Planar coil stellarator

Abstract

Disclosed herein is a stellarator with two sets of coils: a set of encircling coils that encircle the plasma axis, and a set of shaping coils that do not encircle any other coils or plasma. In some embodiments, the encircling coils include structural elements to maintain their shape under magnetic forces. In some embodiments, the shaping coils are attached to one or more structural elements that, together with the shaping coils, constitute a magnetic field shaping unit. Also disclosed is a controller that can modify the current through one or more subsets of the coils to achieve target plasma parameters. Also disclosed is a method for designing the set of shaping coils by discretizing the surface dipole or current potential distribution.

Description

[Technical field]

[0001] Statement regarding federally funded research This invention was made with Government support under DE-AC02-09CH11466 awarded by the U.S. Department of Energy. The Government has certain rights in this invention.

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS This disclosure claims benefit of the filing date of U.S. Provisional Patent Application No. 63 / 319,580, filed March 14, 2022, the entire disclosure of which is incorporated herein by reference.

[0003] The present disclosure is directed to stellarators, and in particular stellarators incorporating one or more planar coils, adapted to confine a plasma, for example, within a gap defined by one or more magnetic field shaping units. [Background technology]

[0004] Nuclear fusion is a process that can be used to release nuclear energy with abundant fuel, with no greenhouse gas emissions and with significantly lower and shorter-lived radioactive waste than conventional fission reactors. Fusion fuel will only fuse at extremely high temperatures where all the material is in a plasma state.

[0005] Magnetic fusion devices aim to confine the fusion plasma using a magnetic field. The two main magnetic fusion approaches are tokamaks and stellarators, both of which utilize a magnetic field with a torus topology.

[0006] Stellarators have the advantage over tokamaks that they operate in a steady state and do not require additional currents driven within the plasma itself. Conventional stellarator designs include non-planar electromagnetic coils with complex 3D curvatures. These electromagnetic coils are difficult to design, manufacture, integrate, and maintain. Some stellarator designs include electromagnetic coils that link other electromagnetic coils, similar to links in a chain. These electromagnetic coils cannot be manufactured separately and then assembled; they must be manufactured together, further increasing the difficulty of their manufacture, integration, and maintenance.

[0007] An example of a stellarator employing complex electromagnetic coils is the Large Helical Device (LHD) experiment conducted by the Japan National Institute for Fusion Science (Yoshimura, Y., et al. 2005. Journal of Physics: Conference Series 25(1):189.). These electromagnetic coils are helical coils, which are non-planar and interconnect with the plasma and other helical coils. These electromagnetic coils must be wound with wires on-site. Stellarators employing such electromagnetic coils are called torsatrons or heliotrons.

[0008] Another example of a stellarator employing complex electromagnetic coils is the Wendelstein 7-X (W7-X) experiment conducted by the Max Planck Institute for Plasma Physics in Germany (Beidler, Craig, et al. 1990. Fusion Technology 17(1):148-68). Referring to FIG. 1A, W7-X uses a combination of an external planar coil 101 and a modular coil 102. The external planar coil is planar 101, interconnected with the plasma and not with any other coils. The modular coil 102 is non-planar, interconnected with the plasma and not with any other coils. Stellarators employing these types of coils may be called Helias, or more generally, modular coil stellarators.

[0009] The National Compact Stellarator Experiment (NCSX) was a proposed experiment that was cancelled during its construction. Several different designs were proposed (Neilson, GH, et al. 2000. In Proceedings of the 42nd Annual Meeting of the APS Division of Plasma Physics Quebec City, Canada.). A proposed "saddle coil design" utilized (i) a toroidal field (TF) coil, which is a planar coil that interconnects with the plasma but not with any other coils, and (ii) a saddle coil, which is a non-planar coil that does not interconnect with the plasma but not with any other coils. An alternative design, called the "optimized background coil and conformal coil design," utilized (i) a background coil that is planar, interconnects with the plasma and with other background coils, and (ii) a saddle coil that is planar, does not interconnect with the plasma and does not interconnect with other coils.

