Apparatus and method for harvesting energy from axially expanding plasma housed by magnetic field

Abstract

A magnetic field system can generate strong dynamically changing magnetic fields to constrain and control particles, objects or plasmas. A coil in a magnetic field system for controlling the plasma may be used to harvest energy from the expanded plasma.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of priority under 35 U.S.C. 119(e) to U.S. application 63 / 386,364, filed December 7, 2022, which is incorporated herein by reference in its entirety for all purposes. Background Art

[0003] Strong magnetic fields can be generated using multiple current-carrying coils driven by high currents and high voltages. Such magnetic fields can be used to confine high-energy particles and / or accelerate particles or objects to high speeds. In some cases, strong magnetic fields can be used to confine plasma. Summary of the Invention

[0004] The described embodiments relate to methods and apparatus for dynamically controlling a plasma contained within a strong magnetic field. The associated plasma includes (i) a coherent structure of plasma and magnetic field (plasmoid), and / or (ii) a magnetic mirror confinement plasma. The magnetic field can be generated using an electromagnetic coil assembly (more succinctly referred to as a "magnetic coil" or "coil") that is controlled to confine the contained plasma and / or impart energy to the contained plasma. In some cases, the magnetic coil can 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 coil can be controlled spatially and temporally to cause the plasma to pulse.

[0005] More specifically, the current flowing through the magnetic coil generates a magnetic field that drives adiabatic compression of the plasma, thereby performing work on the plasma by compressing the plasma in radius and length, and increasing the plasma temperature. As the temperature of the plasma increases, fusion of the constituent ions in the plasma occurs, thereby producing high-energy charged particles that can remain confined in the plasma and increase the energy of the plasma. This increases the temperature of the plasma and causes the plasma to expand axially against the magnetic field applied by the magnetic coil. This plasma expansion cycle causes the magnetic field around the magnetic coil to increase, which in turn generates an electromotive force through Lenz's law, which drives current into an energy storage element coupled to the magnetic coil. In some embodiments, this collected energy can be transferred to a load, including an energy storage system.

[0006] 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 undergo axial expansion, which transfers energy to the magnetic coil. This energy is directed from the magnetic coil to an energy storage component, such as a capacitor.

[0007] Adiabatically compressing the plasma may include increasing the current flowing through the magnetic coils so as to increase the magnitude of the magnetic field.

[0008] Directing energy from the magnetic coil to the energy storage component may include resonantly transferring energy from the magnetic coil to the energy storage component.

[0009] In some cases, the current in at least one magnetic coil is crowbar-shielded to further resist radial expansion of the plasma and promote axial expansion of the plasma as the plasma undergoes compression, heating, and fusion. Alternatively, the magnetic field can be adjusted to radially over-compress (the center of) the plasma as the plasma undergoes compression, heating, and fusion in order to promote axial expansion of the plasma.

[0010] The compression, heating, and fusion may cause radial expansion of the plasma, which generates additional current in the magnetic coils, in which case this additional current may be stored as additional energy in the energy storage component.

[0011] Energy from the energy storage component may be converted into an electrical current, such as a direct current or an alternating current.

[0012] Some embodiments relate to a method of harvesting energy from an expanding plasma, the method comprising: injecting plasma into a vessel; sequentially applying a plurality of currents to a plurality of magnetic coils, the plurality of magnetic coils being arranged to generate a magnetic field within the vessel to sequentially vary the magnetic field applied to the plasma such that the plasma transitions to a stage where the plasma begins to expand in volume within the vessel and the magnetic field resists radial expansion of the expanding plasma; and generating a collectible current in at least one of the plurality of magnetic coils based on the expanding plasma.

[0013] Some embodiments relate to a method of collecting energy from a plasma as the plasma expands in a container, the method comprising: applying a plurality of currents to a plurality of magnetic coils arranged along a length of the container to generate a magnetic field within the container, wherein the magnetic field maintains the plasma in a field-reversed configuration, resists radial expansion of the plasma, and allows the plasma to expand axially along the length of the container; and receiving a collectible current from at least one magnetic coil of the plurality of magnetic coils during the axial expansion of the plasma, wherein the collectible current is generated in the at least one magnetic coil by the plasma as the plasma expands axially.

[0014] Some embodiments relate to a method of confining a plasma and collecting energy from the plasma as the plasma expands, the method comprising: injecting the plasma into a vessel; applying a first plurality of currents to a plurality of magnetic coils arranged to generate a magnetic field within the vessel, wherein the magnetic field prepares the plasma for 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; applying a second plurality of currents to the plurality of magnetic coils, the second plurality of currents altering 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 less than the first radial value, and the the interface having a second length value in the second state; applying a third plurality of currents to the plurality of magnetic coils, the third plurality of currents modifying the magnetic field when the plasma transitions from the second state to a third state in which the plasma has more energy than in the second state and begins to expand beyond at least the second length, wherein the third plurality of currents are selected to generate a magnetic field that resists expansion of a radius of the interface from the second radial value over at least a portion of the length of the interface as the length of the interface increases beyond the second length value; and receiving a collectible current from at least one of the plurality of magnetic coils as the length of the interface increases beyond the second length value, wherein the collectible current is generated by the plasma as it expands beyond the second length.

[0015] Some embodiments relate to a power supply circuit for a magnetic field system, the power supply circuit comprising: a first energy storage component (C1); a first circuit branch coupled to a node of the first energy storage component, the first circuit branch comprising a first switch (SW2), the first switch being arranged to conduct current between the first energy storage component and at least one magnetic coil (130-1) of the magnetic field system when the first switch is in a conducting state; a second circuit branch coupled to the node of the first energy storage component, the second circuit branch comprising a second switch (SW4), the second switch being arranged to conduct current between the first energy storage component and an external load (210) when the second switch is in a conducting state and the first switch is in a non-conducting state; and a third circuit branch coupled to the node of the first energy storage component, the third circuit branch comprising a third switch (SW3), the third switch being arranged to conduct current between the first energy storage component and a second energy storage component (LR) to reverse the polarity of a voltage across the first energy storage component when the third switch is in a conducting state, the first switch is in a non-conducting state, and the second switch is in a non-conducting state.

[0016] All combinations of the aforementioned concepts and the additional concepts discussed in more detail below (provided such concepts are not mutually inconsistent) are considered part of the inventive subject matter disclosed herein. Specifically, all combinations of claimed subject matter appearing at the end of this disclosure are considered part of the inventive subject matter disclosed herein. Terms explicitly employed herein that may also appear in any disclosure incorporated by reference should be given the meaning that best matches the specific concepts disclosed herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Those skilled in the art will appreciate 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 drawn to scale; in some cases, various aspects of the inventive subject matter disclosed herein may be shown exaggerated or enlarged in the drawings to facilitate understanding of different features. In the drawings, like reference numerals generally refer to like features (e.g., functionally similar and / or structurally similar components).

