Planar coil stellarator

Abstract

Disclosed herein is a stellarator comprising two sets of coils, namely a set of encircling coils which encircle the plasma axis, and a set of shaping coils which do not encircle any other coil or the plasma. In some embodiments, the encircling coils include a structural element to maintain their shape under magnetic forces. In some embodiments, the shaping coils are mounted onto one or more structural elements which, together with the shaping coils, constitute a field shaping unit. Also disclosed is a controller which may modify the electrical current flowing in one or more subsets of the coils in order to achieve target plasma parameters. Also disclosed is a method of designing a set of shaping coils by discretizing a surface dipole or current potential distribution.

Claims

1. A stellarator comprising: (a) a field-shaping coil system including one or more field shaping units which define a void adapted to confine a plasma, wherein each field shaping unit comprises: (i) one or more structural mounting elements; and (ii) one or more planar shaping coils disposed on a surface of the one or more structural mounting elements, wherein the one or more planar shaping coils do not interlock with each other, and where each of the one or more shaping coils do not individually encircle the plasma; and (b) a plurality of planar encircling coils which encircle the field-shaping coil system, and wherein each planar encircling coil of the plurality of planar encircling coils do not interlock with each other.

2. The stellarator of claim 1, wherein the stellarator includes between 3 and 100 planar encircling coils.

3. The stellarator of claim 1, wherein each of the one or more planar shaping coils and the plurality of planar encircling coils are comprised of one or more superconducting materials.

4. The stellarator of claim 1, wherein the stellarator comprises at least 4 field shaping units.

5. The stellarator of claim 1, wherein the surface of the one or more structural mounting elements faces the void.

6. The stellarator of claim 1, wherein each of the one or more field shaping units comprises one structural mounting element.

7. The stellarator of claim 6, wherein the one structural mounting element is wedge shaped.

8. The stellarator of claim 1, wherein a shape of each planar shaping coil of the one or more planar shaping coils is substantially rectangular, substantially rectangular with rounded corners, or substantially circular.

9. The stellarator of claim 1, wherein each of the one or more field shaping units comprises between 5 and 100 shaping coils.

10. The stellarator of claim 1, further comprising one or more control coils and/or one or more saddle coils, wherein the one or more control coils and/or the one or more saddles coils are communicatively coupled to a controller.

11. A stellarator comprising: (a) a void adapted to confine a plasma having a plasma axis; (b) a plurality of planar shaping coils, wherein an array comprising the plurality of planar shaping coils encircles the plasma axis, but where any individual planar shaping coil of the plurality of planar shaping coils does not encircle the plasma axis; and (c) a plurality of planar encircling coils, wherein each individual planar encircling coil of the plurality of encircling coils encircles the plasma axis.

12. The stellarator of claim 11, wherein the plurality of planar shaping coils do not interlock one another; and wherein the plurality of planar shaping coils do not interlock any one of the plurality of encircling coils.

13. The stellarator of claim 11, wherein plurality of planar encircling coils do not interlock one another; and wherein the plurality of planar encircling coils do not interlock any one of the plurality of planar shaping coils.

14. The stellarator of claim 11, wherein the plurality of encircling coils and the plurality of planar shaping coils are both comprised of one or more superconducting materials.

15. The stellarator of claim 11, further comprising one or more control coils and/or one or more saddle coils, wherein the one or more control coils and/or the one or more saddle coils are not superconducting coils.

16. A stellarator comprising: (a) a void adapted to confine a plasma, wherein the void comprises at least two faces; (b) at least two planar shaping coils, wherein a first of the at least two planar shaping coils is proximal to a first of the at least two faces but does not encircle the void, and wherein a second of the at least two planar shaping coils is proximal to a second of the at least two faces but does not encircle the void; and (c) a plurality of planar encircling coils, wherein each individual planar encircling coil of the plurality of encircling coils encircles the plasma axis.