[0010] Some experimental designs, such as W7-X and NCSX, incorporate planar trim coils (Rummel, Thomas, et al. 2012. IEEE Transactions on Applied Superconductivity 22(3):4201704-4201704). Planar trim coils are planar, do not interconnect with the plasma, and do not interconnect with any other coils. Planar trim coils are part of the control system, not the magnetic field generation system. Thus, their purpose is to correct magnetic fields that are in some way out of nominal (e.g., due to some inaccuracy in the structure or plasma behavior). At the nominal operating point, the planar trim coils are designed to be inactive. FIG. 1A illustrates the planar trim coils 103 utilized in the W7-X design. In particular, the planar trim coils 103 are positioned on the "outboard" side of the stellarator, away from the center of the device, and also outside the outer planar coils. It is also worth noting that the planar trim coil 103 is constructed from copper and not from a superconducting material like the outer planar coil 102 and modular coils 102 utilized in the W7-X design. It is also worth noting that the planar trim coil 103 is much larger than the minor axis of the plasma and is approximately the same size as the major axis of the plasma.

[0011] TN Todd's 1990 article (Todd, TN 1990 Plasma Physics and Controlled Fusion 32(6):459) and an experiment built at Columbia University in 2004 called the Columbia Non-neutral Torus (CNT, Pedersen, Thomas Sunn et al. 2004. Fusion Science and Technology 46(1):200-208.) describe stellarators that use planar coils. Todd's 1990 article describes a two-coil stellarator where both coils are planar and interconnect with the plasma. Referring to FIG. 1B, CNT uses an interconnect (IL) 104 coil and a poloidal field (PF) 105 coil. The IL coils are planar and interconnect with each other and with the plasma. The PF coils are planar and do not interconnect with the plasma, itself, or any other coils.

[0012] An article written by L. Ku and A.H. Boozer in 2009 (Ku, Long-Poe, and Allen H. Boozer. 2009. Physics of Plasmas 16(8):082506) describes a stellarator that uses TF coils and window glass coils. The TF coils are planar and interconnect with the plasma and not with any other coils. The window glass coils are described by Ku as non-planar. Ku explains that they do not interconnect with the plasma and do not interconnect with any other coils. Furthermore, Ku calls the design "difficult to implement" and considers the concept an "existence proof", indicating that he does not believe the design is practical.

[0013] Some items in the prior art use toroidal field (TF) coils. See the saddle coil design of NCSX in Neilson et al. 2000 and the design in Ku and Boozer 2009. An important aspect of TF coils is that they are planar and encircle the plasma, while their location and orientation exhibits N-fold rotational symmetry. Specifically, if a TF coil system consists of N coils, then the coil system can be rotated 360 degrees. o Rotating it by / N results in the same set of TF coils. This was done to approximate a simple axisymmetric magnetic field such as that in a tokamak.

[0014] From the above, it is clear that stellarators designed thus far have incredibly complex three-dimensional designs, which lead to increased costs and difficulties in controlling the distribution of the 3D magnetic field. It would be desirable to develop stellarators with less complex designs that allow for greater control of the generated magnetic field. Summary of the Invention

[0015] The present disclosure is directed to an improved stellarator design having a simpler and less complicated structure compared to previously developed stellarators. Compared to prior art stellarators, in some embodiments, the stellarators of the present disclosure do not require non-planar coils. Rather, in some embodiments, the stellarators of the present disclosure utilize multiple planar surrounding coils and multiple planar shaped coils. As described herein, in some embodiments, the planar surrounding coils surround the plasma axis, but do not surround any other planar surrounding coils or any planar shaped coils. Furthermore, in some embodiments, the planar shaped coils do not surround the plasma axis, and do not surround any other planar shaped coils or any planar surrounding coils.

[0016] In view of the above, a first aspect of the present disclosure is a stellarator comprising: (a) a magnetic field shaping coil system including one or more magnetic field shaping units defining a gap adapted to confine a plasma, each magnetic field shaping unit comprising: (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; and (b) a plurality of planar surrounding coils surrounding the magnetic field shaping coil system. Because the magnetic field shaping coil system defines a gap that confines the plasma, and because the planar surrounding coils surround the magnetic field shaping coil system, the planar surrounding coils therefore surround the plasma confined within the gap. In some embodiments, the stellarator does not include any non-planar coils.

