Rotating core with electromagnetic plasma compression system

Abstract

A plasma compression system comprises a vessel having an electrically non-conductive vessel wall and annular rotating core rotatable inside the vessel, an electrically-conductive liquid rotatable inside the rotating core to form a liquid liner having a cavity for receiving plasma; and a plurality of implosion drivers surrounding the rotating core. Each implosion driver comprises an electromagnetic coil with at least one pair of current input and output tabs with a coil gap therebetween. The input and output tabs further comprise an input current guide positioned on the current input tab and an output current guide positioned on the current output tab, that serve to guide current along an edge of the current input tab facing the coil gap, around an input tab corner, along an inner radial edge of the coil body, around an output tab corner, then along an edge of the current output tab facing the coil gap.

Description

[0001] ROTATING CORE WITH ELECTROMAGNETIC PLASMA COMPRESSION SYSTEM

[0002] Technical Field

[0003] The present disclosure generally relates to a rotating core fluid compression system using electromagnetic force to compress plasma.

[0004]

[0005] Unless otherwise indicated herein, the materials described in this section are not prior art to the claims in this application and are not admitted to be prior art by inclusion in this section. Magneto-inertial fusion (MIF, also called magnetized target fusion or MTF) is an approach to controlled nuclear fusion which joins aspects of both magnetic confinement fusion and inertial confinement fusion methods, enabling controlled fusion at more modest values of both confinement time and density than those in the purely inertial or magnetic confinement counterparts. Many MIF compression approaches and configurations have been proposed and studied, including the Magnetized Liner Inertial Fusion (MagLIF), Z-pinch configurations, shearflow-stabilized Z pinches, spherical piston-driven liquid metal liners, rotationally stabilized liquid metal liners, and staged-gas-puff Z-pinches. In many of these approaches, a liquid liner is used to capture and transport the heat energy from fusion, to limit radiation damage to the vessel walls, to carry current and contain its magnetic field, to compress a magnetized plasma, and in the case of a liquid lithium liner, to breed tritium fuel.

[0006] Systems for forming a cavity in a liquid liner and for imploding the liquid liner, as known in the prior art, form a substantially cylindrical cavity that is collapsed by radially imploding the liquid liner. One of these approaches is Magnetized Target Fusion (MTF). MTF approaches rely on the implosion of a magnetic flux conserver (liner) around a pre-heated magnetized plasma. Much of the current MTF work grew out of studies on imploding liners for controlled fusion at the Kurchatov Institute of Atomic Energy, which inspired the LINUS project at the Naval Research Laboratory and Los Alamos. In the LINUS system a rotating cylindrical liquid metal liner is driven radially by free pistons. The pistons are driven axially by a high-pressure gas causing radial motion of the free surface of the rotating liquid liner. The initial rotation of the liquid metal is provided by rotating the cylindrical vessel in which the liquid medium is contained. The entire system, including the cylindrical vessel and pistons, is rotated about its longitudinal axis, so that acylindrical cavity is formed along and coaxial with the axis of rotation. In LINUS systems that are large enough to produce power on a commercial scale, the rotational mass of this system would create very large centripetal structural forces.

[0007] Another example of such a prior art system is US patent 10,002,680 B26 / 2018 Laberge et. al. that was developed by General Fusion Inc. in 2009. In this system, a rotating liquid metal liner creates a vortex cavity within a pressure vessel, and implosion of the liner and compression of plasma in the cavity is driven by acoustic pressure waves generated by pistons striking anvils positioned radially around the pressure vessel. These pistons move within bores which are mounted to the outside of the pressure vessel.

[0008] Another example of such a prior art system is US patent 10,798,808 B2 10 / 2020 Zimmerman et al. that was developed by General Fusion Inc. in 2017. In this system, a rotor immersed in a liquid medium circulates the liquid medium to create a liquid liner surrounding a vortex cavity containing plasma, which is then collapsed by compression drivers positioned radially mounted outside of the pressure vessel. In this design, the liquid medium partially fills the compression driver such that the liquid medium spans a gap between the rotor and the non-rotating pressure vessel. When the rotor rotates the liquid liner, the liquid medium in the gap is subject to large shear forces due to fluid coupling, requiring additional energy to overcome the torque and drive the rotor.

[0009] Another example of such a prior art is a plasma compression system in US patent application 18 / 260,700 12 / 2021 Zimmerman et al. that was developed by General Fusion Inc. in 2020. In this system, a gas-filled gap between the vessel wall and the rotor replaces the liquid-filled gap as described in the ‘808 patent, thereby reducing large shear forces that result from fluid coupling. Figure 1 (PRIOR ART) shows a cutaway view of this prior art design. A reduction in shear force results in an important reduction in the energy requirement needed to rotate the rotor. In this system a magnetized plasma is generated by a coaxial plasma injector and injected into a spherical tokamak flux conserver. The flux conserver is formed by rotating the liquid metal, which creates centrifugal force in the liquid metal. This moves the liquid metal against the inner wall of the rotor. The liquid metal cylinder containing the plasma is then compressed using a plurality of compression drivers mounted to an outer surface of the vessel wall. The primary source of compression for the driver pistons may be generated by for example pneumatic, spring, or electromagnetic force acting upon the driver pistons. Further detail on this design may be foundin US patent application 18 / 260,700. This system has produced positive experimental liner compression results, however involves complexity in the synchronous timing of the driver and pusher pistons to achieve symmetrical liner implosion.