[0018] Figure 1 Depicted is an example of a magnetic field system for generating a strong magnetic field.

[0019] Figure 2 Depicts Figure 1 An example of a power circuit for delivering current to, recovering, and harvesting energy from at least one magnetic coil in a system.

[0020] Figure 3A Depicted in Figure 1Magnetic field and plasma injection during the operating cycle of the system.

[0021] Figure 3B Depicted in Figure 1 Magnetic field and plasma configurations for the first time during the system's operating cycle.

[0022] Figure 3C Depicted in Figure 1 The magnetic field and plasma configuration at a second time during the operating cycle of the system.

[0023] Figure 3D Depicted in Figure 1 The magnetic field and plasma configuration at a third time during the operating cycle of the system.

[0024] Figure 3E Depicted in Figure 1 Magnetic field and plasma configuration at a fourth time during the operating cycle of the system.

[0025] Figure 4A Shown in Figure 1 Example of the temporal variation of the plasma interface radius during an operating cycle of the magnetic field system.

[0026] Figure 4B Shown in Figure 1 Example of the temporal evolution of the interface length during an operating cycle of a magnetic field system.

[0027] Figure 4C Draws Figure 1 1. Example of current in the end coil 130-1 of the magnetic coil system.

[0028] Figure 4D Draws Figure 1 1. Example of current in the middle coil 130-2 of the magnetic coil system.

[0029] Figure 4E Draws Figure 1 1. Example of current in the center coil 130-3 of the magnetic coil system.

[0030] Figure 5 Depicts Figure 1 Additional details of the magnetic field system's energy harvesting circuitry.

[0031] Figure 6A Depicts the Figure 5 Energy harvesting circuits and Figure 2 The voltage waveform associated with the power supply circuit.

[0032] Figure 6B Depicts the Figure 5 Energy harvesting circuits and Figure 2The current waveform associated with the power supply circuit. DETAILED DESCRIPTION

[0033] Figure 1 An example of a magnetic field system 100 is depicted that can be used to generate a strong dynamic magnetic field (e.g., with a peak field value between 0.01 tesla (T) and 50 T). The system 100 includes a plurality of magnetic coils 130-1, 130-2, 130-3 arranged to cooperatively generate a magnetic field within a container 150. To cooperatively generate the magnetic field, the magnetic coils 130 are spaced sufficiently close to each other so that the magnetic field generated by any one coil adds to the magnetic field generated in the container 150 by at least one other coil in the system. For example, the space between adjacent coils 130-2, 130-3 can be equal to or less than the inner diameter D of the coils. The magnetic coils 130 can generate a strong magnetic field within the container 150 adjacent to the magnetic coils 130. In the illustration, the container 150 and the magnetic coils 130 are depicted in a cross-sectional view.

[0034] For some applications (particle or object acceleration), the container 150 can be a tube with at least one open end, or can form a ring. For other applications (plasma physics), the container 150 can be, for example, part of a larger vacuum chamber with at least one inlet port for introducing the plasma. In such cases, the container can be made of a dielectric material (e.g., quartz) and / or other relevant vacuum-compatible materials. In some cases, the container 150 can be a linear tube with an inlet port at each end for injecting plasma from one or both ends. Related implementations of plasma include (i) coherent structures of plasma and magnetic fields (plasma clumps), and / or (ii) magnetic mirror confinement of plasma. In some embodiments, two plasma clumps are injected at each end of the container and accelerated toward each other and collided at the center of the container. The collision can include a controlled merging of the injected plasmas so that the resulting merged plasma maintains the same general structure of the injected plasmas. The collision can produce a completely merged plasma, a partial merging of the plasmas, or no merging, with the two plasma clumps remaining separate. In other embodiments, a single plasma clump can already be present in the container or injected from one side.

[0035] The magnetic coil may include a multi-turn winding in some cases. In other cases, the magnetic coil may be formed as a single-turn or multi-fed, fractional-turn magnetic coil. The single-turn or fractional-turn coil may include a solid, conductive or superconducting core. The inner diameter of the coil (enclosing the space in which the strong magnetic field is generated) may be between 1 centimeter (cm) and 300 cm. Examples of such coils are described in International Patent Application PCT / US2022 / 033424, entitled “Inertially-Damped Segmented Coils for Generating High Magnetic Fields,” filed on June 14, 2022, which is incorporated herein by reference in its entirety.

[0036] Each of the magnetic coils 130 can be fed with current from one or more power supply circuits 120-1, 120-2, 120-3 (only one power supply circuit is shown for each magnetic coil to simplify the illustration). The current can be provided by one or more power supply lines 125 connected to each coil. The peak amount of current delivered to each coil can be, for example, between 100,000 amperes (A) and 200,000,000 A.

[0037] Each power supply circuit in the power supply circuit 120 (hereinafter referred to as Figure 2 100 ). The magnetic field system 100 (described in more detail) may include a power source (e.g., a voltage source), at least one energy storage component (e.g., a battery, a compensated pulse generator, a flywheel, or a capacitor; capacitors are particularly useful in applications requiring rapid energy release), and at least one switch that controls the flow of current from the at least one energy storage component to the associated magnetic coil. The switch(es) in each power circuit 120 may be controlled (e.g., by the controller 110) independently of the switch(es) in the other power circuits 120 in the system. Thus, the current waveform and timing of the current waveform delivered to each of the magnetic coils 130 may be controlled largely independently of the current delivered to the 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 of the magnetic coils 130.

[0038] The controller 110 can communicate with at least one of the power supply circuits 120 to at least control the delivery of current from the at least one power supply circuit to one or more of the magnetic coils 130 (e.g., by activating switch(es) of the power supply circuit). In some embodiments, the controller 110 can additionally control the amount of current delivered by the power supply circuit. In some cases, the controller 110 can further control the waveform of the delivered current (e.g., by selecting between discrete capacitive and / or resistive components in the power supply circuit 120 and / or tuning tunable capacitive and / or resistive components). In some cases, the controller 110 can include a computer. In other cases, the controller can include a field programmable gate array, a programmable logic circuit, an application specific integrated circuit, a digital signal processor, or some combination thereof.