[0017] In some embodiments, the stellarator further comprises one or more controllers. In some embodiments, the stellarator further comprises one or more control coils and / or one or more saddle coils. In some embodiments, the one or more control coils and / or the one or more saddle coils are communicatively coupled to the controller.

[0018] In some embodiments, each of one or more of the planar shaped coils is a superconducting coil. In some embodiments, each of the plurality of planar surrounding coils is a superconducting coil. In some embodiments, the plurality of planar shaped coils and the plurality of planar surrounding coils are both superconducting coils.

[0019] In some embodiments, the stellarator includes between about 3 and about 100 planar surrounding coils. In some embodiments, the stellarator includes between about 5 and about 50 planar surrounding coils. In some embodiments, the stellarator comprises at least four planar surrounding coils. In some embodiments, the plurality of planar surrounding coils includes one or more superconducting materials. In some embodiments, the plurality of planar surrounding coils are not interconnected with each other. In some embodiments, the plurality of planar surrounding coils are not interconnected with each other and with any of the one or more forming coils.

[0020] In some embodiments, the stellarator comprises at least four magnetic field shaping units. In some embodiments, each of the one or more magnetic field shaping units comprises one structural mounting element. In some embodiments, the one structural mounting element is wedge-shaped or approximately wedge-shaped. In some embodiments, each of the one or more magnetic field shaping units comprises two or more structural mounting elements.

[0021] In some embodiments, the one or more planar shaped coils are not interconnected with each other. In some embodiments, the one or more planar shaped coils are not interconnected with each other and are not interconnected with any of the plurality of planar surrounding coils.

[0022] In some embodiments, each of the one or more magnetic field shaping units comprises about 5 to about 150 shaped coils. In some embodiments, each of the one or more magnetic field shaping units comprises about 5 to about 100 shaped coils. In some embodiments, each of the one or more magnetic field shaping units comprises about 5 to about 50 shaped coils. In some embodiments, each of the one or more magnetic field shaping units comprises about 5 to about 25 shaped coils. In some embodiments, a surface of the one or more structural mounting elements faces the air gap.

[0023] In some embodiments, each of the planar shaped coils of the one or more planar shaped coils is generally rectangular, generally rectangular with rounded corners, or generally circular in shape. In some embodiments, each of the planar shaped coils of the one or more planar shaped coils is generally rectangular, generally rectangular with rounded corners, or circular in shape.

[0024] A second aspect of the present disclosure is a stellarator comprising: (a) a magnetic field shaping coil system including one or more magnetic field shaping units defining a gap adapted to confine a plasma, each magnetic field shaping unit comprising: (i) one or more structural mounting elements; and (ii) one or more shaping coils disposed on a surface of the one or more structural mounting elements; and (b) a plurality of surrounding coils surrounding the plasma and the magnetic field shaping coil system, the one or more shaping coils and the plurality of surrounding coils comprising one or more superconducting materials. In some embodiments, each of the one or more shaping coils disposed on a surface of the one or more structural mounting elements does not surround the plasma. In some embodiments, the one or more shaping coils are planar. In some embodiments, each surrounding coil of the plurality of surrounding coils is planar.

[0025] In some embodiments, the shape of each of the one or more shaped coils is generally rectangular, generally rectangular with rounded corners, or generally circular. In some embodiments, the shape of each of the one or more shaped coils is generally rectangular, generally rectangular with rounded corners, or circular. In some embodiments, each of the one or more magnetic field shaping units comprises about 5 to about 100 shaped coils. In some embodiments, each of the one or more magnetic field shaping units comprises about 5 to about 50 shaped coils. In some embodiments, the one or more planar shaped coils are not interconnected with each other. In some embodiments, the one or more planar shaped coils are not interconnected with each other and are not interconnected with any one of the surrounding coils of the plurality of surrounding coils.

[0026] In some embodiments, each of the one or more magnetic field shaping units comprises one structural mounting element. In some embodiments, the one structural mounting element is wedge-shaped or approximately wedge-shaped. In some embodiments, each of the one or more magnetic field shaping units comprises two or more structural mounting elements.

