. 3B. The current to the magnetic coil may be adjusted to return the plasma to the initial state for the next operating cycle.

[0051] During this process, portions of plasma 310 may leak out the edge of vessel 150. The magnetic field accelerates the escaping portion of plasma, creating a plume of high-speed particles that travel along the vessel's longitudinal axis and away from the center of vessel 150. Particles may continuously leak out of vessel 150 throughout the process shown in Figures 3A-3E. In some cases, plasma 310 may decay into an open field line plasma after time t4.

[0052] New plasma may be injected in each cycle (e.g., after time t) to replenish the supply of components that can react when the plasma is compressed in the next cycle. Plasma removal and injection may be controlled by one or more magnetic coils located at the ends of the magnetic field assembly 100. The process of plasma injection, compression, constrained expansion, energy collection, and product removal may then be repeated cyclically during operation of the magnetic field system 100.

[0053] Plasma configurations in addition to or other than those described above may be achieved in some implementations of the system. For example, in a third state, the axial expansion of the plasma may be asymmetric, and the plasma may be expelled in one direction (e.g., to create a thrust effect). In some cases, the plasma may oscillate between different states one or more times during an operating cycle (e.g., one or more times between the plasma state at time t2 shown in FIG. 3C and the plasma state at time t3 shown in FIG. 3D).

[0054] In some implementations, the supply circuit 120 may be used to utilize electrical energy collected from the magnetic coil 130 during plasma expansion. For example, a portion of the collected electrical energy (which may exceed the energy supplied to the magnetic coil in combination with energy recovered from the energy recovery circuit) may be stored in an energy storage section of the power supply circuit and / or an additional energy storage section that can be switched into connection with the magnetic coil. Another portion of the collected energy may be provided to a load 210, as described in connection with FIG. 2 and further explained below. The load 210 may be any device that consumes or stores electrical energy, including a power grid. At least a portion of the stored energy may be used during one or more intervals of an operating cycle (e.g., when the plasma expands from a fully expanded volume to an initial state volume V o When the magnetic field system is in a closed state, the stored energy may be dumped to an external load. A portion of the stored energy may be retained for the next operating cycle of the magnetic field system.

[0055] 4A-4E plot example dynamics of plasma and current characteristics over an operating cycle of the magnetic field system of FIG. 1 according to some implementations. In this example, the plasma separatrix radius r s can evolve with time for at least part of a compression / expansion cycle, as shown in Figure 4A. s is the initial radius r at time t0 si The operating cycle begins with the increasing magnetic field, which reaches a minimum radius r at time t3. min In some cases, the separatrix radius can then be reduced to the separatrix length l, as further shown in FIG. s is allowed to expand within the magnetic field system 100, so that it remains approximately constant (e.g., r min (within 10% or 20% of the radius r) s To maintain the local magnetic pressure P acting radially on the sidewall of the plasma, B is approximately equal to the local plasma pressure P acting radially outward. Alternatively, rs Maintaining a nearly constant value can be expressed as maintaining the plasma sidewall beta β approximately equal to 1, where β=P / P B In some cases, the separatrix radius may be controlled in a way that allows some expansion of the separatrix radius (e.g., up to 50% during the time interval t3 to t4). s Such control of (whether limited to a substantially constant or controllably expandable) may be achieved by controlling the current waveform applied to the magnetic coil 130 of the magnetic field system 100. At a later stage in the operating cycle (after t4), as the current pulse applied to at least a portion of the magnetic coil 130 is reduced, the separatrix radius and length may return to their initial state and may return to their initial values ​​for the start of the next operating cycle.

[0056] The duration of the operating cycles shown in FIGS. 4A-4E may be from about or exactly 1 microsecond to about or exactly 1,000 milliseconds (or any subrange within this range). However, shorter or longer durations may be possible in some implementations. In some cases, each operating cycle may further include a recovery interval (e.g., between time t4 and the application of a current pulse to the magnetic coil in the next operating cycle). The recovery interval may allow time for heat dissipation and / or reinitialization of system components (e.g., heat dissipation within vessel 150, heat dissipation and resetting of switches in supply circuit 120, recharging energy storage in supply circuit 120, removal of spent plasma, injection of new plasma, etc.).