[0010] One common challenge across these MTF approaches is achieving a symmetrical implosion. To achieve commercially relevant MTF experiments, which heats plasma by compression, a magnetic flux conserver made of metal is one method for plasma confinement, and an understanding of the compression trajectory of this metal liner is crucial to the design and operation of the machine. It is known that symmetric and controlled compression trajectory of the plasma liner is important because plasma confinement and compression to fusion conditions depend in part on the symmetric implosion of the liner surrounding the plasma. Researchers at Los Alamos National Laboratory proposed to generate a high-density field reversed configuration (FRC) plasma using a conical azimuthal discharge (theta-pinch) and inject it into a cylindrical aluminum liner that would later be compressed using an axial discharge (Z-pinch). The idea was supported by their work on high-speed compression of aluminum liners. Radiographs presented showed excellent symmetry up to a radial compression of 13:1 for a 1-mm-thick solid metal liner with a 50 mm radius. In that experiment, the liner’s inner surface velocity reached 5 km / s, considerably reducing the growth of inner surface perturbations. Later work by MSNW LLC is described in US9524802B2 (assigned to Helion Inc) in which a solid aluminum metal liner is compressed by the electromagnetic force generated by theta-pinch discharge coils. General Fusion Inc has also developed solid lithium liner compression systems using theta-pinch methods. Compression of plasma using solid metal liners with theta-pinch devices is helpful to understand how to achieve symmetric compression of plasma, however, solid metal liners are not practical for commercial power plants requiring repeated compression cycles at rates on the order of 1 Hertz. One solution to repeatedly reforming the liner into a cylindrical shape on a practical time scale is to use liquid metal for the liner. Important advantages of liquid metal liners are their ability to efficiently transfer thermal energy to auxiliary power generation equipment, to shield the surrounding structures and personnel from radiation damage, to eliminate radiation embrittlement damage to the liner itself, and if the liquid contains lithium and its isotopes, to breed tritium fuel in the liner itself. As with solid metal liner implosion, one common challenge is achieving a symmetrical implosion of the liquid liner. For MTF systems that compress plasma using metalliners and theta-pinch methods, it is known that the theta-pinch coils must be designed to minimize magnetic asymmetry during liner implosion and plasma compression.

[0011] It is, therefore, desirable to provide an improvement to existing MTF theta-pinch systems for symmetrically imploding a liquid metal liner and compressing plasma.

[0012] Summary

[0013] According to one aspect of the invention, there is provided a plasma compression system comprising a plasma containment vessel having a substantially electrically non-conductive vessel wall, a substantially electrically non-conductive annular rotating core rotatable inside the vessel about an axis, and a plurality of electromagnetic implosion drivers. The annular rotating core contains an electrically-conductive liquid medium inside the rotating core that forms a liquid liner having a vortex cavity for receiving plasma when the rotating core is rotated. The rotating core comprises an outer surface spaced from an inner surface of the vessel wall to define an annular gap. The plurality of implosion drivers surround the rotating core, with each implosion driver comprising an electromagnetic coil with a body having at least one pair of a current input tab and a current output tab, a coil gap between the current input tab and current output tab, and a plurality of substantially electrically non-conductive current guides positioned on the body to guide current to flow from the current input tab along an input tab edge of the coil gap around an input tab comer of the coil body, along an inner radial edge of the electromagnetic coil body, around an output tab comer of the coil body, and to the current output tab along an output tab edge of the coil gap. The electromagnetic coils may be interposed between the rotating core and the vessel wall, or mounted around an outer surface of the vessel wall. Driving the current through the electromagnetic coils creates an implosive electromagnetic force in the conductive liquid liner that compresses the cavity and any plasma inside the cavity. The current in the plasma induces mirror current on the inner surface of the radially translating liner, the associated magnetic fields repel each other, confining and compressing the plasma as the liner collapses inward.

[0014] At least one of the plurality of electromagnetic coils can further comprise at least one auxiliary magnetic flux control loop at the distal end of at least one of the current guides. The at least one auxiliary flux control loop and current guides have dimensions and locations selected to provide a magnetic flux density at a region adjacent the input and output tab corners of the coilbody that is substantially the same as the magnetic flux density at a region around the inner radial edge of the coil body at a selected operating current.

[0015] The inner radial edge of at least one of the electromagnetic coils is scalloped; i.e has a plurality of embossments and / or depressions extending along an inner radius of the electromagnetic coil, to create a current path that follows closely the inner perimeter of the coil thus reducing azimuthal non-uniformities in the generated magnetic field.

[0016] The plurality of electromagnetic coils can be stacked along an axis of the rotating core in groups of parallel sections, wherein coil gaps of two adjacent sections are azimuthally misaligned.

[0017] The implosion drivers can comprise a plurality of electromagnetic coils electrically connected in two sets, wherein a first set of the electromagnetic coils is positioned near an axial bottom of the vessel and are electrically connected sequentially in series, and a second set of the electromagnetic coils is positioned near an axial top of the vessel and are electrically connected in series. In one aspect, there are eight electromagnetic coils with the first set having four electromagnetic coils and the second set having four electromagnetic coils.

[0018] In another aspect, a radial thickness of the rotating core between the inner surface and outer surface is higher at the axial ends than at the centre, thereby forming a corresponding cylindrical liquid liner that has a radial thickness that is lower at its axial ends than at its centre.

[0019] In another aspect, the rotating core may have a substantially uniform radial thickness, but the inner surface curves radially inwards from an axial midsection to the axial ends of the rotating core, thereby resulting in the rotating core having a smaller axial diameter at the axial ends relative to the axial midsection. The electromagnetic coils at the axial ends can have a corresponding smaller diameter than the electromagnetic coils at the axial midsection, to thereby form a corresponding cylindrical liquid liner that has a radial thickness that is lower at its axial ends than at its centre.