[0039] In some cases, control of the current delivery to the magnetic coils can be distributed among the power supply circuits or among the trigger control circuits coupled to the power supply circuits. For example, controller 110 can issue a command signal to deliver current to end coil 130-1. The command signal can be received by end power supply circuit 120-1, or the command signal can be received by the trigger control circuit coupled to the end power supply circuits. When triggering first coil 130-1, end power supply circuit 120-1 or the trigger control circuit can issue a trigger command signal to middle power supply circuit 120-2 or a trigger control circuit coupled to middle power supply circuit 120-2. In this way, all magnetic coils can be triggered, and the triggering cycle can be repeated.

[0040] In some embodiments, there can be one or more predetermined delays between the activation of the power supply circuits 120 to energize their associated magnetic coils 130 in a sequential activation order. For example, a magnetic coil 130-1 near the end of the coil assembly can be energized first by its associated power supply circuit 120-1, and then the activation of the power supply circuits proceeds inward so that the center coil(s) 130-3 is energized last in the sequence. In some cases, the delay timing can be electronically programmable by the controller 110 or the trigger control circuit. In some embodiments, the delay timing can be designed using circuit delay elements connected to the power supply circuits 120 that delay subsequent trigger command signals after the initial trigger command signal is provided to at least one of the power supply circuits.

[0041] Regardless of how the trigger timing is determined, Figure 1With the magnetic field system 100, it is possible to independently control (at least to some extent) the powering of each magnetic coil in the magnetic coils 130. By independently controlling the amplitude, waveform, and timing of the current delivered to each magnetic coil in the magnetic coils 130, a dynamic and pulsating strong magnetic field can be generated in the container 150. Fiber optic cables and high-speed switches can be used to provide trigger command signals to the magnetic coils 130 in rapid succession. In some cases, adjacent coils can be triggered within 10 nanoseconds of each other. This rapid sequencing of trigger command signals can allow the plasma to be carefully controlled by the magnetic coils to form, maintain, and transition the plasma between different states. An exemplary circuit for controlling the triggering of the power supply circuit is described in international patent application PCT / US2022 / 033319, entitled "High-Speed ​​Switching Apparatus for Electromagnetic Coils," filed on June 13, 2022, which is incorporated herein by reference in its entirety.

[0042] Figure 2 An example of a power supply circuit 120-1 is depicted, which may be used to deliver current to Figure 1 The magnetic field system 100 of the at least one magnetic coil 130-1 and receives current from the at least one magnetic coil. The one or more magnetic coils 130-1 connected to the power supply circuit 120-1 can be modeled as an inductor L1. In operation, the power supply circuit 120-1 can store energy and deliver energy to the (multiple) magnetic coils 130-1 to generate a magnetic field that contains and controls the plasma in the container 150 (for example, to compress the plasma in radial and axial directions). The power supply circuit 120-1 may include an energy recovery circuit portion that recovers some of the energy delivered to the magnetic coils for storage and subsequent use in the next operating cycle, as further described below. The energy recovery circuit portion includes, but is not limited to, the inductor L R and directional switch SW3. The power supply circuit may also include an energy harvesting circuit 245 that can receive energy from the magnetic coil 130-1 to provide to the external load 210, as further described below. The energy harvesting circuit 245 may include a switch that, when activated, receives current from the energy storage component C1, which may be implemented as one or more capacitors.

[0043] The power supply circuit 120-1 includes an energy storage component (modeled as a capacitor C1), a source (modeled as a voltage source V supp), switch SW1, and directional switches SW2, SW3 with diodes D1, D2. For example, the directional switches may include silicon controlled rectifiers (SCRs), but other switches may be used. In operation, switch SW1 may be closed (with switches SW2, SW3, and SW5 open) to provide an initial charge to the energy storage component C1. Switch SW1 may then be opened and switch SW2 closed to deliver a current pulse to the magnetic coil(s) 130-1. Unused energy from the pulse and / or electrical energy collected from the magnetic coil(s) 130-1 (which, combined with the unused energy from the pulse, may exceed the amount of energy stored in capacitor C1 before the pulse began) may pass through capacitor C1 and accumulate charge in the capacitor. In some embodiments, when a peak charge (of opposite polarity) has accumulated in capacitor C1 (which may be sensed by the optional sensing and control circuit 220), switch SW2 may be opened and switch SW3 closed to provide an initial charge to the energy storage component C1 by including another energy storage component (in this example, an inductor L R ) of the recovery circuit branch to reverse the recovery energy in the energy storage component C1. The reversal can recharge the capacitor C1 to the initial polarity in the next operating cycle.

[0044] The sensing and control circuit 220 (if used) may include a voltage sensor to detect the voltage on the charging node of the energy storage component C1 and logic circuitry to output control signals to one or more of the switches SW2, SW3, SW5, and / or the energy harvesting circuit 245. If additional energy is harvested from the magnetic coil (which can be detected by the sensing and control circuit 220 as a voltage exceeding a threshold voltage at the energy storage component), the energy harvesting 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 into a waveform or DC voltage suitable for the power application (e.g., a conventional two-phase or three-phase AC waveform). In some embodiments, the load 210 may include an electrical grid. Other power supply circuits 120-1 that can recover unused energy through the magnetic coil(s) 130-1 are also possible, and exemplary power supply circuits can be found in international patent application PCT / US2022 / 032277, filed on June 3, 2022, entitled “Energy Recovery in Electrical Systems,” which is incorporated herein by reference in its entirety and included in the appendix attached to this application.

[0045] Figure 3A 、 Figure 3B 、 Figure 3C and Figure 3D Describes the Figure 1FIG. 1 is a simplified time-sequential image of exemplary magnetic field lines B (dashed lines) of the magnetic field system 100 and the configuration of the contained plasma 310.

[0046] The diagram depicts an exemplary embodiment of a method for energizing a plasma 310 using a pulsating high magnetic field and extracting energy directly and repeatedly from the plasma. In one embodiment, when the magnetic field system 100 causes two or more plasmas to collide, as described above in conjunction with Figure 3A and Figure 3B As described above, the plasma energy and size may increase because the kinetic energy of the traveling plasma 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 coil(s), thereby generating additional current in the coils. The additional current may supplement the current provided by the energy storage component C1 and / or be recovered or collected.

[0047] To simplify the drawing, the container 150, power supply circuit 120, and controller 110 have been omitted, and only the magnetic coil assembly 300 is shown along with the plasma. Magnetic field lines B are schematically depicted with dashed lines, and the spatial extent of the plasma 310 is schematically depicted with solid lines (for example, the solid line may be the location of the plasma's interface). The interface is the location of the last closed magnetic field line within the plasma 310. A cross-sectional view of the magnetic coil assembly 300 and plasma 310 is shown, but the magnetic coil assembly 300 and plasma 310 are three-dimensional. For example, the magnetic coil 130 and plasma 310 are symmetrical about a central axis 305 passing through the container. Although only five coils are shown in the figure, there may be 10 to 100 coils or more in the magnetic field system 100. In addition, the illustration may only be for the central portion of the magnetic field system. Additional coils may be present at each end of the system to form the plasma and inject the plasma from each end toward the center of the magnetic field system, where the plasma merges.