[0057] 4C-4E show the r s and l s 1 shows an example current waveform that can produce the dynamic behavior of s and l sThe dynamic behavior of the coil 130-1 can be determined. The example waveform shows that during the time interval t0-t2, higher current first reaches the end coil 130-1, then the middle coil 130-2, and finally the central coil 130-3. The waveform during the time interval t3-t4 is plotted against the separatrix radius r as described above. s Approximately its minimum value r min or may be controlled to expand in a controlled manner as shown in FIG. 4A. In some cases, the separatrix radius r s The controlled expansion of the plasma 310 may improve particle confinement time and stability.

[0058] 4D shows an example of a current waveform applied to the intermediate coil 130-2, which may be similar to the current waveform applied to the central coil 130-1 during the time interval t3 to t4, since the separatrix radius is also constrained to a substantially constant value by the intermediate coil or can controllably expand.

[0059] 4E shows an example of a current waveform applied to the central coil 130-3. The current waveform applied to the central coil may decrease more rapidly than the current waveforms applied to the middle and end coils during the time interval t3-t4 to allow for expansion of the length and radius of the plasma 310 at the ends of the plasma 310. This faster decrease in current in the central coil may be beneficial in allowing the expanding plasma 310 to drive more magnetic flux through the end coils of the magnetic field system 100, generating more collectible current.

[0060] 3A-3E are rudimentary diagrams depicting plasma configurations at time snapshots; the plasma may rapidly pass through these configurations during an operating cycle of the system. Similarly, the waveforms in FIGS. 4A-4E rudimentary illustrate the evolution of the current applied to the magnetic coils 130 of the magnetic field system 100. Similarly, for certain configurations, such as a crowbar configuration in which the central coil maintains or overpressures the center of the plasmoid, the diagrams may look even different (e.g., longer or faster axial expansion, longer peak currents maintained in the central coil). At any given time snapshot, the plasma 310 can be said to be in a particular state, having a particular size, configuration, and energy. Thus, the plasma 310 can rapidly pass through many states during an operating cycle of the system 100.

[0061] FIG. 5 illustrates an exemplary energy collection circuit 245 that can be used in the magnetic field systems of FIGS. 1 and 2. In FIG. 5, the circuit 245 includes an aperture switch SW4 (implemented as a MOSFET), a capacitor C2, and a power converter 510 (e.g., a DC-AC converter). Other types of power converters can be used in other implementations (e.g., a DC-DC converter). Power from the power converter 510 can be provided to any suitable load, including a commercially available AC power grid. The energy collection circuit 245 can further include an inductor L2 (e.g., operating at least partially as a choke) at its input that couples to an energy storage unit C1 of the supply circuit 120-1, as shown in FIG. 2. The energy storage unit C1 is the same component from which energy is recovered via the energy recovery circuits described above in International Patent Application PCT / US2022 / 032277, entitled "Energy Recovery in Electrical Systems." Thus, the energy collection circuit 245 can function in combination with these energy recovery circuits in the magnetic field system 100. In high power applications, the components of the energy harvesting circuit 245 must be able to handle high voltages and large amounts of current (e.g., at least 10 3 bolts and at least 10 3It should be able to handle (amps).

[0062] The aperture switch SW4 is a switch that can be opened when current is flowing through the switch. Examples of such a switch include a silicon-controlled rectifier or an insulated gate bipolar transistor (IGBT). Another example of such a switch is a power metal-oxide semiconductor field-effect transistor (power MOSFET). Other types of aperture switches can be used in the energy collection circuit 245.

[0063] Capacitor C2 may be used to temporarily store energy received from magnetic coil 130-1 for power conversion by power converter 510. In some implementations, capacitor C2 may not be included, and instead energy storage C1 of supply circuit 120-1 is used to store a portion of the harvested energy before power conversion by power converter 510 and delivery to external load 210. In such implementations, inductor and / or switch SW4 may be directly coupled to energy storage C1.

[0064] 6A and 6B show voltage and current waveforms associated with the energy harvesting circuit 245 of FIG. 5 and the supply circuit 120-1 of FIG. 2, respectively. These waveforms may occur during each operating cycle of the magnetic field system 100, which may be repeated periodically (e.g., once every 10 seconds, once every second, or more than once every second). FIG. 6A shows the voltage across capacitors C1 and C2. FIG. 6B plots the current flow in capacitor C1.

[0065] To begin an operating cycle at time t1, the voltage on energy storage C1 is charged to an initial value by supply circuit 120-1. The initial value in FIG. 6A is normalized to 1 but can be any value between 100 volts and 100 kV. While C1 is charging, switch SW1 (FIG. 2) closes to deliver energy to energy storage C1, and switches SW2, SW3, and SW4 open to prevent current flow in their respective circuit branches.