17. The stellarator of claim 16, wherein the at least two faces are on opposite sides of the confined plasma.

18. The stellarator of claim 16, wherein the at least two planar shaping coils do not interlock one another; and wherein the at least two planar shaping coils do not interlock any one of the plurality of encircling coils.

19. The stellarator of claim 16, wherein plurality of planar encircling coils do not interlock one another; and wherein the plurality of planar encircling coils do not interlock any one of the at least two planar shaping coils.

20. The stellarator of claim 16, wherein the plurality of encircling coils and the at least two planar shaping coils are both comprised of one or more superconducting materials.

21. The stellarator of claim 16, further comprising one or more control coils and/or one or more saddle coils; wherein the one or more control coils and/or the one or more saddle coils are not superconducting coils.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) For a general understanding of the features of the disclosure, reference is made to the drawings. In the drawings, like reference numerals have been used throughout to identify identical elements.

(2) FIG. 1A depicts the components of the Wendelstein 7-X stellarator and, in particular, the arrangement of the external planar coils, modular coils, and planar trim coils in relation to each other and relative to the confined plasma.

(3) FIG. 1B depicts the components of the CNT stellarator and, in particular, the arrangement of the IL and PF coils.

(4) FIG. 2A illustrates a stellarator according in accordance with some embodiments of the present disclosure. In particular, FIG. 2A illustrates a plurality of planar encircling coils encircling the field-shaping coil system and hence the plasma.

(5) FIG. 2B illustrates a top-down view of a stellarator according in accordance with some embodiments of the present disclosure.

(6) FIG. 2C illustrates a cross sectional view of a stellarator according in accordance with some embodiments of the present disclosure.

(7) FIG. 2D illustrates a top-down view of a stellarator according in accordance with some embodiments of the present disclosure, where the stellarator is depicted as including one or more optional saddle coils.

(8) FIG. 2E illustrates a cross sectional view of a stellarator according in accordance with some embodiments of the present disclosure, where the stellarator is depicted as including one or more optional saddle coils.

(9) FIG. 3A illustrates a coil design having a circular winding pattern.

(10) FIG. 3B illustrates a coil design having a rectangular winding pattern.

(11) FIG. 3C illustrates a coil design having a rectangular winding pattern, but where the edges are rounded.

(12) FIG. 4A illustrates a cross sectional view of a stellarator showing a field shaping unit and an encircling coil in accordance with one embodiment of the present disclosure.

(13) FIG. 4B illustrates a top-down view of a portion of a stellarator showing a field shaping unit having a wedge-like shape as viewed from this angle.

(14) FIG. 5 shows a cross sectional view of a stellarator and, in particular, depicts one or more encircling coils encircling a field shaping system in accordance with one embodiment of the present disclosure.

(15) FIG. 6 provides a flowchart illustrating a method of designing a set of shaping coils by discretizing a surface dipole or current potential distribution in accordance with one embodiment of the present disclosure.

DETAILED DESCRIPTION

(16) It should also be understood that, unless clearly indicated to the contrary, in any methods claimed herein that include more than one step or act, the order of the steps or acts of the method is not necessarily limited to the order in which the steps or acts of the method are recited.

(17) As used herein, the singular terms a, an, and the include plural referents unless context clearly indicates otherwise. Similarly, the word or is intended to include and unless the context clearly indicates otherwise. The term includes is defined inclusively, such that includes A or B means including A, B, or A and B.

(18) As used herein in the specification and in the 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 shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as only one of or exactly one of, or, when used in the claims, consisting of, will refer to the inclusion of exactly one element of a number or list of elements. In general, the term or as used herein shall only be interpreted as indicating exclusive alternatives (i.e., one or the other but not both) when preceded by terms of exclusivity, such as either, one of only one of or exactly one of. Consisting essentially of, when used in the claims, shall have its ordinary meaning as used in the field of patent law.