[0048] To begin an operating cycle for some embodiments, two or more plasma pellets 310a, 310b may be injected into the magnetic coil assembly 300, as shown in FIG. Figure 3A As will be understood by those skilled in the art, a plasmoid is a coherent structure of plasma and magnetic field. Plasmoids 310a, 310b may be formed in the end regions of the magnetic coil assembly 300 and then accelerated toward each other using the magnetic coil 130. The plasmoids may merge within the container 150 of the magnetic coil assembly to form a single plasma 310, as shown. Figure 3B The merging of the plasmoids may add heat to the plasma 310. The plasma 310 may reach a first state in which the plasma is stable and has an interface radius r sand axial length l s (in the ±z directions.) Note that in other configurations, the plasmons may partially merge or not merge, but remain close together in a more confined space.

[0049] At a first time t=t1, the magnetic field system 100 can be placed in an initial or first state of an operating cycle. Currents I1, I2, and I3 can be applied to the system's magnetic coils 130 to generate a magnetic field B that confines the plasma 310 to a first spatial extent. The (multi-cluster) plasma can have a toroidal shape and be a field-reversed configuration (FRC) plasma. For example, the plasma can be mostly or fully ionized, with fully magnetized electrons and possibly also magnetized ions. In addition, the plasma can have a significant diamagnetic current and a plasma beta value β greater than or equal to 30%. The β value is the ratio of the pressure of the plasma given by Equation 2 to the magnetic pressure on the plasma given by Equation 1 below, averaged over the surface of the plasma. The magnitudes of the currents I1, I2, and I3 at time t1 can be approximately equal in the initial state or increase slightly with distance from the center of the container to confine the plasma to the center of the container 150 and coil assembly 300. Due to the current applied to the magnetic coil 130, an azimuthal current (indicated by the dots and crosses) circulating around the plasma can be maintained in the container 150. In this initial state, the interface of the plasma can have an initial radius r perpendicular to the axis 305. s and half length l in the direction along axis 305 s / 2. The initial volume V of the plasma that may exist within the interface o .

[0050] Subsequently, the current delivered to the magnetic coil 130 is increased to energize the plasma 310 and transition the plasma from the initial state to the second state. At a second time t=t2 at which the second state occurs, the volume of the plasma may be reduced compared to the volume of the plasma in the first state. Figure 3C The reduction in volume of the plasma is schematically depicted. Increasing the currents I1, I2, and I3 increases the strength of the magnetic field B, which increases the magnetic pressure on the plasma 310, thereby forcing the plasma radially inward and reducing the volume of the plasma and increasing the internal temperature and pressure of the plasma. The increased magnetic pressure is depicted in the figure as wide black arrows pointing to the top and bottom of the page. This increased pressure is primarily applied radially around the perimeter of the plasma. Pressure can also be applied at the ends of the plasma, thereby reducing its length. The local magnetic pressure P acting on the plasma is B It can be expressed as

[0051]

[0052] where B is the local scalar magnitude of the magnetic field B, and μ o is the magnetic permeability of free space.

[0053] To further confine the plasma, the current applied to the magnetic coils 130 can be applied differently for each coil and in a time-sequential manner. For example, the initial increase in current I3 applied to the coils at the ends of the coil assembly (sometimes referred to as magnetic mirror coils) can be greater than the increase in current I1 initially applied to the coil(s) at the center of the coil assembly 300 to form magnetic field lobes 340 near the ends of the coil assembly. Figure 3C The dotted lines generally indicate the contours of equal magnetic field strength. The lobes 340 can exert magnetic pressure on the ends of the plasma to reduce its length.

[0054] like Figure 3D As shown, these lobes 340 can increase and / or propagate inwardly toward the center of the coil assembly 300 by sequentially and temporally staggering increases in the current applied to each adjacent coil in a direction moving toward the center of the coil assembly 300 (e.g., in conjunction with Figures 4C to 4E For example, the peak increase in current I3 may reach the center magnetic coil 130-3 before the peak increase in current I2 reaches the magnetic coil 130-2. This temporal application of currents may increase the magnetic pressure acting axially on the plasma, such as Figure 3C and Figure 3D In response to the magnetic pressure, the plasma 310 exerts pressure back on the magnetic field, as indicated by the wide grey arrows in the figure. The reaction pressure within the plasma can be expressed as

[0055] P=nk B T (2)

[0056] Where n is the characteristic density value of the plasma (which may be half of the peak density of the plasma), k B is the Boltzmann constant, and T is the peak temperature of the plasma.

[0057] like Figure 3D As shown in FIG, when the plasma 310 reaches the minimum volume V at time t3, min When the magnetic coils cannot compress it further, the energy of the plasma may increase or be increased. For example, an internal reaction (e.g., a nuclear reaction) may occur, or energy from another source (e.g., a high-power laser, a particle beam, or microwave heating) may be imparted to the plasma 310. A rapid increase in plasma energy or plasma generation energy may indicate another state of the plasma. Exemplary nuclear reactions include, but are not limited to, fusion (e.g., DT fusion, DD fusion, and / or 3 He-D fusion).

[0058] As the energy increases, the plasma 310 may begin to expand into an elongated shape as it transitions to another state, such as Figure 3E As shown in . During the expansion of the plasma, energy can be released from the plasma and collected by the magnetic coil assembly 300. The expanding plasma increases the magnetic field around the magnetic coil, thereby generating an electromotive force via Lenz's law. The electromotive force drives current through the magnetic coil (resonantly) into the energy storage element. This current recharges the energy storage components in at least some of the power supply circuits 120. In some embodiments, the energy collected from the expanding plasma, together with the energy recovered from the energy recovery circuit, may exceed the energy delivered to the coil(s), with a portion of the excess energy being made available by the system via the energy collection circuit, which enters another energy storage device or powers the external load 210. Such energy collection represents a direct coupling of energy from the plasma.

[0059] In addition, regardless of the plasma expansion, energy can be extracted from the plasma by other means. For example, a working gas can be passed over and around the plasma to release heat. In other embodiments, charged particles or neutrons can be ejected from the plasma and transfer energy to a receiving material (e.g., a photovoltaic energy recovery system for charged particles, or a molten blanket for neutrons). In some embodiments, the heat generated by the plasma during energy generation can be captured and converted into electrical energy (e.g., by generating steam and driving a steam turbine). Such conversion processes represent indirect coupling of energy from the plasma 310.