[0020] In another aspect, the plurality of electromagnetic coils are stacked along an axis of the rotating core in an axially spaced arrangement, with an axial space absent of coils at a midsection of the rotating core.

[0021] In another embodiment, two or more coils within the stacked assembly of coils may be discharged at varying time delay or advance to produce a corresponding delay or advance in the movement of the liquid liner, and thus shape the imploding liner or control asymmetry in the liner collapse.In another embodiment, two or more coils within the stacked assembly of coils may be discharged at varying voltages to produce a corresponding varying acceleration in the movement of the liquid liner, and thus shape the imploding liner or control asymmetry in the liner collapse.

[0022] In another aspect, there is provided a method for compressing plasma with the plasma compression system, wherein the method comprises: rotating the rotating core to form the liquid liner with the vortex cavity; injecting plasma into the vortex cavity; and driving current to each electromagnetic coil of the plurality of implosion drivers to create an implosive electromagnetic force in the liquid liner. Parameters for the driving current of each electromagnetic coil are selected to compress the liquid liner in accordance with a selected liquid liner compression profile wherein axial ends of the liquid liner converge more rapidly than a midsection of the liquid liner. Selecting the driving current parameters for each electromagnetic coil can include selecting one or more of a time delay, a voltage, and a charge that applies more or a longer duration of electromagnetic force at the ends relative to at the midsection of the liquid liner.

[0023] Brief Description of the Drawings

[0024] FIG. 1 (PRIOR ART) is a cutaway perspective view of a prior art plasma compression system having a containment vessel with a vessel wall, an annular rotating core inside the containment vessel, and a plurality of driver pistons attached to the outer surface of the vessel wall of the containment vessel.

[0025] FIG. 2 is a cutaway perspective view of a plasma compression system according to one embodiment of the invention, having a containment vessel with a substantially electrically non-conductive vessel wall, an annular rotating core inside the containment vessel and a plurality of electromagnetic implosion drivers located outside of and surrounding the containment vessel.

[0026] FIG. 3 is a schematic cross-sectional view of the plasma compression system shown in FIG. 2 having a substantially electrically non-conductive vessel wall, a substantially electrically non-conductive annular rotating core inside the vessel, and a plurality of electromagnetic implosion drivers positioned outside of the containment vessel. A current direction along the implosion drivers is indicated as I(t).FIG. 4 is a schematic cross-sectional view of the plasma compression system according to another embodiment having a substantially electrically non-conductive vessel wall, a substantially electrically non-conductive annular rotating core inside the vessel, and a plurality of electromagnetic implosion drivers positioned outside of the rotating core and inside of the containment vessel. The current direction along the implosion drives is indicated as I(t).

[0027] FIG. 5a (PRIOR ART) is a top-down view of a section of a single-turn electromagnetic coil of an implosion driver, showing a coil gap between a current input tab and a current output tab.

[0028] FIG. 5b is a schematic top-down view of a section of a single-turn electromagnetic coil having optimized current guide slots according to one embodiment of the implosion drivers.

[0029] FIG. 5c is a schematic top-down view of a section of a single-turn electromagnetic coil having auxiliary magnetic flux control loops according to another embodiment.

[0030] FIG. 6a is schematic perspective view of an axially stacked group of four implosion drivers comprising single-turn electromagnetic coils with their respective coil gaps aligned, thereby providing azimuthal clocking of the electromagnetic coils, according to one embodiment.

[0031] FIG. 6b is a schematic perspective view of an axially stacked group of four implosion drivers, wherein each single-turn electromagnetic coil has an azimuthal clocking of 90° relative to an adjacent electromagnetic coil, according to another embodiment.

[0032] FIG. 7 is a schematic plan view of a single-turn electromagnetic coil having a scalloped inner radius according to another embodiment.

[0033] FIG. 8 is a schematic cross-sectional view of the plasma compression system having axially stacked implosion drivers comprising eight electromagnetic coils electrically connected in two sets of four coils, according to another embodiment.

[0034] FIG. 9 is a schematic cross-sectional cutaway view of the plasma compression system according to another embodiment, wherein the rotating core has a radial thickness that varies along its axis, wherein the radial thickness is higher at the axial ends than at the axial centre, thereby causing a conforming liquid liner (shown in crosshatch) to form with thinner radial walls at its axial ends than at the axial centre.

[0035] FIG. 10 is a schematic cross-sectional cutaway view of a rotating core of the plasma compression system embodiment having a plurality of electromagnetic implosion drivers comprising electromagnetic coils positioned outside of the rotating core, wherein the inside radiusof the coils at the axial ends of the rotating core are smaller than the inside radius of the coils at the midsection of the rotating core.

[0036] FIGS.11(a) - 11(d) are simulated images of an electromagnetic compression driving a liquid medium in the plasma containment vessel at different time periods in a compression operation.

[0037] Detailed Description of Specific Embodiments

[0038] Embodiments of the invention relate generally to a plasma compression system comprising a plasma containment vessel having a substantially electrically non-conductive vessel wall, a substantially electrically non-conductive annular rotating core rotatable inside the vessel along an axis, an electrically-conductive liquid medium rotatable inside the rotating core to form a liquid liner vortex having a cavity for receiving plasma; and a plurality of electromagnetic implosion drivers surrounding the rotating core. Each of the plurality of electromagnetic implosion drivers comprises an electromagnetic coil with a body having at least one pair of a current input tab and a current output tab. A coil gap between the current input tab and the output tab extends from radially outwardly extending ends of the input and output tabs to input and output tab comers at the radial inner edge of the coil. Each pair of input and output tabs further comprises a pair of substantially electrically non-conductive current guides, namely, an input current guide positioned on the current input tab and an output current guide positioned on the current output tab. The input and output current guides serve to guide current to flow along an edge of the current input tab facing the coil gap, around the input tab comer, along an inner radial edge of the coil body, around the output tab comer, then along an edge of the current output tab facing the coil gap. Driving the current through the plurality of electromagnetic coils creates an implosive electromagnetic force in the liquid liner that compresses the cavity and plasma inside the cavity.