(19) The terms comprising, including, having, and the like are used interchangeably and have the same meaning. Similarly, comprises, includes, has, and the like are used interchangeably and have the same meaning. Specifically, each of the terms is defined consistent with the common United States patent law definition of comprising and is therefore interpreted to be an open term meaning at least the following, and is also interpreted not to exclude additional features, limitations, aspects, etc. Thus, for example, a device having components a, b, and c means that the device includes at least components a, b, and c. Similarly, the phrase: a method involving steps a, b, and c means that the method includes at least steps a, b, and c. Moreover, while the steps and processes may be outlined herein in a particular order, the skilled artisan will recognize that the ordering steps and processes may vary.

(20) As used herein in the specification and in the claims, the phrase at least one, in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase at least one refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, 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) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements 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 elements); etc.

(21) Reference throughout this specification to one embodiment or an embodiment means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrases in one embodiment or in an embodiment in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

(22) Electromagnetic coils may be described according to their shape and/or topology. For instance, an electromagnetic coil may have a planar shape (a coil that lines within one flat plane) or non-planar shape. Planar electromagnetic coils may be fabricated by conventional means and wound with electrical wire under tension. Topology refers to whether an electromagnetic coil links, threads, or interlocks with another coil, in the manner of chain links. Topology may also refer to whether an electromagnetic coil interlocks the plasma or not.

(23) Stellarators

(24) The present disclosure is directed to an improved stellarator design which has a simpler, less complex structure as compared with stellarators developed to-date.

(25) Described herein are stellarators incorporating a plurality of encircling coils and a plurality of shaping coils. With reference to FIGS. 2A-2C, stellarators of the present disclosure comprise a field shaping system 203 which surrounds a void 201 that confines a plasma 200. In some embodiments, the void 201 is configured such that a largest dimension from a plasma axis 205 of any contained plasma 200 to an outer edge of the contained plasma (not shown) is less than 20 meters, such as less than 10 meters, such as less than 5 meters, such as less than 4 meters, such as less than 3 meters, such as less than 2 meters, such as less than 1 meter, such as less than 0.5 meters, etc.

(26) In some embodiments, the plasma 200 has a topology which substantially approximates that of a torus. In some embodiments, the plasma 200 is centered around a plasma axis 205, which is a magnetic field line that maps onto its own origin after one toroidal rotation. In some embodiments, the plasma axis 205 has a topology of a loop or one that substantially approximates a loop.

(27) The field shaping system 203 comprises a plurality of field shaping units 210. In some embodiments, the field shaping system 203 may comprise at least 2, at least 4, at least 6, at least 8, at least 10, at least 12, at least 16, at least 20, at least 24, at least 30, at least 36, at least 48, at least 54, at least 60, at least 70, at least 80, at least 90, at least 100, at least 110, at least 120, at least 130, at least 150, at least 170 field shaping units 210.

(28) In some embodiments, each of the field shaping units 210 includes one or more structural mounting elements 211 having a surface 215. In some embodiments, the surface 215 of each field shaping unit 211 faces the void 201. In some embodiments, each field shaping unit 210 further includes one or more additional components 216. The one or more additional components include, but are not limited to, a first wall to handle plasma flux, a structure which mounts to the first wall, a breeding blanket to breed radioisotopes from the fusion neutron flux, a cryostat, and/or neutron shielding.

(29) In some embodiments, each field shaping unit 210 comprises a single structural mounting element 211. In other embodiments, each field shaping unit 210 comprises two structural mounting elements 211. In yet other embodiments, each field shaping unit 210 comprises three structural mounting elements 211. In further embodiments, each field shaping unit 210 comprises four or more structural mounting elements 211. In some embodiments, the structural mounting element 211 is comprised of steel. In some embodiments, the structural mounting element 211 comprises a metal. In some embodiments, the structural mounting element 211 comprises a composite material, such as G-10.