[0027] In some embodiments, a plurality of surrounding coils surround the plasma confined within the gap. In some embodiments, the stellarator includes about 3 to about 100 surrounding coils. In some embodiments, the stellarator includes at least 4 surrounding coils.

[0028] In some embodiments, the multiple planar surrounding coils are not interconnected with each other. In some embodiments, the multiple planar surrounding coils are not interconnected with each other or with the one or more shaped coils.

[0029] In some embodiments, the stellarator further comprises one or more control coils and / or one or more saddle coils, hi some embodiments, the one or more control coils and / or the one or more saddle coils are communicatively coupled to the controller.

[0030] A third aspect of the present disclosure is a stellarator comprising: (a) an air gap adapted to confine a plasma having a plasma axis; (b) a plurality of planar shaping coils, where an array including the plurality of planar shaping coils surrounds the plasma axis, but no individual planar shaping coil of the plurality of planar shaping coils surrounds the plasma axis; and (c) a plurality of planar surrounding coils, where each individual planar surrounding coil of the plurality of surrounding coils surrounds the plasma axis. In some embodiments, each of the plurality of planar shaping coils is a superconducting coil. In some embodiments, the plurality of planar shaping coils and the plurality of planar surrounding coils are both superconducting coils. In some embodiments, the plasma is a deuterium plasma.

[0031] In some embodiments, the plurality of planar shaped coils are not interconnected with each other. In some embodiments, the plurality of planar shaped coils are not interconnected with each other and are not interconnected with any one of the plurality of surrounding coils.

[0032] In some embodiments, the plurality of planar surrounding coils are not interconnected with each other. In some embodiments, the plurality of planar surrounding coils are not interconnected with each other and are not interconnected with any of the plurality of planar forming coils.

[0033] In some embodiments, the stellarator further comprises one or more control coils and / or one or more saddle coils. In some embodiments, the one or more control coils and / or the one or more saddle coils are not superconducting coils.

[0034] In some embodiments, each of the planar shaped coils of the one or more planar shaped coils is generally rectangular, generally rectangular with rounded corners, or generally circular in shape. In some embodiments, each of the planar shaped coils of the one or more planar shaped coils is generally rectangular, generally rectangular with rounded corners, or circular in shape.

[0035] In some embodiments, the stellarator comprises about 10 to about 10,000 formed coils. In some embodiments, the stellarator comprises about 100 to about 2,000 formed coils. In some embodiments, the stellarator comprises about 100 to about 1,000 formed coils. In some embodiments, the stellarator includes about 3 to about 100 planar surrounding coils. In some embodiments, the stellarator includes about 5 to about 50 planar surrounding coils. In some embodiments, the stellarator includes at least 4 planar surrounding coils.

[0036] A fourth aspect of the present disclosure is a stellarator comprising: (a) a gap adapted to confine a plasma, the gap including at least two sides; (b) at least two planar shaping coils, a first of the at least two sides being adjacent to the first of the at least two sides but not surrounding the gap, and a second of the at least two sides being adjacent to the second of the at least two sides but not surrounding the gap; and (c) a plurality of planar surrounding coils, each individual planar surrounding coil of the plurality of surrounding coils surrounding a plasma axis. In some embodiments, the at least two sides are on opposite sides of the confined plasma.

[0037] In some embodiments, the at least two faces are on opposite sides of the confined plasma.

[0038] In some embodiments, the at least two planar shaped coils are not interconnected with each other. In some embodiments, the at least two planar shaped coils are not interconnected with each other and with none of the plurality of surrounding coils.

[0039] In some embodiments, the plurality of planar surrounding coils are not interconnected with each other. In some embodiments, the plurality of planar surrounding coils are not interconnected with each other and with none of the at least two planar forming coils.

[0040] In some embodiments, the at least two planar shaped coils include one or more superconducting materials. In some embodiments, the plurality of surrounding coils include one or more superconducting materials. In some embodiments, the plurality of surrounding coils and the at least two planar shaped coils both include one or more superconducting materials.

[0041] In some embodiments, the stellarator further comprises one or more control coils and / or one or more saddle coils. In some embodiments, the one or more control coils and / or the one or more saddle coils are not superconducting coils.