[0066] At time t1, SW1 opens (transitioning to a non-conductive state) and SW2 closes (transitioning to a conductive state), supplying current to magnetic coil 130-1 and generating a magnetic field that helps compress the plasma within vessel 150. A similar effect occurs in the other supply circuits 120 in the system, as described above in connection with Figures 3A-3D and 4C-4E. As current flows out of energy storage C1 (shown in Figure 6B), the voltage across the capacitor drops (shown in Figure 6A), causing the plasma to compress to a minimum size at time t3 (shown in Figure 3D).

[0067] In some implementations, switch SW2 closes in response to a control signal from sensing and control circuit 220. For example, sensing and control circuit 220 detects a voltage level that exceeds a preset threshold voltage and issues a control signal to close switch SW2. In other implementations, switch SW2 closes automatically. For example, switch SW2 is implemented as an SCR that automatically closes when the voltage across the switch exceeds a threshold (e.g., exceeds the breakover voltage of the switch).

[0068] At time t3, reactions within the plasma may begin to expand the length of the plasma (axially along the vessel 150, as shown in FIGS. 3E and 4B and described above, by the interval t3-t4). This expansion may generate a back electromotive force in the magnetic coil 130, which imparts additional energy and current flow to the coil (as described above). This additional energy causes an increase in current flow, shown over the interval t3-t4 in FIG. 6B. This increased current flow may contribute to the recharging of energy storage C1.

[0069] The increase in current flow in the magnetic coils over the interval t3–t4 is due to the increase in the radius r of the separatrix as the plasma expands axially. s For example, the current flow is in a direction that increases the magnetic field generated by the coil, which acts to compress the plasma.

[0070] At time t5, energy storage C1 has received enough charge to begin the next stage of operation. When C1 is sufficiently recharged or charged beyond a certain value, switch SW2 opens, preventing further charging of energy storage C1. In some cases, switch SW2 may open in response to detecting a voltage across C1 exceeding a threshold level. For example, sensing and control circuit 220 may detect the voltage across C1 and issue a control signal to open switch SW2. In other implementations, switch SW2 can open automatically. For example, the switch may be implemented as an SCR that automatically opens when the current through the switch drops below a threshold (e.g., a latching current).

[0071] When SW2 opens, or shortly thereafter at time t6, the energy harvesting circuit 245 is activated. Activation may include closing switch SW4 to allow current from the magnetic coil 130-1 to flow through inductor L2 to capacitor C2 (if present) and / or power converter 510. FIG. 6A shows the charging of capacitor C2 until time t7, when switch SW4 opens. The opening and closing of switch SW4 may be responsive to control signals from the sensing and control circuit 220. In this manner, energy may be harvested from the magnetic field system 100. The period t1-t7 may be between 1 microsecond and 100 milliseconds (e.g., 10 microseconds, 100 microseconds, 1 millisecond, 10 milliseconds, or any other value between 1 microsecond and 100 milliseconds) for some magnetic field systems, although shorter or longer periods may be possible.

[0072] In some implementations, the charge on energy storage C1 is transferred via switch SW3 and inductor L R The energy recovery circuit branch including switch SW4 may be reversed. For example, after time t7, switch SW3 is closed to reverse the polarity of the voltage across C1 and then opened. In other cases, the charge on energy storage C1 may be reversed prior to energy harvesting using energy harvesting circuit 245. For example, switch SW3 may be closed to reverse the polarity of the voltage across C1 and then opened before switch SW4 is closed. Operating the system in this manner reverses the polarity of the voltage stored on capacitor C2 but functionally charges the capacitor for use in future cycles.

[0073] In some implementations of the magnetic field system 100, the energy collected from the expanding plasma by the energy collection circuit 245 is the majority or only energy obtained from the magnetic field system 100. This energy may be retained for future device operation and / or provided to an external load. In some cases, this energy may be a small percentage of the total energy generated by the plasma after reactions occur (or the energy generated by the plasma itself may be small), but it may also be excess energy from the system if the system uses an energy recovery circuit to recharge the energy storage unit C1, as described above. The energy recovery circuit may provide sufficient system efficiency so that the energy collected by the expanding plasma is excess energy for other uses.

[0074] Although the above energy collection discussion has primarily been in terms of the plasma expanding axially along the vessel 150, the radial expansion of the plasma along the central coil 130-1 may also contribute to the generation of the back EMF of the coil 130 and harvestable energy from the system. That is, in some systems, both axial and radial expansion of the plasma may occur during the time interval t3-t4.