(30) The field shaping unit 210 may have any size and shape. In some embodiments, the field shaping unit 210 defines an extruded circular annulus cross section structure. In other embodiments, the field shaping unit 210 has an arbitrary shape, such as a shape having a non-constant crosssection. For example, and as illustrated in FIG. 4B, in some embodiments, the field shaping unit 410 has a wedge shape (as seen from a perspective perpendicular to the plasma axis and the direction of curvature, arranged such that the narrower portion of the wedge faces the direction of plasma axis curvature, and the wider portion of the wedge faces opposite the direction of plasma axis curvature). In some embodiments, the field shaping unit 410 is substantially wedge shaped. In other embodiments, the field shaping unit 210 has a shape similar to or the same as a cross sectional shape of the plasma at that location. In other embodiments, the field shaping unit has about the cross sectional shape of the plasma, with some constant normal offset distance.

(31) In some embodiments, one or more shaping coils 212 are disposed on the surface 215 of each of the one or more structural mounting elements 211. It is believed that the one or more shaping coils 212 of the present disclosure are relatively easy to manufacture, assemble, and integrate into a field shaping unit. Moreover, it is believed that the one or more field shaping coils 212 allow precise control over the shape of the plasma.

(32) Each of the one or more shaping coils 212 are planar coils. A planar coil is one whose shape substantially lies within one flat plane. In some embodiments, each of the shaping coils 212 individually do not encircle the plasma axis 205. Said another way, any one shaping coil 212 does not encircle the plasma 200 or the plasma axis 205. For instance, and as depicted in FIGS. 4 and 5, the shaping coils 412 or 512 are disposed on surface 415 or 515 of a structural mounting element 411 or 511, respectively, and each individual shaping coil 412 or 512 does not encircle the plasma axis.

(33) While any individual shaping coil 212 does not encircle the plasma axis 205, collectively an array including a plurality of shaping coils 212 mounted on the surfaces 215 of one or more structural mounting elements 211 would encircle the plasma axis 205. This is illustrated in FIG. 4A which shows a plurality of shaping coils 412 arranged on a surface 415 of a structural mounting element 411. As depicted, no one shaping coil 412 encircles the plasma confined in the void 401. However, the collective of all shaping coils 412 as arranged on the surface 415 of the one or more structural mounting elements 411 does encircle the plasma and/or the void 401. This concept is further illustrated in FIG. 5, which again illustrates that no one shaping coil 512 encircles the plasma confining void 501. In some embodiments, individual shaping coils 512 may be positioned on opposite sides of the plasma or on different faces of the void.

(34) Each of the one or more shaping coils 212, 412 or 512 do not interlock with any other shaping coil, such as illustrated in at least FIGS. 2A, 4A and 5. Additionally, each of the one or more shaping coils do not interlock with any of the encircling coils 230 described herein (see FIGS. 2A, 4A, and 5). In some embodiments, the one or more shaping coils 212 are removably coupled to the surface 215 of the one or more surface mounting elements 211.

(35) In some embodiments, the planar shaping coils have a mean coil radius which is smaller than a major radius of the plasma and smaller than a minor radius of the plasma. As used herein, the major radius of the plasma is the mean distance between the plasma axis and the geometric center of the stellarator. As used herein, the minor radius of the plasma is the mean closest distance between each point on the plasma boundary and the plasma axis. The plasma boundary is sometimes represented by a set of toroidal Fourier amplitudes; for this case, the major radius is represented by the amplitude of the mode with toroidal mode number 0 and poloidal mode number 0; and the minor radius is represented by the amplitudes of the mode with toroidal mode number 0 and poloidal mode number 1.

(36) The shaping coils 212 may have different sizes and shapes. For instance, and with reference to FIG. 3A, in some embodiments the shaping coils 212 may be circular or substantially circular. In other embodiments, the shaping coils may be rectangular or substantially rectangular (FIG. 3B). In yet other embodiments, the shaping coils may be rectangular with rounded corners or substantially rectangular with rounded corners (FIG. 3C). In some embodiments, each field shaping unit 210 may comprise one or more coils having different shapes. For instance, a field shaping unit 210 may comprise 10 shaping coils where 3 of the shaping coils may have a substantially circular shape, 4 of the shaping coils may have a substantially rectangular shape, and 3 of the coils may have a substantially rectangular shape with rounded corners (not depicted).