[0042] In some embodiments, the shape of each of the at least two planar shaped coils is generally rectangular, generally rectangular with rounded corners, or generally circular. In some embodiments, the shape of each of the one or more planar shaped coils is generally rectangular, generally rectangular with rounded corners, or circular. In some embodiments, the stellarator comprises about 10 to about 10,000 shaped coils. In some embodiments, the stellarator comprises about 100 to about 2,000 shaped coils. In some embodiments, the stellarator comprises about 100 to about 1,000 shaped coils. In some embodiments, the stellarator includes about 3 to about 100 planar surrounding coils. In some embodiments, the stellarator includes at least 4 planar surrounding coils.

[0043] A fifth aspect of the present disclosure is a stellarator comprising: (a) a plurality of structural supports; (b) one or more magnetic field shaping units operably connected to the plurality of structural supports, each magnetic field shaping unit comprising one or more planar surface mounted shaping coils; and (c) a plurality of planar surrounding coils, wherein the plurality of structural supports, the one or more magnetic field shaping units, and the plurality of surrounding coils collectively define a gap adapted to confine a plasma therein.

[0044] In some embodiments, the stellarator comprises between about 10 and about 10,000 planar surface mounted formed coils. In some embodiments, the stellarator comprises between about 100 and about 2,000 planar surface mounted formed coils. In some embodiments, the stellarator comprises between about 100 and about 1,000 formed planar surface mounted coils. In some embodiments, the stellarator comprises between about 3 and about 100 planar surrounding coils. In some embodiments, the stellarator comprises between about 5 and about 50 planar surrounding coils. In some embodiments, the stellarator comprises at least 4 planar surrounding coils. In some embodiments, the plurality of planar surrounding coils comprises one or more superconducting materials. In some embodiments, the plurality of planar surrounding coils are not interconnected with each other. In some embodiments, the plurality of planar surrounding coils are not interconnected with each other or with any of the planar surface mounted formed coils.

[0045] In some embodiments, the stellarator comprises at least four magnetic field shaping units. In some embodiments, each of the one or more planar surface mounted formed coils are not interconnected with each other. In some embodiments, the stellarator comprises at least four magnetic field shaping units. In some embodiments, each of the one or more planar surface mounted formed coils are not interconnected with each other or with any of the surrounding coils. In some embodiments, each planar formed coil of the one or more planar surface mounted formed coils is generally rectangular, generally rectangular with rounded corners, or generally circular in shape. In some embodiments, each planar formed coil of the one or more planar surface mounted formed coils is generally rectangular, generally rectangular with rounded corners, or circular in shape.

[0046] In some embodiments, each of the one or more magnetic field shaping units comprises about 5 to about 100 planar surface mounted formed coils. In some embodiments, each of the one or more magnetic field shaping units comprises about 5 to about 50 planar surface mounted formed coils. In some embodiments, the one or more planar surface mounted formed coils comprise a superconducting material.

[0047] In some embodiments, the stellarator further comprises one or more controllers.

[0048] In some embodiments, the stellarator further comprises one or more control coils and / or one or more saddle coils. In some embodiments, the one or more control coils and / or the one or more saddle coils are communicatively coupled to the controller. In some embodiments, each of the one or more shaping coils does not individually surround the plasma.

[0049] For a general understanding of the features of the present disclosure, reference is made to the drawings, in which like reference numbers are used throughout to identify identical elements. [Brief description of the drawings]