[0039] The electromagnetic coil in the plasma compression system is a type of theta-pinch coil. Theta-pinch coils are used in a variety of applications, including compressing cylindrical and spherical targets of various sizes and materials. These materials can include electrically-conductive solids, liquids, or plasma targets. Typically, these applications are very sensitive to the symmetry of the collapse of the target, because asymmetry in the object being compressed leads to instability in the shape of the collapse. In the case of compressing conductive plasma, asymmetry in the shape of the plasma during collapse is known to reduce plasma lifetime andheating, which reduces the probability of achieving fusion conditions. As will be described in further detail below, the plasma compression system provides means for improving stability during plasma compression.

[0040] Referring now to the Figures and according to one embodiment, FIG. 2 shows a cutaway view of a plasma compression system having a plasma formation injector (1), a rotating core (2) within a vessel (3), and electromagnetic implosion drivers surrounding the vessel (3). The implosion drivers comprise an assembly of multiple single-turn theta-pinch coils (4) (referred alternatively as “electromagnetic coils”). According to some embodiments and as shown FIGS. 2 and 3, the electromagnetic coils (4) surround the outside of the vessel (3); however in an alternate embodiment as shown in FIG. 4, the electromagnetic coils (4) are enclosed inside of the vessel (3), but outside of the rotating core (2). (for clarity, FIGS. 3 and 4 do not show the conductive liner or ancillary elements of the plasma compression system).

[0041] The electromagnetic coils (4) operate in a transient nature by rapidly inducing an electric current into a conductive target, i.e. the liquid medium forming the liquid liner. This induced current interacts with the magnetic field according to the Lorentz Force and becomes a pressure on the outer surface of the liquid liner, which forces it to collapse inwards.

[0042] Rapid target collapse is important for compressing plasma targets because the lifetime of MTF plasmas is in the order of milliseconds. Rapid collapse using theta pinch coil magnetic force against a conductive target is a function of a rapid rise in the current within coil. For the current in the coil to rise rapidly, the impedance of the coil must be very small, which typically results in a coil of very few turns, and commonly a single turn. Coils with few numbers of turns are very prone to asymmetries due to the location of a gap located between the current input and output tabs. FIG. 5a (PRIOR ART) illustrates a prior art single turn coil design showing a coil gap (5) located between one pair of current input (6) and output tabs (7).

[0043] The pair of current input and output tabs (6, 7) of the electromagnetic coil (4) create a small perturbation in the internal magnetic field, generating a non-uniform circumferential field density. The location of the current input tab (6) into the electromagnetic coil (4) is a source of asymmetry on the magnetic field for several reasons. First, the magnetic field is reduced at the coil gap (5) area between the current input tab (6) and output tab (7) of the electromagnetic coil (4). This produces a localized area of reduced field strength between the electromagnetic coil (4) and target, which produces a localized area of reduced magnetic force against the target.Another issue that arises with such a prior art electromagnetic coil (4) is the that the magnetic field density in an annular gap between a liner (17) and the coil 4 (the ‘liner-coil gap’) can be asymmetric. Electric current vectors (indicated by arrows (16)) preferentially follow the path of lowest impedance. In a coil geometry that is thin and wide, the current path (16) does not effectively flow into the input tab comer (14) of the coil (4). If a low or no current flows into this comer (14), the magnetic field density in a region (15) of the liner-coil gap adjacent this corner (14) will be significantly lower than the magnetic field density in a region (18) of the liner-coil gap further along the coil (4).

[0044] In the case where the target of the electromagnetic field generated by the coil (4) is a liquid metal liner, the reduced localized magnetic force against the liner target produces asymmetry during the collapse of the liner. Such asymmetry in the liner collapse produces instability in the plasma during the compression of the plasma, which reduces the probability of achieving fusion conditions in the plasma. According to some embodiments, the following features of the plasma compression system improve the level of symmetry of the magnetic field and thereby the Lorentz Force acting on the outer surface of the target, thus reducing asymmetry in the liner collapse and improving stability of the plasma compressed during the liner collapse:

[0045] Current Guide

[0046] Referring to FIG. 5b and according to one embodiment, the electromagnetic coil (4) comprises a pair of substantially electrically non-conductive current guides (8), which in this embodiment are fiberglass-filled slots at the input and output tabs (6, 7) of the electromagnetic coil (4). However, in alternative embodiments (not shown), the electromagnetic coil (4) can comprise multiple pairs of input and output tabs each with their respective pair of current guides. An input tab current guide (8) located at the input tab (6) functions to force the current supplied at the input tab (6) (shown by the arrows (16) in FIG. 5b) to travel along an edge of the input tab (6) facing the coil gap (5) before the current path turns at the input tab corer (14) to flow in the azimuthal direction along the inner radial edge of the electromagnetic coil (4), then is guided by an output tab current guide (8) located at the output tab (7) to turn and flow along an edge of the output tab (7) facing the coil gap (5). In this embodiment, the slots extend through the thickness of the coil body; however in an alternative embodiment (not shown), the slots can be grooves that extend partially into the coil body. The current guides (8) each terminate near the inner edge of the electromagnetic coil (4) and serve to reduce current path shortcuts and to minimize a localizedreduction in the magnetic field at each inside comer (14) of the coil at the input and output tabs (6, 7) (4).