(37) In some embodiments, the stellarator of the present disclosure may include between about 10 and 10,000 shaping coils. In other embodiments, the stellarator of the present disclosure may include between about 50 and 5,000 shaping coils. In yet other embodiments, the stellarator of the present disclosure may include between about 100 and 5,000 about shaping coils. In further embodiments, the stellarator of the present disclosure may include between about 100 and 4,000 about shaping coils. In yet further embodiments, the stellarator of the present disclosure may include between about 100 and 3,000 about shaping coils. In even further embodiments, the stellarator of the present disclosure may include between about 100 and 2,000 about shaping coils. In even further embodiments, the stellarator of the present disclosure may include between about 100 and 1,000 about shaping coils.

(38) In some embodiments, a field shaping unit 210 may include between about 5 and about 150 shaping coils 212. In other embodiments, a field shaping unit 210 may include between about 5 and about 100 shaping coils 212. In yet other embodiments, a field shaping unit 210 may include between about 5 and about 80 shaping coils 212. In further embodiments, a field shaping unit 210 may include between about 5 and about 70 shaping coils 212. In even further embodiments, a field shaping unit 210 may include between about 5 and about 60 shaping coils 212. In yet even further embodiments, a field shaping unit 210 may include between about 5 and about 50 shaping coils 212. In yet even further embodiments, a field shaping unit 210 may include between about 5 and about 45 shaping coils 212. In yet even further embodiments, a field shaping unit 210 may include between about 5 and about 40 shaping coils 212. In yet even further embodiments, a field shaping unit 210 may include between about 5 and about 35 shaping coils 212. In yet even further embodiments, a field shaping unit 210 may include between about 5 and about 30 shaping coils 212. In yet even further embodiments, a field shaping unit 210 may include between about 5 and about 25 shaping coils 212.

(39) With reference to FIG. 2, the stellarator of the present disclosure also includes a plurality of encircling coils 230 which encircle the plasma axis 205. Each of the encircling coils 230 are arranged around an exterior of the field shaping system 203 and encircle it. This is further illustrated in FIGS. 4 and 5 which show encircling coils 430 and 530 encircling the plasma and/or void 401 or 501, respectively; but where the encircling coils 430 and 530 are exterior to any field shaping unit 410 or 510.

(40) Each encircling coil 230 of the plurality of encircling coils are planar. Moreover, each encircling coil 230 of the plurality of encircling coils are non-interlocking with any other encircling coil 230. Additionally, each encircling coil 230 of the plurality of encircling coils are do not interlock with any of the shaping coils 212. Said another way, any encircling coil 230 does not interlock with any other planar encircling coil 230 or with any other shaping coil 212, such as depicted in FIGS. 2A, 2B, and 5. In some embodiments, each encircling coil 230 is supported by a structural component 231. In some embodiments, the structural component 231 and the field shaping units 210 may be coupled to other structural members 540 which react to unbalanced forces and torques.

(41) In some embodiments, the encircling coils do not exhibit the N-fold rotational symmetry of toroidal field (TF) coils. If the encircling coils are N-fold rotationally symmetric, like TF coils in the prior art, then the planar shaping coils require some irreducible quantity of current length (Amperes*meters) in order to correct this field. If the encircling coils are allowed to not be N-fold rotationally symmetric, the current-length requirements of the planar shaping coils can be reduced by a large factor. It is believed that this requirement may be reduced by nearly a factor of 10 by allowing the encircling coils to be positioned more favorably.