[0060] According to some embodiments, when plasma 310 expands from a state at time t3 to another state at a later time t4, the plasma may be confined in at least one dimension, for which Figure 3E For example, the current applied to the inner magnetic coil(s) 130-2, 130-3 can be controlled (e.g., using a feedback loop or by applying a predetermined waveform to the coils) to locally resist the expansion of the interface radius or maintain a constant interface radius r as the plasma 310 expands. s , or allow r s To maintain a constant interface radius, an increasing or constraining current may be applied to at least a portion of the magnetic coil 130 (eg, the inner coil 130 - 2 ).

[0061] In some cases, a circuit across the coil power supply lines can be used to maintain current in one or more of the coils to counteract plasma expansion. In some embodiments, this is achieved using a crowbar circuit. The circuit can be within the power supply circuit and activated by the power supply circuit (e.g., by the sensing and control circuit 220 closing switch SW5). In some embodiments, the sensing and control circuit 220 can 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 harvesting circuit 245. For example, the sensing and control circuit 220 can initially crowbar one or more coils 130-3 (and possibly coil 130-2) near the center of the vessel 150 to counteract radial plasma expansion at that location. As the plasma expands axially and reaches coils not protected by the crowbar (coil 130-1 and possibly coil 130-2), current can increase in these coils, generating energy and providing that energy to their corresponding energy storage components C1 for energy harvesting. The coils into which the plasma expands can be coils 130 used to guide the plasma in other ways. Additionally or alternatively, the coil into which the plasma expands may be an additional auxiliary coil 135 ( Figure 1 shown in ).

[0062] Crowbaring the center coil 130-3 prevents the plasma from expanding radially at the center of the vessel 150, and instead causes (greater) axial expansion of the plasma. If desired, the current flowing through the center coil 130-3 can also be increased to radially over-compress the plasma at the center of the vessel 150, thereby causing increased collective energy generation and / or the plasma to elongate (axially expand) a greater amount and / or at a faster rate, thereby potentially generating more collectible energy via axial expansion than would otherwise be possible.

[0063] In one embodiment, the circuit is timed so that the majority of the back EMF is generated after the peak current is reached in the coil. As a result, the net back EMF helps current flow in the direction of the entire circuit and helps recharge capacitor C1.

[0064] In a system that provides feedback control of the current applied to the coil 130, a voltage can be sensed across the magnetic coil to detect changes in the interface radius of the plasma. (As one skilled in the art will appreciate, the interface radius can be determined based on the voltage and magnetic field.) Additionally or alternatively, a diamagnetic probe and / or other magnetic sensor (e.g., a sensing coil ring surrounding the magnetic coil) can be located at one or more locations along the axis of the vessel 150 to detect changes in the radius of the plasma interface at one or more locations along the axis of the vessel 150. sThere may be multiple sensors at each location along the axis of the container 150. The sensed voltage and / or magnetic field may be processed in a feedback loop to determine the control interface radius r s The amount of current applied to each magnetic coil.

[0065] During the operating cycle between times t1 and t3, the increase in the current value of at least one of the magnetic coils may be 1.5 to 10,000 times (or any sub-range therein) the initial current value at time t1. During the time interval from t1 to t3, the magnitude of the magnetic field at the center of the vessel 150 may increase by a multiple having a value in the range of 1.5 to 10,000 (or any sub-range therein), and the plasma volume may decrease by a factor having a value in the range of 2 to 1,000 (or any sub-range therein). Compared to the initial value r before the current increase si In comparison, the radius of the interface of the plasma may be reduced by a factor having a value in the range of 1.5 to 20 (or any sub-range within this range, for example, 1.5 to 5). si The length of the interface may be between 1 cm and 100 cm. The length of the interface may be reduced by a factor having a value in the range of 1.5 to 50 (or any sub-range therein) compared to the initial value of the length before the current is increased to compress the plasma 310. The initial length of the interface may be between 5 cm and 5 m. The time interval from t1 to t3 may be a duration in the range of 1 nanosecond to 100 milliseconds (or any sub-range therein).

[0066] By maintaining a constant interface radius (or allowing r s The plasma 310 continues to be well coupled to the coil assembly 300. The plasma and its azimuthal current wall can then be allowed to expand primarily along the axial direction of the coil assembly 300, thereby achieving a maximum length at time t4, as shown in FIG. Figure 3E As the plasma expands axially, the current in the magnetic coil 130 can be sequentially controlled to maintain a fixed and substantially uniform interface radius r along at least the central portion of the coil assembly 300. s In some cases, the radius r may be allowed sExpand in a controllable manner. The axial flux of the plasma current and the associated magnetic field can generate (multiple) currents in one or more magnetic coils of the coil assembly 300 or in one or more auxiliary magnetic coils distributed along the container 150. The generated (multiple) currents can be collected as usable energy. Such a method of collecting energy represents a direct coupling of energy from the plasma. In some cases, the same coil used to control plasma expansion (e.g., maintaining a substantially constant interface radius as the plasma expands axially) is used to collect energy from the expanding plasma.

[0067] After time t4, plasma 310 may have imparted a certain amount of energy to the coil assembly and cooled to the point where it can no longer provide collectible energy and / or maintain its expanded volume. In some cases, plasma 310 may then begin to contract back to Figure 3B The current to the magnetic coil can be adjusted so that the plasma returns to the initial state during the next operating cycle.

[0068] During this process, portions of the plasma 310 may leak out of the end of the vessel 150. The magnetic field accelerates the leaked portion of the plasma, thereby generating a high-speed particle jet that moves away from the center of the vessel 150 along the longitudinal axis of the vessel. Figures 3A-3E 1. In some cases, plasma 310 may decay into an open field line plasma after time t4.

[0069] New plasma can be injected each cycle (e.g., after time t9) to replenish the supply of components that can react when the plasma is compressed in the next cycle. The removal and injection of plasma can be controlled by one or more magnetic coils located at the end of the magnetic field assembly 100. The steps of plasma injection, compression, confined expansion, energy collection, and product removal can then be repeated cyclically during operation of the magnetic field system 100.

[0070] Plasma configurations in addition to or different from the above-described states can be realized in some embodiments of the system. For example, in the third state, the axial expansion of the plasma can be asymmetric, and the plasma can even be ejected in one direction (e.g., to produce a propulsion effect). In some cases, the plasma can oscillate between different states one or more times during an operating cycle (e.g., in Figure 3C The plasma state at time t2 depicted in Figure 3D oscillates one or more times between the plasma states at time t3 depicted in FIG).