[0050] [Figure 1A] 1 depicts the arrangement of the components of the Wendelstein 7-X stellarator, specifically the outer planar coil, the modular coils, and the planar trim coils, relative to each other and to the confined plasma. [Figure 1B] 1 depicts the arrangement of the components of a CNT stellarator, specifically, the IL coil and the PF coil. [Figure 2A] 2A illustrates a stellarator according to some embodiments of the present disclosure. Specifically, FIG. 2A illustrates a magnetic field shaping coil system, and thus a plurality of planar surrounding coils that surround the plasma. [Figure 2B] 1 illustrates a top-down view of a stellarator, according to some embodiments of the present disclosure. [Figure 2C] 1 illustrates a cross-sectional view of a stellarator according to some embodiments of the present disclosure. [Figure 2D] 1 illustrates a top-down view of a stellarator according to some embodiments of the present disclosure, where the stellarator is depicted as including one or more optional saddle coils. [Figure 2E] 1 illustrates a cross-sectional view of a stellarator according to some embodiments of the present disclosure, the stellarator being depicted as including one or more optional saddle coils. [Figure 3A] A coil design is shown having a circular winding pattern. [Figure 3B] A coil design is shown having a rectangular winding pattern. [Figure 3C] A coil design is shown that has a rectangular winding pattern but with rounded edges. [Figure 4A] 1 illustrates a cross-sectional view of a stellarator showing a magnetic field shaping unit and surrounding coils according to one embodiment of the present disclosure. [Figure 4B] 1 illustrates a top-down view of a portion of a stellarator showing the magnetic field shaping unit having a wedge shape when viewed from this angle. [Diagram 5] 1 shows a cross-sectional view of a stellarator, specifically depicting one or more surrounding coils surrounding a magnetic field shaping system, according to one embodiment of the present disclosure. [Figure 6] 1 provides a flow chart illustrating a method for designing a set of shaped coils by discretizing surface dipole or current potential distributions according to one embodiment of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0051] It is also to be understood that, unless expressly stated to the contrary, in any method claimed in this specification that includes two or more steps or actions, the order of the method steps or actions is not necessarily limited to the order in which the method steps or actions are recited.

[0052] As used herein, the singular terms "a," "an," and "the" include plural referents unless the context clearly dictates otherwise. Similarly, the word "or" is intended to include "and" unless the context clearly dictates otherwise. The term "includes" is defined inclusively, such that "including A or B" means including A, B, or A and B.

[0053] 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, but also including two or more of, a number or list of elements, and optionally including additional unlisted items. Only terms clearly indicated otherwise, 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, as used herein, the term "or" should be interpreted as indicating exclusive alternatives (i.e., "one or the other, but not both") only when preceded by a term 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.

[0054] Terms such as "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 consistently with the general U.S. patent law definition of "comprising," and therefore is interpreted as being open-ended, meaning "at least the following," and also not excluding additional features, limitations, aspects, and the like. 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 with steps a, b, and c" means that the method includes at least steps a, b, and c. Additionally, although steps and processes may be outlined in a particular order herein, one of ordinary skill in the art will recognize that the ordering of steps and processes may vary.

[0055] As used herein in the specification and 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 element specifically listed in the list of elements, and not excluding any combination of elements in the list of elements. This definition also allows that elements other than the elements specifically identified in the list of elements to which the phrase "at least one" refers may optionally be present, 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 to, in one embodiment, at least one, optionally, two or more A, and no B (and optionally including elements other than B); in another embodiment, at least one, optionally, two or more B, and no A (and optionally including elements other than A); in yet another embodiment, at least one, optionally, two or more A, and at least one, optionally, two or more B (and optionally including other elements), etc.

[0056] References throughout this specification to "one embodiment" or "one embodiment" mean that a particular feature, structure, or characteristic described in connection with an embodiment is included in at least one embodiment. Thus, the appearances of the phrases "in one embodiment" or "in one embodiment" in various places throughout this specification do not necessarily all refer to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0057] Electromagnetic coils may be described according to their shape and / or topology. For example, electromagnetic coils may have a planar shape (coils aligned in one plane) or a non-planar shape. Planar electromagnetic coils may be manufactured by conventional means and wound with wire under tension. Topology refers to whether an electromagnetic coil links, threads, or interconnects with another coil in the manner of a chain link. Topology may also refer to whether an electromagnetic coil interconnects a plasma.

[0058] Stellarator The present disclosure is directed to an improved stellarator design having a simpler and less complicated structure compared to previously developed stellarators.

[0059] Described herein is a stellarator incorporating multiple surrounding coils and multiple shaping coils. With reference to Figures 2A-2C, the stellarator of the present disclosure comprises a magnetic field shaping system 203 surrounding a gap 201 that confines a plasma 200. In some embodiments, the gap 201 is configured such that the maximum dimension from the plasma axis 205 of any contained plasma 200 to an outer edge (not shown) of the contained plasma 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.