(42) In some embodiments, the stellarators of the present disclosure include between about 3 and about 150 encircling coils. In other embodiments, the stellarators of the present disclosure include between about 3 and about 100 encircling coils. In yet other embodiments, the stellarators of the present disclosure include between about 3 and about 75 encircling coils. In further embodiments, the stellarators of the present disclosure include between about 3 and about 50 encircling coils. In yet further embodiments, the stellarators of the present disclosure include between about 3 and about 25 encircling coils. In even further embodiments, the stellarators of the present disclosure include between about 3 and about 15 encircling coils. In yet even further embodiments, the stellarators of the present disclosure include between about 3 and about 10 encircling coils. In some embodiments, the spacing between each encircling coil may range from between about 10 cm to about 1 m.

(43) The shaping coils 212 and the encircling coils 230 may be comprised of one or more superconducting materials. A superconductor is a material that achieves superconductivity. Superconductivity is the property of certain materials to conduct direct current (DC) electricity without energy loss when they are cooled below a critical temperature (referred to as T.sub.c). An electric current in a superconductor can persist indefinitely. Exemplary superconducting materials include, but are not limited to, NbTi, Nb.sub.3Sn, MgB.sub.2, LaBaCuO.sub.x, LSCO (e.g., La.sub.2?xSr.sub.xCuO.sub.4, etc.), YBCO (e.g., YBa.sub.2Cu.sub.3O.sub.x or YBa.sub.2Cu.sub.3O.sub.7), REBCO, bismuth-based cuprate superconductors (BSCCO) (including Bi.sub.2Sr.sub.2CaCu.sub.2O.sub.8 (Bi-2212) and Bi.sub.2Sr.sub.2Ca.sub.2Cu.sub.3O.sub.10 (Bi-2223)), TBCCO (e.g., Tl.sub.2Ba.sub.2Ca.sub.2Cu.sub.3O.sub.10 or Tl.sub.mBa.sub.2Ca.sub.n?1Cu.sub.nO.sub.2n+m+2+?), HgBa.sub.2Ca.sub.2Cu.sub.3O.sub.x, and other mixed-valence copper-oxide perovskite materials. In some embodiments, the shaping coils and the encircling coils may be comprised on the same materials. In other embodiments, the shaping coils and the encircling coils may be comprised on different materials.

(44) With reference to FIGS. 2D and 2E, in some embodiments, the stellarators of the present disclosure further include one or more additional coils 240, such as one or more control coils and/or one or more saddle coils. In some embodiments, the control coils and/or the saddles are planar. In some embodiments, the control coils and/or the saddles are non-planar. In some embodiments, the control coils and/or the saddles are superconducting. In some embodiments, the control coils and/or the saddles are non-interlocking and, in particular, they do not interlock any other of the disclosed coils (e.g., encircling coils, shaping coils) or the plasma axis. In some embodiments, the control coils and/or the saddle coils are disposed between the plasma boundary and the field shaping system. In some embodiments, the control coils and/or the saddle coils are disposed outward of the field shaping system, on the non-plasma-axis-facing side. Control coils are coils included as a contingency against unexpected sources of error. These errors may arise from errors in assembly of the magnet system, or from unexpected plasma physics. Before the error is measured, the correct electrical current for the control coils is not known. During normal operation of the stellarator, if the stellarator and plasma are operating at their design points, the control currents have zero electric current. The design of the stellarator magnetic field does not include contributions from the control coils.

(45) In some embodiments, the stellarator is communicatively coupled to one or more controllers. In some embodiments, the one or more controllers are configured to control each of the one or more field-shaping units and optionally the one or more encircling coils. In some embodiments, one or more controllers are adapted to control a subset of the shaping coils disposed on a surface of a field shaping unit. In some embodiments, one or more controllers may be adapted to control one or more of the optional control coils and/or the optional saddle coils. In some embodiments, the one or more controllers include one or more power supplies which may be configured to increase or decrease the electrical current flowing in a subset of the encircling coils and/or the shaping coils. In some embodiments, the one or more controllers include a switching system which may be configured to connect one or more power supplies to certain subsets of encircling coils and/or shaping coils.