[0075] conclusion While various inventive embodiments have been described and illustrated herein, those skilled in the art will readily envision various other means and / or structures for performing the functions and / or obtaining one or more of the results and / or advantages described herein, and each such variation and / or modification is deemed to be within the scope of the inventive embodiments described herein. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are intended to be exemplary, and that the actual parameters, dimensions, materials, and / or configurations will depend on the particular application for which the teachings of the present invention are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific inventive embodiments described herein. Accordingly, the foregoing embodiments are presented by way of example only, and it should be understood that, within the scope of the appended claims and their equivalents, the inventive embodiments may be practiced otherwise than as specifically described and claimed. The inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and / or method described herein. Furthermore, any combination of two or more such features, systems, articles, materials, kits, and / or methods is included within the inventive scope of the present disclosure, if such features, systems, articles, materials, kits, and / or methods are not mutually inconsistent.

[0076] Also, various inventive concepts may be embodied as one or more methods, examples of which are provided. The acts performed as part of a method may be ordered in any suitable manner. Thus, although exemplary embodiments are shown as sequential acts, embodiments may be constructed in which acts are performed in a different order than shown, which may include performing some acts simultaneously.

[0077] All definitions defined and used herein should be understood to control for any dictionary definitions, definitions in documents incorporated herein by reference, and / or ordinary meaning of the defined terms.

[0078] The indefinite articles "a" and "an" as used herein in the specification and claims should be understood to mean "at least one," unless expressly indicated to the contrary.

[0079] As used herein in the specification and claims, the term "and / or" should be understood to mean "one or both" of the components so conjoined, i.e., components that are conjunctively present in some cases and disjunctively present in other cases. Multiple components listed with "and / or" should be construed in the same manner, i.e., "one or more" of the components so conjoined. Other components, whether related or unrelated to the components specifically identified, may optionally be present other than the components specifically identified by the "and / or" clause. Thus, as a non-limiting example, a reference to "A and / or B" can refer in one embodiment to A only (optionally including components other than B), in another embodiment to B only (optionally including components other than A), in yet another embodiment to both A and B (optionally including other components), etc.

[0080] As used herein in the specification and claims, "or" should be understood to have the same meaning as "and / or" as defined above. For example, when separating items in a list, "or" or "and / or" should be interpreted as being inclusive, i.e., including at least one of the number or list of elements, but including two or more, and optionally, additional unlisted items. When used in the claims, only terms clearly indicated to the contrary, such as "only one of," or "exactly one of," or "consisting of," will refer to the inclusion of exactly one element of the number or list of elements. Generally, as used herein, the term "or" will only be interpreted as indicating exclusive alternatives (i.e., "one of, or the other, but not both") when preceded by exclusive language, such as "either," "one," "only one," or "exactly one." When used in the claims, "consisting essentially of" shall have its ordinary meaning as used in the field of patent law.

[0081] As used herein and in the claims, the phrase "at least one," in reference to a list of one or more elements, means at least one element selected from any one or more of the elements in the list of elements, but it should be understood that it does not necessarily include at least one of each and every element specifically listed in the list of elements, nor does it exclude any combinations of elements in the list of elements. This definition also allows for the optional presence of elements other than those specifically identified in the list of elements to which the phrase "at least one" refers, whether related to the specifically identified elements or not. Thus, as non-limiting examples, one may refer to "at least one of A and B" (or, equivalently, "at least one of A or B" or, equivalently, "at least one of A and / or B"; in one embodiment, for at least one, optionally including more than one A, and no B (and optionally including components other than B); in another embodiment, for at least one, optionally including more than one B, and no A (and optionally including components other than A); in yet another embodiment, for at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other components); etc.

[0082] In the claims, as well as in the above specification, all transitional phrases such as "comprise," "include," "carry," "have," "contain," "include," "hold," "comprise," and the like, are to be understood as open-ended, i.e., meaning including, but not limited to. As set forth in the U.S. Manual of Patent Examining Procedure, Section 2111.03, only the transitional phrases "consisting of" and "consisting essentially of" shall be closed or semi-closed transitional phrases, respectively.