[0071] In some embodiments, the power supply circuit 120 can be used to utilize electrical energy harvested from the magnetic coil 130 during plasma expansion. For example, a portion of the harvested electrical energy (which, combined with energy recovered from the energy recovery circuit, may exceed the energy supplied to the magnetic coil) can be stored in (a plurality of) energy storage components of the power supply circuit and / or in additional energy storage components that can be switched into connection with the magnetic coil. Another portion of the harvested energy can be provided to the load 210, such as in combination with Figure 2 As described and further described below. Load 210 can be any device that consumes or stores electrical energy, including an electrical grid. At least some of the stored energy can be used during one or more time intervals of an operating cycle (e.g., during the contraction of the plasma from its fully expanded volume to its initial state volume V o Some of the stored energy can be retained for the next operating cycle of the magnetic field system.

[0072] Figures 4A to 4E According to some embodiments, Figure 1 Example dynamics of plasma and current characteristics for an operating cycle of a magnetic field system. For this example, the plasma interface radius r s can evolve over time during at least a portion of a compression / expansion cycle, e.g. Figure 4A As shown in the figure. The interface radius r s It can be at time t0 with an initial radius r si The operating cycle begins and at time t3 the magnetic field is reduced to a minimum radius r min Then, for some cases, due to the allowed length l of the interface s Expanding within the magnetic field system 100, such as Figure 4B As further shown, the interface radius can therefore remain substantially constant between times t3 and t4 (e.g., at r min To maintain a roughly constant radius r s , the local magnetic pressure P acting radially on the side wall of the plasma B is approximately equal to the local plasma pressure P acting radially outward. Alternatively, maintaining r s The approximately constant can be expressed as maintaining the plasma sidewall ββ approximately equal to 1, where β = P / P B In some cases, the interface radius can be controlled in a manner that allows some expansion of the interface radius (e.g., as much as 50% expansion during the time interval from t3 to t4). This can be achieved by controlling the current waveform applied to the magnetic coil 130 of the magnetic field system 100. sSuch control (whether constrained to be substantially constant or allowed to controllably expand) is achieved. In the later stages of the operating cycle (after t4), when the current pulse applied to at least a portion of the magnetic coil 130 decreases and returns to the initial value for the start of the next operating cycle, the radius and length of the interface can return to the initial state.

[0073] The duration of the operating cycle, e.g. Figures 4A to 4E , can be from about or exactly 1 microsecond to about or exactly 1,000 milliseconds (or any subrange therein). However, in some embodiments, shorter or longer durations may be possible. In some cases, each operating cycle may also include a recovery interval (e.g., between time t4 and the application of a current pulse to the magnetic coil for the next operating cycle). The recovery interval can allow time for system components to dissipate heat and / or reinitialize (e.g., dissipate heat in the vessel 150, dissipate heat and reset switches in the power circuit 120, recharge energy storage components in the power circuit 120, remove spent plasma, inject new plasma, etc.).

[0074] Figures 4C to 4E Depicts examples of current waveforms that may be applied to Figure 1 The system has some magnetic coils 130 to generate respectively Figure 4A and Figure 4B The r depicted in s and l s The shape of the waveform can determine the dynamic behavior of s and l s The exemplary waveforms indicate that during the time interval t0 to t2, the higher current reaches the end coil 130-1 first, then the middle coil 130-2, and finally the center coil(s) 130-3. The waveforms during the time interval from t3 to t4 may be obtained by dividing the interface radius r by t1 as described above. s constrained to approximately its minimum value r min Or as Figure 4A In some cases, the interface radius r s The controlled expansion of can improve the particle confinement time and stability of the plasma 310.

[0075] Figure 4D An example of a current waveform applied to the middle coil 130-2 is depicted. The current waveform applied to the middle coil can be similar to the current waveform applied to the center coil(s) 130-1 during the time interval from t3 to t4, as the interface radius can also be constrained by the middle coil to a substantially constant value or allowed to controllably expand.

[0076] Figure 4E An example of a current waveform applied to the center coil 130-3 is depicted. During the time interval from t3 to t4, the current waveform applied to the center coil can decrease more rapidly than the current waveforms applied to the middle and end coils to allow the length and radius of the plasma 310 to expand at the ends of the plasma 310. This faster decrease in current to the center coil can be beneficial in allowing the expanding plasma 310 to drive more magnetic flux through the end coils of the magnetic field system 100 and generate more collectible current.

[0077] Figures 3A to 3E The depictions of the plasma configurations in are crude illustrations of the plasma configurations at snapshots in time and the plasma may rapidly pass through these configurations during an operating cycle of the system. Similarly, Figures 4A to 4E The waveform roughly indicates the evolution of the current applied to the magnetic coil 130 of the magnetic field system 100. Similarly, in certain configurations, such as a crowbar circuit configuration where the center coil(s) maintain or over-compress the center of the plasma puff, the diagram may appear more different (e.g., longer or faster axial expansion, peak current maintained longer on the center coil). At any snapshot in time, the plasma 310 can be considered to be in a specific state with a specific size, configuration, and energy. Therefore, the plasma 310 can quickly pass through many states during an operating cycle of the system 100.

[0078] Figure 5 Describes the Figure 1 and Figure 2 An exemplary energy harvesting circuit 245 for use with a magnetic field system. Figure 5 , circuit 245 includes an open switch SW4 (implemented as a MOSFET), a capacitor C2, and a power converter 510 (e.g., a DC to AC converter). Other types of power converters (e.g., a DC to DC converter) may be used in other embodiments. Power from power converter 510 may be provided to any suitable load, including a commercial AC grid. Energy harvesting circuit 245 may also include an inductor L2 at its input (e.g., operating at least partially as a choke), the inductor coupled to energy storage component C1 of power supply circuit 120-1, as shown in FIG. Figure 2As shown. Energy storage component C1 is the same component into which energy is recovered via the energy recovery circuit described above and in the aforementioned International Patent Application PCT / US2022 / 032277 entitled “Energy Recovery in Electrical Systems.” Thus, energy harvesting circuit 245 can work in conjunction with these energy recovery circuits in magnetic field system 100. For high power applications, the components of energy harvesting circuit 245 should be able to handle high voltages and large amounts of current (e.g., at least 10 3 Volts and at least 10 3 ampere).

[0079] The open switch SW4 is a switch that can be opened when current flows 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 open switches can be used in the energy harvesting circuit 245.