[0047] As current (16) is forced into the input and output tab comers (14) by the current guides (8), the local current density at the corners (14) is increased, which in turn increases the magnetic field density in the regions (15) adjacent to these corners (14), compared to prior art designs such as that shown in FIG. 5a. The positioning of the current guides (8) are selected so that the at the intended operating currents, the magnetic field densities at the regions (15) adjacent the corners (14) and the region (18) adjacent the rest of the coil (4) are generally balanced. This creates a more symmetric poloidal field which increases symmetry in the magnetic field. The increased symmetry is expected to improve the symmetry of the Lorentz force against the liquid liner (9), stabilize the liner collapse shape, and improve the plasma stability and compression.

[0048] In an alternative embodiment, the current guide (8) is an empty slot that provides a substantially electrically non-conductive air gap for the current guide. In some other embodiments the slot is filled with a substantially electrically non-conductive material other than fiberglass (not shown).

[0049] The input current guide (8) has a proximal end at the outer radial edge of the coil (4) near the input tab (6), and extends along the coil body and terminates at a distal end in the vicinity of the input tab corner (14). The output current guide (8) has a proximal end at the outer radial edge of the coil (4) near the output tab (6) and extends along the coil body and terminates at a distal end in the vicinity of the output tab corner (14).

[0050] The specific location of the current guides (8) can be determined by determining the expected magnetic field densities in the region (18) around the coil (4) and in the region (16) adjacent the input and output tab comers (14) (without the current guides) at the intended operating current, and adjusting the location of the current guides (8) until the expected magnetic field densities (18) and (15) are substantially the same.

[0051] Auxiliary Magnetic Flux Loop

[0052] According to another embodiment and referring to FIG. 5c, the distal end of each current guide (8) is enlarged to provide an auxiliary magnetic flux control (herein referred to as an auxiliary flux control loop (10)) along with the slots of the current guide (8). Similar to the current guides (8), the role of the auxiliary flux control loop 10 is to locally affect the magnetic fielddensity in the regions (15) adjacent to the input and output tab comers (14). Generally speaking, making the auxiliary flux loops (10) larger will decrease the magnetic reluctance, and thus increase the magnetic field strength in the coil-liner gap region (15). The properties (dimensions, shape and position) of the auxiliary magnetic flux control loop (10) are selected in conjunction with the properties of the current guides (8) to achieve a substantially same magnetic field densities at regions (15) and (18).

[0053] The exact properties of the auxiliary flux control loop (10) may be calculated with a computer simulation, applying the following principles:

[0054] In addition to the magnetic field strength being affected by the current density, it is also affected by the reluctance of the magnetic circuit that the magnetic flux will exist within. Magnetic reluctance, or magnetic resistance, is defined as the ratio of magnetomotive force to magnetic flux. It represents the opposition to magnetic flux, and depends on the geometry of the auxiliary flux loop 10. The local magnetic field strength (B local) is determined by the density of the magnetic flux (phi) acting on a given cross sectional area (Area), related as:

[0055]

[0056] The amount of magnetic flux (phi) is determined by the magnetomotive force (MMF) and the total reluctance (R total), as:

[0057]

[0058] The magnetomotive force is determined by the amount of current flowing in the coil, and the reluctance is determined by how difficult it is for that current to establish a magnetic field, analogous to the electrical resistance that acts in an electric circuit. The actual reluctance in a 3D problem is difficult to calculate without a computer simulation, but an approximation that can be made for the reluctance that exists in (15) as:

[0059]

[0060] < < Where the total reluctance is the summation of the reluctance within the coil-liner gap (R_coil.liner.gap), the reluctance in the auxiliary flux loop (R aux. flux, loop), as well as some additional reluctance (R other) that can not be readily modified.

[0061] In some embodiments, the auxiliary flux loop 10 are cutouts achieved by removing additional material from the coil body (4) at that location. Like the current guides (8), the cutouts may be filled with a substantially electrically non-conductive material like fiberglass or be an empty air gap.

[0062] Clocking of the Current Input Tabs

[0063] According to some embodiments, as shown in FIGS. 6a and 6b, the implosion drivers comprise multiple electromagnetic coils (4) stacked in a spaced arrangement along the axial length of the rotating core (2). As shown in FIG. 6a and according to one embodiment, the implosion driver has a EM coil assembly comprising multiple axially stacked electromagnetic coils (4) with their respective current input and output tabs (6, 7) aligned. This will produce asymmetry of the magnetic field in only one area of the conductive liner (9). In this arrangement, the electrical impedance of the coils is unaffected, but in another embodiment and as shown in FIG. 6b, each of these electromagnetic coils (4) is clocked to a different azimuthal angle. This clocking reduces localized asymmetry in the magnetic field by misaligning the coil gaps (5) of the input and output tabs (6), (7) of adjacent electromagnetic coils (4). In the embodiment shown in FIG. 6b, a group of four implosion drivers each comprise an electromagnetic coil (4) stacked in parallel sections along an axis of the rotating core. The current input and output tabs (6) of each electromagnetic coil (4) are clocked at 90° relative to an adjacent electromagnetic coil (4) such that the coil gaps (5) of adjacent electromagnetic coils (4) are azimuthally misaligned. However, a different number of coils can be provided with their coil gaps clocked at different angles, according to alternative embodiments (not shown).