[0060] In some embodiments, the plasma 200 has a topology that roughly approximates that of a torus. In some embodiments, the plasma 200 is centered about a "plasma axis" 205, which is the magnetic field lines that map to their origin after one toroidal rotation. In some embodiments, the plasma axis 205 has a topology of a loop or roughly approximates a loop.

[0061] The magnetic field shaping system 203 includes a plurality of magnetic field shaping units 210. In some embodiments, the magnetic field shaping system 203 may include 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, or at least 170 magnetic field shaping units 210.

[0062] In some embodiments, each of the magnetic field shaping units 210 includes one or more structural mounting elements 211 having a surface 215. In some embodiments, the surface 215 of each magnetic field shaping unit 211 faces the gap 201. In some embodiments, each magnetic 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 for handling the plasma flux, a structure mounted to the first wall, a breeding blanket for breeding radioisotopes from the fusion neutron flux, a cryostat, and / or neutron shielding.

[0063] In some embodiments, each magnetic field shaping unit 210 comprises a single structural mounting element 211. In other embodiments, each magnetic field shaping unit 210 comprises two structural mounting elements 211. In yet other embodiments, each magnetic field shaping unit 210 comprises three structural mounting elements 211. In further embodiments, each magnetic field shaping unit 210 comprises four or more structural mounting elements 211. In some embodiments, the structural mounting elements 211 comprise steel. In some embodiments, the structural mounting elements 211 comprise metal. In some embodiments, the structural mounting elements 211 comprise a composite material, such as G-10.

[0064] The magnetic field shaping unit 210 may have any size and shape. In some embodiments, the magnetic field shaping unit 210 defines an extruded circular annulus cross section structure. In other embodiments, the magnetic field shaping unit 210 has any shape, including a shape with a non-constant cross section. For example, as illustrated in FIG. 4B, in some embodiments, the magnetic field shaping unit 410 has a wedge shape (positioned such that, from a perspective perpendicular to the plasma axis and the curvature direction, the narrower portion of the wedge faces the curvature direction of the plasma axis and the wider portion of the wedge faces the curvature direction of the plasma axis). In some embodiments, the magnetic field shaping unit 410 is generally wedge shaped. In other embodiments, the magnetic field shaping unit 210 has a shape similar to or the same as the cross-sectional shape of the plasma at that location. In other embodiments, the magnetic field shaping unit has a cross-sectional shape of the plasma with a certain normal offset distance.

[0065] In some embodiments, one or more shaping coils 212 are disposed on a 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 incorporate into a magnetic field shaping unit. Furthermore, it is believed that the one or more magnetic field shaping coils 212 can enable precise control of the shape of the plasma.

[0066] Each of the one or more shaped coils 212 is a planar coil. A "planar" coil is one whose shape is substantially in one plane. In some embodiments, each of the shaped coils 212 does not individually surround the plasma axis 205. Stated differently, no one shaped coil 212 surrounds the plasma 200 or the plasma axis 205. For example, as depicted in Figures 4 and 5, the shaped coils 412 or 512 are disposed on a surface 415 or 515 of a structural mounting element 411 or 511, respectively, and each individual shaped coil 412 or 512 does not surround the plasma axis.

[0067] While no individual shaped coil 212 surrounds the plasma axis 205, an array including multiple shaped coils 212 attached to a surface 215 of one or more structural mounting elements 211 will collectively surround the plasma axis 205. This is illustrated in FIG. 4A, which shows multiple shaped coils 412 disposed on a surface 415 of a structural mounting element 411. As shown, the shaped coils 412 do not surround the plasma confined within the gap 401. However, the collective of all shaped coils 412 disposed on a surface 415 of one or more structural mounting elements 411 surrounds the plasma and / or gap 401. This concept is further illustrated in FIG. 5, which again illustrates that no individual shaped coils 512 surround the plasma confinement gap 501. In some embodiments, the individual shaped coils 512 may be positioned on opposite sides of the plasma or on different sides of the gap.