[0080] Capacitor C2 can be used to temporarily store energy received from magnetic coil(s) 130-1 for power conversion by power converter 510. In some embodiments, capacitor C2 may not be included, and instead energy storage component C1 of power supply circuit 120-1 may be used to store a portion of the harvested energy before power conversion by power converter 510 and delivery to external load 210. In such embodiments, inductor and / or switch SW4 may be directly coupled to energy storage component C1.

[0081] Figure 6A and Figure 6B Depicted respectively with Figure 5 The energy harvesting circuit 245 and Figure 2 These waveforms may occur during each operating cycle of the magnetic field system 100, and the operating cycle may be repeated regularly (e.g., once every 10 seconds, once every second, or more than once per second). Figure 6A The traces in show the voltage across capacitor C1 and across capacitor C2. Figure 6B The current in capacitor C1 is plotted.

[0082] To start the operation cycle at time t1 , the voltage across the energy storage component C1 is charged to an initial value by the power supply circuit 120 - 1 . Figure 6A The initial value in is normalized to 1, but can be anything from 100V to 100kV. When C1 is charging, switch SW1 ( Figure 2) are closed to deliver energy to the energy storage component C1, and switches SW2, SW3, and SW4 are opened to prevent current flow in their respective circuit branches.

[0083] At time t1, SW1 is opened (transitioned to a non-conducting state) and SW2 is closed (transitioned to a conducting state) to provide current to the magnetic coil(s) 130-1, thereby generating a magnetic field that helps compress the plasma in the vessel 150. Similar actions occur above in conjunction with Figures 3A to 3D as well as Figures 4C to 4E In the other power supply circuits 120 in the system. When the current flows out of the energy storage component C1 (in Figure 6B As shown in the figure), the voltage across the capacitor drops (at Figure 6A As shown in FIG), the plasma is compressed to its minimum size at time t3, as shown in FIG. Figure 3D As shown in .

[0084] In some embodiments, 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 exceeding a preset threshold voltage and issues a control signal to close switch SW2. In other embodiments, switch SW2 closes automatically. For example, switch SW2 may be 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).

[0085] At time t3, the reaction in the plasma may induce an expansion of the length of the plasma (axial expansion along the container 150, as shown in FIG. Figure 3E and Figure 4B t3 to t4 in FIG and as described above). This expansion can generate a back EMF in the magnetic coil(s) 130, which imparts additional energy and current in the coil(s) (as described above). This additional energy causes the current to increase, Figure 6B This increased current can help to recharge the energy storage component C1.

[0086] The increased current in the magnetic coil during the time interval from t3 to t4 can help limit the radius r of the interface as the plasma expands axially. s For example, the direction of the current increases the magnetic field generated by the coil(s) and serves to compress the plasma.

[0087] At time t5, energy storage component C1 has received sufficient charge to initiate the next phase of operation. When C1 has been fully recharged or charged above a certain value, switch SW2 opens to prevent further charging of energy storage component C1. In some cases, switch SW2 can open in response to detecting that the voltage across C1 exceeds a threshold level. For example, sensing and control circuit 220 can detect the voltage across C1 and issue a control signal to open switch SW2. In other embodiments, switch SW2 can open automatically. For example, the switch can be implemented as an SCR that automatically opens when the current through the switch drops below a threshold (e.g., a holding current).

[0088] When SW2 is opened, or shortly thereafter at time t6, energy harvesting circuit 245 is activated. Activation may include closing switch SW4 to allow current from magnetic coil(s) 130-1 to flow through inductor L2 and to capacitor C2 (if present) and / or power converter 510. Figure 6A The capacitor C2 is charged until time t7 when switch SW4 is opened. The closing and opening of switch SW4 can be responsive to a control signal from sensing and control circuit 220. In this way, energy can be harvested from magnetic field system 100. For some magnetic field systems, the time span from t1 to t7 can be 1 microsecond to 100 milliseconds (e.g., 10 microseconds, 100 microseconds, 1 millisecond, 10 milliseconds, or any other value between 1 microsecond and 100 milliseconds), although shorter or longer time spans are possible.

[0089] In some embodiments, the charge on the energy storage component C1 can be stored using a switch SW3 and an inductor L R The energy recovery circuit branch is 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 component C1 can be reversed before energy harvesting using energy harvesting circuit 245. For example, switch SW3 can 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 accumulated on capacitor C2 while still functionally charging the capacitor for future cycles.

[0090] For some embodiments 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 can be retained for future device operations and / or provided to an external load. Although in some cases, this energy may be a small percentage of the total energy generated by the plasma after the reaction occurs (or the energy generated by the plasma itself may be small), when the system uses the energy recovery circuit to recharge the energy storage component C1 as described above, this energy may be excess energy from the system. The energy recovery circuit can provide sufficient system efficiency so that the energy collected from the expanding plasma becomes excess energy for other applications.

[0091] Although the above discussion of energy harvesting is directed to plasma expansion primarily axially along the vessel 150, radial expansion of the plasma along the center coil 130-1 can also contribute to the back EMF in the coil(s) 130 and generate harvestable energy from the system. That is, in some systems, both axial and radial expansion of the plasma can occur during the time interval from t3 to t4.

[0092] Conclusion

[0093] Although various inventive embodiments have been described and illustrated herein, a person of ordinary skill in the art will readily devise various other means and / or structures for performing the functions described herein and / or obtaining the results and / or one or more advantages described herein, and each of such variations and / or modifications is considered to be within the scope of the inventive embodiments described herein. More generally, one skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are intended to be exemplary, and that actual parameters, dimensions, materials, and / or configurations will depend on the specific application or applications in which the teachings of the present invention are used. A person skilled in the art will recognize or be able to ascertain many equivalents to the specific inventive embodiments described herein using no more than routine experimentation. Therefore, it should be understood that the foregoing embodiments are presented by way of example only, and that within the scope of the appended claims and their equivalents, embodiments of the present invention may be practiced in ways other than those specifically described and claimed. Inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and / or method described herein. In addition, any combination of two or more such features, systems, articles, articles, kits, and / or methods is included within the scope of the present disclosure, provided that such features, systems, articles, materials, kits, and / or methods are not mutually inconsistent.

[0094] Furthermore, various inventive concepts may be embodied as one or more methods, examples of which have been provided. The actions performed as part of a method may be ordered in any suitable manner. Thus, embodiments may be constructed in which actions are performed in an order different from that shown, which may include performing some actions simultaneously, even though shown as sequential actions in illustrative embodiments.

[0095] All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and / or ordinary meanings of the defined terms.

[0096] Unless explicitly stated to the contrary, the indefinite articles "a" and "an" as used herein in the specification and claims should be understood to mean "at least one."