[0064] Tab clocking in the coil has several advantageous effects. Clocking reduces the absolute magnitude of the asymmetry by a factor of 1 / M, where “M” is the number of positions that the tabs can be clocked to. Clocking increases the mode number of the induced asymmetry from N=1 to N=M. The higher the mode number, the less sensitive the target is to its effect, N=1 is a bad mode number for most experiments involving theta-pinch coils. Clocking results in asymmetries that are not continuous along the length of the coil (4), instead they exist as a local pocket of fieldirregularity. This reduces the initiation of axial buckles, which are a common issue for theta-pinch devices.

[0065] Note that the electrical circuit used to electrically connect the multiple parallel sections of the electromagnetic coils (4) may be of a parallel or series, of combination of parallel and series, circuit design.

[0066] Electromagnetic Coil with Scalloped Inner Radial Edge

[0067] According to another embodiment and referring to FIG. 7, the implosion driver comprises scalloping (12) extending around the inner radial edge of the electromagnetic coil (4) that compensates for a non-uniform circumferential conduction path in the electromagnetic coil (4).

[0068] The scalloping (12) comprises a series of embossment and / or depression features extending around the inner edge of the electromagnetic coil (4). The features of the scalloping (12) can be selected to increase the gap between the conductive liner (9) and electromagnetic coil (4) and reduce the local b-field density when too high. Similarly, if the flux density is too low, the features of the scalloping (12) can be selected to decrease the inner radius.

[0069] In the embodiment shown in FIG. 7, the implosion driver (4) comprise holes (11) that extend through the body of the electromagnetic coil (4) to accommodate mechanical tie rods (not shown), and which also serve to contribute to an asymmetry in the magnetic field between the electromagnetic coil (4) and the conductive liner (9). These holes (11) result in a higher b-field density, and therefore the features of the scalloping (12) extending around the inner radial edge of the electromagnetic coil (4) are selected to normalize the b-field density and increase symmetry of the electromagnetic force applied to the liner and the plasma target.

[0070] Electromagnetic Coil Spacing

[0071] Localized magnetic field symmetry for a single coil or set of coils is important to control local symmetry of liner collapse. However, also important is to control macro-scale shaping of the liner collapse. Liner collapse shaping is important to better confine the plasma for greater compression. Although plasma can be compressed using a cylindrical liner, there is a tendency for the plasma to ‘squeeze out’ of the ends of the cylinder during collapse, thereby reducing plasma compression. In addition to using coils to accomplish liner collapse in general, it would be advantageous to use the electromagnetic coils (4) to control the shape of the imploding liner to produce a spheroidal liner shape that traps the plasma at the center of the imploding liner.One way to produce a spheroidal liner shape is to selectively position the electromagnetic coils (4) relative to one another in a way that creates shaped magnetic field forces that bear on the liner to produce the desired liner shape. FIG. 8 shows an assembly of theta pinch electromagnetic coils (4) placed around the outer wall of the vessel (3). The electromagnetic coils (4) have differential placement, for example are more concentrated at the axial top and bottom of the vessel, with none placed at the midsection (13) of the vessel (3). The result is a larger magnetic field is created at the axial ends of the vessel (3) relative to the midsection (13). When current flows into the electromagnetic coils (4) in this configuration, the larger magnetic field at the axial ends of the vessel (3) produces greater acceleration of the conductive liner (9) at its axial ends. Not shown is the corollary to FIG. 4, whereby the differential placement of the electromagnetic coils (4) may be located inside of the vessel (3) and outside of the rotating core (2). This differential placement of coils can be used to collapse the conductive liner (9) into a spheroidal shape that may be advantageous for plasma compression.

[0072] Another way to produce a spheroidal liner shape using theta pinch electromagnetic coils (4) is to control the shape of the liner itself prior to compression. FIG. 9 is a diagram that shows where a liquid liner (9) is rotated inside of a rotating core (2). The inner surface of the rotating core (2) is curved radially inwards at its axial ends, whereby the axial ends of the rotating core (2) are of smaller inside diameter than its midsection. This produces a conforming shape in the liquid liner (9) having less mass at its axial ends relative to its mass at its midsection. When a current is applied to the surrounding coils (4), the Lorenz force produced bears on the liquid liner (9). Because the axial ends of the liquid liner (9) are thinner and have less mass than the midsection, the axial ends of the liquid liner (9) experience greater acceleration for a given magnetic force relative to the midsection of the liner. This differential acceleration produces a spheroidal shape in the collapsing liner (9), and such shape is advantageous to confining plasma during compression. It can be appreciated that this design may be varied by placing the electromagnetic coils (4) on the outside of the vessel (3), and also that the rotating core (2) shaping embodiment may be combined with differential coil spacing designs as shown in FIG. 8 and described above.

[0073] Another way to produce a spheroidal liner shape using theta pinch coils is by varying the spacing between the theta pinch electromagnetic coils (4) and the conductive liquid liner (9), where they are placed closer together, for a given current in the electromagnetic coils (4) more force is applied to the liquid liner (9) for a longer period of time, resulting in greater acceleration. FIG. 10shows a design where the inner radii of the electromagnetic coils (4) surrounding the rotating core (2) are smaller at the axial ends (i.e. coils are closer to the liner) than at the midsection of the rotating core (2). It can be appreciated that this design may be varied by placing a similar configuration of the electromagnetic coils (4) on the outside of the vessel (3) instead of inside the vessel (3). This design can also be combined with other liner shaping means such as differential coil spacing, rotating core shaping, coil clocking, or current guides.