Claims

1. adiabatically compressing a plasma in a magnetic field generated by a magnetic coil, causing the plasma to compress, heat, and fuse, the compression, heating, and fusion causing the plasma to expand axially, and the axial expansion of the plasma transferring energy to the magnetic coil; directing the energy from the magnetic coil to an energy storage device; A method for harvesting energy from a plasma, comprising:

2. The method of claim 1 , wherein the plasma is a field-reversed configuration (FRC) plasma.

3. The method of claim 1 , wherein adiabatically compressing the plasma comprises increasing the current through the magnetic coil to increase the amplitude of the magnetic field.

4. The method of claim 1 , wherein directing the energy from the magnetic coil to the energy storage comprises resonantly transferring the energy from the magnetic coil to the energy storage.

5. 10. The method of claim 1, further comprising the step of crowbarring a current in at least one of the magnetic coils to further resist radial expansion of the plasma and promote axial expansion of the plasma during compression, heating and fusion of the plasma.

6. The method of claim 1 , further comprising the step of radially overpressuring the plasma to promote the axial expansion of the plasma during compression, heating and fusion of the plasma.

7. 2. The method of claim 1, further comprising the steps of: the compression, heating, and fusion causing a radial expansion of the plasma, the radial expansion of the plasma generating additional current in the magnetic coil, and storing the additional current as additional energy in the energy storage unit.

8. The method of claim 1 further comprising converting energy from the energy storage into electrical current.

9. 9. The method of claim 8, wherein the energy storage comprises at least one capacitor and the current is direct current.

10. 9. The method of claim 8, wherein the energy storage comprises at least one capacitor and the current is an alternating current.

11. 1. A system for collecting energy from a plasma, comprising: a magnetic coil that adiabatically compresses the plasma using a magnetic field, causing compression, heating, and fusion in the plasma, the compression, heating, and fusion causing the plasma to expand axially, and the axial expansion of the plasma transferring energy to the magnetic coil; an energy storage unit operatively connected to the magnetic coil and receiving the energy from the magnetic coil; A system comprising:

12. The system of claim 11 , wherein the plasma is a field-reversed configuration (FRC) plasma.

13. The system of claim 11 , wherein the magnetic coil resonantly transfers the energy to the energy storage unit.

14. The system of claim 11 , wherein the magnetic coil radially overpressures the plasma, promoting axial expansion of the plasma.

15. 12. The system of claim 11, wherein the compression, heating, and fusion cause a radial expansion of the plasma, the radial expansion of the plasma producing an additional current in the magnetic coil, and the energy storage unit receiving the additional current from the magnetic coil.

16. 12. The system of claim 11, further comprising at least one supply circuit operatively connected to the magnetic coil for supplying current to the magnetic coil to generate the magnetic field.

17. 17. The system of claim 16, wherein the at least one supply circuit crowbars current in at least one of the magnetic coils during compression, heating, and fusion of the plasma to further resist radial expansion of the plasma and promote axial expansion of the plasma.

18. 1. A method of collecting energy from an expanding plasma in a vessel, comprising: applying current to a magnetic coil disposed along the length of the vessel to generate a magnetic field within the vessel, the magnetic field maintaining the plasma in a field-reversed configuration, resisting radial expansion of the plasma and allowing axial expansion of the plasma along the length of the vessel; receiving in an energy storage unit a current collected from at least one of the magnetic coils during axial expansion of the plasma, the collected current being generated by at least one of the magnetic coils due to the axial expansion of the plasma; A method comprising:

19. 20. The method of claim 18, wherein the energy storage comprises at least one capacitor.

20. 20. The method of claim 19, further comprising converting energy from the energy storage into electrical current.

21. A supply circuit for a magnetic field system, comprising: a first energy storage unit (C1); a first circuit branch connected to a node of the first energy storage unit, the first circuit branch having a first switch (SW2), wherein when the first switch is in a conductive state, a current is conducted between the first energy storage unit and at least one magnetic coil (130-1) of the magnetic field system; a second circuit branch connected to a node of the first energy storage unit, the second circuit branch having a second switch (SW4), wherein a current is conducted between the first energy storage unit and an external load (210) when the second switch is in a conducting state and the first switch is in a non-conducting state; a third circuit branch connected to a node of the first energy storage unit, the third circuit branch having a third switch (SW3), and when the third switch is in a conductive state, the first switch is in a non-conductive state, and the second switch is in a non-conductive state, the first energy storage unit and the second energy storage unit (L Ｒ a third circuit branch in which a current is conducted between the first energy store and the second energy store, reversing the polarity of the voltage across the first energy store; A supply circuit for a magnetic field system comprising:

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