(46) Embodiments of the subject matter and the operations described in this disclosure may be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this disclosure may be implemented as one or more computer programs, i.e., one or more modules of computer program instructions, encoded on computer storage medium for execution by, or to control the operation of, data processing apparatus.

(47) In some embodiments, the controller includes a processor and a non-transitory computer readable storage medium operably coupled to the processor. A computer storage medium can be, or can be included in, a computer-readable storage device, a computer-readable storage substrate, a random or serial access memory array or device, or a combination of one or more of them. Moreover, while a computer storage medium is not a propagated signal, a computer storage medium can be a source or destination of computer program instructions encoded in an artificially generated propagated signal. The computer storage medium can also be, or can be included in, one or more separate physical components or media (e.g., multiple CDs, disks, or other storage devices). The operations described in this disclosure may be implemented as operations performed by a data processing apparatus on data stored on one or more computer-readable storage devices or received from other sources. In some embodiments, the non-transitory computer readable storage medium contains instructions that, when executed by the processor, cause the processor to adjust a strength of a field generated by one or more coils in order to contain plasma within the magnetic fields.

(48) Methods of Designing a Stellarator

(49) In some embodiments, a method is provided for designing a stellarator using shaping and encircling coils. As seen in FIG. 6, the method 600 may include determining 610 a continuous surface dipole or surface current potential distribution that produces any required fields for confining a plasma using a surface current, given an optimized plasma target and an encircling coil array as in Merkel 1987 (Merkel, P. 1987. Nuclear Fusion 27 (5): 867.) or Landreman 2017 (Landreman, Matt. 2017. Nuclear Fusion 57 (4): 046003). The method may also include receiving parameters and then defining 620 a configuration of shaping coils by discretizing the continuous surface dipole or current potential distribution. Non-limiting examples of parameters that may be received are the resolution of the surface to be discretized into coils, a cutoff current below which a coil is removed from the design, and/or the maximum coil linear dimension. The method may also include modeling 630, e.g., via a simulation, a reconstructed plasma, and comparing 640 properties of the reconstructed model plasma to the optimized plasma target. In some embodiments, the reconstructed model plasma is modeled using a free-boundary plasma solver.

(50) In some embodiments, the method may include optimizing the target plasma properties and magnetic field coil requirements via an iterative process. After the comparing step 640, the method may include adjusting 650 a parameter used to define (determine) the configuration of shaping coils, then repeating 625 the steps of defining 620, generating 630, and comparing 640, until an acceptable comparison is achieved. The iteratively defining the configuration of shaping coils, generating the reconstructed model plasma, comparing properties, and adjusting a parameter used to define the configuration of shaping coils.

(51) After the comparing step 640, the method may include defining 660 forces on a subset of the coils, such as any of the encircling coils and/or any of the shaping coils or any subset thereof. Once the force on a subset of the coils has been defined, the method may also include designing 670 one or more structural members 540 and/or structural components 231 to react to the forces on a subset of the coils.

(52) All of the U.S. patents, U.S. patent application publications, U.S. patent applications, foreign patents, foreign patent applications and non-patent publications referred to in this specification and/or listed in the Application Data Sheet are incorporated herein by reference, in their entirety. Aspects of the embodiments can be modified, if necessary to employ concepts of the various patents, applications, and publications to provide yet further embodiments.

(53) Although the present disclosure has been described with reference to a number of illustrative embodiments, it should be understood that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the spirit and scope of the principles of this disclosure. More particularly, reasonable variations and modifications are possible in the component parts and/or arrangements of the subject combination arrangement within the scope of the foregoing disclosure, the drawings, and the appended claims without departing from the spirit of the disclosure. In addition to variations and modifications in the component parts and/or arrangements, alternative uses will also be apparent to those skilled in the art.