[0074] It can be appreciated that any of these designs and methods for liner shaping using theta pinch coils may also include means for control of the amount of current sent to individual coils, or means to control timing of the current introduced to individual coils, to produce differential acceleration of the liner to produce advantageous liner shape during collapse.

[0075] Various means exist to initiate and shape the controlled collapse of a liner using theta-pinch electromagnetic coils, to create compression of a stabilized plasma into fusion conditions. FIGs.

[0076] 11(a) - 11(d) are images of a simulation of a method of electromagnetic compression driving a liquid medium to form the liquid liner (9) in the vessel at different time periods in a compression operation. The conductive liquid liner (9) can be a liquid metal and is rotated inside of a substantially non-conductive rotating core (2) contained inside of a substantially non-conductive vacuum vessel (3). The rotation of the liquid liner (9) forms the liner into a cylinder shape (FIG. Ila). When the electromagnetic coils (4) are energized with high current, a magnetic force is exerted upon the conductive liquid liner (9) resulting in an inward implosion of the liquid liner (9) toward the center of the vortex formed by the rotating core (2). This design compresses the plasma contained within the rotating core (2). Not shown is the remaining time sequence images showing the rebound of the liquid liner after plasma compression.

[0077] The shaped metal liner compresses the plasma mostly via the magnetic field, which is repelled from the liquid liner (9) due to Lenz’s Law. Because the magnetic field can also be modified by external coils, the current in those coils (9) can be used to further control and shape the plasma. The shape of the plasma over time strongly affects its stability and structure and that shape is controlled by both the liner and the externally applied magnetic fields.

[0078] Controlling Liner Collapse and Plasma Compression

[0079] Several different methods to radially compress a liquid metal liner and confine a plasma within have been described. To summarize, the liquid metal liner (9) containing plasma can bepushed inwards by a ramping magnetic field provided by the electromagnetic coils (4) of the implosion drivers. The plasma-confining liner (9) can be a liquid metal that is manipulated to create a hollow tube structure. In some embodiments, the compression system selectivity applies spatially nonuniform compression force along the cylindrical longitudinal axis (Z). The distribution of the nonuniform compression force along the cylindrical longitudinal axis is carefully chosen to dynamically shape the liner to maximize the plasma stability and therefore the plasma’s lifetime, allowing the plasma to be compressively heated. For example, applying more force, or applying force for longer, near the ends of the cylinder will cause the ends of the cylinder to converge more rapidly than the center region. Dynamically shaping the liner, while radially compressing it, contributes to maintaining plasma stability during compression.

[0080] The plasma is an ionized gas that is confined by a magnetic field. The magnetized plasma occupies a volume that is approximately toroidal in shape. The structure of the magnetic fields within this volume is a factor for determining the plasma stability. A stable plasma will prevent thermal energy from quickly escaping and respond to externally applied perturbations (such as from small ripples in the liner) by blocking them from penetrating deep into the plasma volume. Conversely, the magnetic fields in an unstable plasma will quickly become disordered and permit thermal energy to escape much faster than the plasma can be compressed. Plasmas can be made magnetically stable by, for example, increasing the strength of the toroidal magnetic field, decreasing the gas pressure, or manipulating the geometry and structure of the magnetic field using external coils and / or an evolving liner geometry that is built into and / or dynamically controlled by the compression system.

[0081] Ideal magnetohydrodynamic (MHD) instabilities are the most deleterious for plasma performance, followed closely by resistive MHD instabilities. Ideal MHD instabilities are driven by either current gradients, which tend to cause long-wavelength modes (such as saw-teeth or kink modes), or by pressure gradients, which tend to cause short wavelength modes (such as ballooning modes). Both types of ideal instabilities are generally well understood and can be avoided by careful manipulation of the plasma. On the other hand, resistive instabilities are always possible and are more difficult to predict because multiple modes can couple together, so non-local evaluation is required. For example, neoclassical tearing modes (NTM) can occur anywhere a magnetic configuration crosses two surfaces with the same rational twist ratio.While particular elements, embodiments and applications of the present disclosure have been shown and described, it will be understood, that the scope of the disclosure is not limited thereto, since modifications can be made by those skilled in the art without departing from the scope of the present disclosure, particularly in light of the foregoing teachings. Thus, for example, in any method or process disclosed herein, the acts or operations making up the method / process may be performed in any suitable sequence and are not necessarily limited to any particular disclosed sequence. Elements and components can be configured or arranged differently, combined, and / or eliminated in various embodiments. The various features and processes described above may be used independently of one another, or may be combined in various ways. All possible combinations and sub-combinations are intended to fall within the scope of this disclosure. Reference throughout this disclosure to “some embodiments,” “an embodiment,” or the like, means that a particular feature, structure, step, process, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, appearances of the phrases “in some embodiments,” “in an embodiment,” or the like, throughout this disclosure are not necessarily all referring to the same embodiment and may refer to one or more of the same or different embodiments. Indeed, the novel methods and systems described herein may be embodied in a variety of other forms; furthermore, various omissions, additions, substitutions, equivalents, rearrangements, and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions described herein.

[0082] Various aspects and advantages of the embodiments have been described where appropriate. It is to be understood that not necessarily all such aspects or advantages may be achieved in accordance with any particular embodiment. Thus, for example, it should be recognized that the various embodiments may be carried out in a manner that achieves or optimizes one advantage or group of advantages as taught herein without necessarily achieving other aspects or advantages as may be taught or suggested herein.