[0097] As used herein in the specification and claims, the phrase "and / or" should be understood to mean "either or both" of the components so combined, i.e., the components are present in combination in some cases and separately in other cases. Multiple components listed by "and / or" should be interpreted in the same manner, i.e., "one or more" of the components so combined. In addition to the components specifically identified by the "and / or" clause, other components may optionally be present, whether or not related to those specifically identified. Thus, as a non-limiting example, when used in conjunction with open language (e.g., "comprising"), a reference to "A and / or B" may refer to only A (optionally including components other than B) in one embodiment; to only B (optionally including components other than A) in another embodiment; to both A and B (optionally including other components) in yet another embodiment; etc.

[0098] 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 inclusive, i.e., including at least one of a plurality or series of components, but also more than one, and optionally, additional unlisted items. Only terms that clearly indicate the contrary, such as "only one of..." or "exactly one of..." or "consisting of..." when used in the claims will refer to including exactly one of a plurality or series of components. In general, the term "or" as used herein should be interpreted as indicating exclusive alternatives (i.e., "one or the other, but not both") only when preceded by an exclusive term such as "any one," "one of," "only one of," or "exactly one of." When used in the claims, "consisting essentially of..." should have its ordinary meaning as used in the field of patent law.

[0099] As used herein in the specification and claims, when referring to a list of one or more components, the phrase "at least one" should be understood to mean at least one component selected from any one or more components in the list of components, but does not necessarily include at least one of each component specifically listed in the list of components, and does not exclude any combination of components in the list of components. This definition also allows for the optional presence of components other than the components specifically identified in the list of components to which the phrase "at least one" refers, whether or not related to those components specifically identified. Thus, as a non-limiting example, in one embodiment, "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") may refer to at least one, optionally including more than one A, without B (and optionally including components other than B); in another embodiment, to at least one, optionally including more than one B, without A (and optionally including components other than A); in yet another embodiment, to at least one, optionally including more than one A, and at least one, optionally including more than one B (and optionally including other components); and so on.

[0100] In the claims and the foregoing description, all transitional phrases, such as "comprises," "comprising," "carrying," "having," "containing," "involving," "having," "consisting of," and the like, are to be construed as open-ended, meaning including but not limited to. Only the transitional phrases "consisting of" and "consisting essentially of" are to be closed or semi-closed transitional phrases, respectively, as set forth in Section 2111.03 of the United States Patent Office Manual of Patent Examining Procedures.

Claims

1. A method for collecting energy from plasma, the method comprising: adiabatically compressing the plasma using a magnetic field using a magnetic coil so that the plasma undergoes compression, heating, and fusion, wherein the compression, heating, and fusion cause the plasma to undergo axial expansion, and the axial expansion of the plasma transfers energy to the magnetic coil; and Energy is directed from the magnetic coil to an energy storage component.

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

3. The method of claim 1 , wherein adiabatically compressing the plasma comprises: The current flowing through the magnetic coil is increased to increase the magnitude of the magnetic field. 4 . The method of claim 1 , wherein directing energy from the magnetic coil to an energy storage component comprises resonantly transferring energy from the magnetic coil to the energy storage component.

5. The method of claim 1 , further comprising, while the plasma undergoes the compression, heating, and fusion: The current in at least one of the magnetic coils is crowbar protected to further resist radial expansion of the plasma and promote axial expansion of the plasma.

6. The method of claim 1 , further comprising, while the plasma undergoes the compression, heating, and fusion: The plasma is over-compressed in a radial direction to promote axial expansion of the plasma.

7. The method of claim 1 , wherein the compression, heating, and fusion cause radial expansion of the plasma, the radial expansion of the plasma generating additional current in the magnetic coil, and further comprising: The excess current is stored as excess energy in the energy storage component.

8. The method according to claim 1, further comprising: Energy from the energy storage component is converted into electrical current.

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

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

11. A system for collecting energy from a plasma, the system comprising: a magnetic coil configured to adiabatically compress the plasma using a magnetic field so as to cause the plasma to undergo compression, heating, and fusion, wherein the compression, heating, and fusion cause the plasma to undergo axial expansion, and the axial expansion of the plasma transfers energy to the magnetic coil; as well as An energy storage component is operatively coupled to the magnetic coil to receive energy from the magnetic coil.

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

13. The system of claim 11, wherein the magnetic coil is configured to resonantly transfer energy to the energy storage component.

14. The system of claim 11, wherein the magnetic coil is configured to radially over-compress the plasma to promote axial expansion of the plasma.

15. The system of claim 11, wherein the compression, heating, and fusion cause radial expansion of the plasma, the radial expansion of the plasma generating additional current in the magnetic coil, and wherein the energy storage component is configured to receive the additional current from the magnetic coil.

16. The system of claim 11, further comprising: At least one power supply circuit is operatively coupled to the magnetic coil to supply current to the magnetic coil to generate a magnetic field.

17. The system of claim 16, wherein the at least one power circuit is configured to crowbar current in at least one of the magnetic coils to further resist radial expansion and promote axial expansion of the plasma as the plasma undergoes the compression, heating, and coalescence.

18. A method of collecting energy from a plasma as it expands in a container, the method comprising: applying current to magnetic coils disposed along the length of the vessel to generate a magnetic field within the vessel, wherein the magnetic field maintains the plasma in a field-reversed configuration, resists radial expansion of the plasma, and permits axial expansion of the plasma along the length of the vessel; and Collected current from at least one of the magnetic coils during the axial expansion of the plasma is received in an energy storage component, wherein the collected current is generated by at least one of the magnetic coils through the axial expansion of the plasma.

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

20. The method according to claim 19, further comprising: Energy from the energy storage component is converted into electrical current.

21. A power supply circuit for a magnetic field system, the power supply circuit comprising: a first energy storage component (C1); a first circuit branch coupled to a node of the first energy storage component, the first circuit branch comprising a first switch (SW2) arranged to conduct current between the first energy storage component and at least one magnetic coil (130-1) of the magnetic field system when the first switch is in an on state; a second circuit branch coupled to a node of the first energy storage component, the second circuit branch comprising a second switch (SW4) arranged to conduct current between the first energy storage component and an external load (210) when the second switch is in a conducting state and the first switch is in a non-conducting state; as well as a third circuit branch coupled to a node of the first energy storage component, the third circuit branch comprising a third switch (SW3) arranged to connect the first energy storage component to the second energy storage component (L) when the third switch is in a conducting state, the first switch is in a non-conducting state and the second switch is in a non-conducting state; R ) to reverse the polarity of the voltage across the first energy storage component.

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