[0083] Conditional language used herein, such as, among others, "can," "could," "might," "may," “e.g.,” and the like, unless specifically stated otherwise, or otherwise understood within the context as used, is generally intended to convey that certain embodiments include, while other embodiments do not include, certain features, elements and / or steps. Thus, such conditional language is not generally intended to imply that features, elements and / or steps are in any way required for one or more embodiments or that one or more embodiments necessarily include logicfor deciding, with or without operator input or prompting, whether these features, elements and / or steps are included or are to be performed in any particular embodiment. No single feature or group of features is required for or indispensable to any particular embodiment. The terms “comprising,” “including,” “having,” and the like are synonymous and are used inclusively, in an open-ended fashion, and do not exclude additional elements, features, acts, operations, and so forth. Also, the term “or” is used in its inclusive sense (and not in its exclusive sense) so that when used, for example, to connect a list of elements, the term “or” means one, some, or all of the elements in the list.

[0084] The example calculations, simulations, results, graphs, values, and parameters of the embodiments described herein are intended to illustrate and not to limit the disclosed embodiments. Other embodiments can be configured and / or operated differently than the illustrative examples described herein.

Claims

Claims1. A plasma compression system comprising:a plasma containment vessel having a substantially electrically non-conductive vessel wall;an annular rotating core rotatable inside the vessel about an axis, the rotating core comprising an outer surface spaced from an inner surface of the vessel wall to define an annular gap, the annular rotating core being substantially electrically non-conductive;an electrically-conductive liquid medium inside the rotating core that forms a liquid liner having a vortex cavity for receiving plasma when the rotating core is rotated; anda plurality of electromagnetic implosion drivers surrounding the rotating core, each electromagnetic implosion driver comprising an electromagnetic coil having an annular body with at least one pair of a current input tab and a current output tab, a coil gap between the current input tab and the current output tab, and a plurality of substantially electrically non-conductive current guides positioned on the coil body to guide current to flow from the current input tab along an input tab edge of the coil gap, around an input tab comer of the coil body, along an inner radial edge of the electromagnetic coil body, around an output tab comer of the coil body, and to the current output tab along an output tab edge of the coil gap;wherein driving the current through the plurality of electromagnetic coils creates an implosive electromagnetic force in the conductive liquid liner that compresses the vortex cavity.

2. The plasma compression system according to claim 1, wherein each of the plurality of electromagnetic implosion drivers are positioned between the outer surface of the rotating core and the vessel wall.

3. The plasma compression system according to claim 1, wherein the plurality of electromagnetic implosion drivers are positioned around an outer surface of the vessel wall.

4. The plasma compression system according to any one of claims 1 to 3, wherein at least one of the plurality of electromagnetic coils further comprises at least one auxiliary flux control loop at the distal end of at least one of the current guides.

5. The plasma compression system according to claim 4, wherein the at least one auxiliary flux control loop and current guides have dimensions and locations selected to provide a magnetic flux density at a region adjacent the input and output tab comers of the coil body that is substantially the same as the magnetic flux density at a region around the inner radial edge of the coil body at a selected operating current.

6. The plasma compression system according to any one of claims 1 to 5, wherein the plurality of implosion drivers comprise a plurality of electromagnetic coils stacked along the rotating core axis in groups of parallel sections, wherein the coil gaps between of two adjacent parallel sections are azimuthally misaligned.

7. The plasma compression system according to any one of claims 1 to 6, wherein the inner radial edge of at least one of the electromagnetic coils is scalloped.

8. The plasma compression system according to any one of claims 1 to 7, wherein the plurality of electromagnetic implosion drivers comprise two electrically connected sets of electromagnetic coils, wherein a first set is positioned towards an axial bottom of the vessel and are electrically connected sequentially in series, and a second set of the electromagnetic coils are positioned towards an axial top of the vessel and are electrically connected sequentially in series.

9. The plasma compression system according to any one of claims 1 to 8, wherein a radial thickness of the annular rotating core is higher at axial ends than at a centre of the rotating core.

10. The plasma compression system according to any one of claims 1 to 9, wherein the inner surface of the rotating core curves radially inwards from an axial midsection to axial ends of the rotating core.

11. The plasma compression system according to claim 10, wherein the plurality of implosion drivers comprise a plurality of electromagnetic coils stacked along an axis of the rotating core, with the electromagnetic coils located at the axial ends of the rotating core having a smaller diameter than a diameter of the electromagnetic coils located at the axial midsection of the rotating core.

12. The plasma compression system according to any one of claims 1 to 11 wherein the plurality of electromagnetic implosion drivers comprise two groups of electromagnetic coils stacked along the axis of the rotating core and spaced apart at an axial midsection of the rotating core.

13. The plasma compression system according to any one of claims 1 to 12 wherein the current guides comprise a slot in the coil body containing a substantially electrically non-conductive material.

14. The plasma compression system according to claim 13 wherein the slot is a channel that extends through the coil body.

15. The plasma compression system according to claim 13 or 14 wherein the substantially electrically non-conductive material is fiberglass.

16. A method for compressing plasma with the plasma compression system of any one of claims 1 to 15, the method comprising:rotating the rotating core to form the liquid liner with the vortex cavity;injecting plasma into the vortex cavity; anddriving current to each electromagnetic coil of the plurality of implosion drivers to create an implosive electromagnetic force in the liquid liner, wherein parameters for thedriving current of each electromagnetic coil are selected to compress the liquid liner in accordance with a selected liquid liner compression profile wherein axial ends of the liquid liner converge more rapidly than a midsection of the liquid liner.

17. The method according to claim 16, wherein selecting the driving current parameters for each electromagnetic coil includes selecting one or more of a time delay, a voltage, and a charge that applies more or a longer duration of electromagnetic force at the ends relative to at the midsection of the liquid liner.

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