[0068] Each of the one or more shaped coils 212, 412, or 512 is not interconnected with any other shaped coils, at least as illustrated in Figures 2A, 4A, and 5. In addition, each of the one or more shaped coils is not interconnected with any of the surrounding coils 230 described herein (see Figures 2A, 4A, and 5). In some embodiments, the one or more shaped coils 212 are removably coupled to a surface 215 of the one or more surface mounting elements 211.

[0069] In some embodiments, the planar shaped coil has an average coil radius that is smaller than the semimajor axis of the plasma and smaller than the semiminor axis of the plasma. As used herein, the "semimajor axis" of the plasma is the average distance between the plasma axis and the geometric center of the stellarator. As used herein, the "semiminor axis" of the plasma is the average closest distance between each point on the plasma boundary and the plasma axis. The plasma boundary may be represented by a set of toroidal Fourier amplitudes, where the semimajor axis is represented by the amplitude of the mode with toroidal mode number 0 and poloidal mode number 0, and the semiminor axis is represented by the amplitude of the mode with toroidal mode number 0 and poloidal mode number 1.

[0070] The shaped coils 212 may have different sizes and shapes. For example, referring to FIG. 3A, in some embodiments, the shaped coils 212 may be circular or approximately circular. In other embodiments, the shaped coils may be rectangular or approximately rectangular (FIG. 3B). In yet other embodiments, the shaped coils may be rectangular with rounded corners or approximately rectangular with rounded corners (FIG. 3C). In some embodiments, each magnetic field shaping unit 210 may include one or more coils having different shapes. For example, the magnetic field shaping unit 210 may include ten shaped coils, where three of the shaped coils may have a substantially approximately circular shape, four of the shaped coils may have a substantially rectangular shape, and three of the coils may have a substantially rectangular shape with rounded corners (not shown).

[0071] In some embodiments, the stellarator of the present disclosure may include between about 10 and 10,000 formed coils. In other embodiments, the stellarator of the present disclosure may include between about 50 and 5,000 formed coils. In still other embodiments, the stellarator of the present disclosure may include between about 100 and 5,000 formed coils. In further embodiments, the stellarator of the present disclosure may include between about 100 and 4,000 formed coils. In still further embodiments, the stellarator of the present disclosure may include between about 100 and 3,000 formed coils. Even further embodiments, the stellarator of the present disclosure may include between about 100 and 2,000 formed coils. Even further embodiments, the stellarator of the present disclosure may include between about 100 and 1,000 formed coils.

[0072] In some embodiments, the magnetic field shaping unit 210 may include between about 5 and about 150 formed coils 212. In other embodiments, the magnetic field shaping unit 210 may include between about 5 and about 100 formed coils 212. In still other embodiments, the magnetic field shaping unit 210 may include between about 5 and about 80 formed coils 212. In further embodiments, the magnetic field shaping unit 210 may include between about 5 and about 70 formed coils 212. Even further embodiments, the magnetic field shaping unit 210 may include between about 5 and about 60 formed coils 212. Even still further embodiments, the magnetic field shaping unit 210 may include between about 5 and about 50 formed coils 212. Even still further embodiments, the magnetic field shaping unit 210 may include between about 5 and about 45 formed coils 212. Even still further embodiments, the magnetic field shaping unit 210 may include between about 5 and about 40 formed coils 212. In even further embodiments, the magnetic field shaping unit 210 may include from about 5 to about 35 shaping coils 212. In even further embodiments, the magnetic field shaping unit 210 may include from about 5 to about 30 shaping coils 212. In even further embodiments, the magnetic field shaping unit 210 may include from about 5 to about 25 shaping coils 212.

[0073] 2, the stellarator of the present disclosure also includes a number of surrounding coils 230 that surround the plasma axis 205. Each of the surrounding coils 230 is disposed around and surrounds the exterior of the magnetic field shaping system 203. This is further illustrated in Figures 4 and 5, which show surrounding coils 430 and 530 surrounding the plasma and / or gap 401 or 501, respectively, although the surrounding coils 430 and 530 are external to any magnetic field shaping units 410 or 510.

[0074] Each of the surrounding coils 230 of the plurality of surrounding coils is planar. Moreover, each of the surrounding coils 230 of the plurality of surrounding coils is not interconnected with any of the other surrounding coils 230. In addition, each of the surrounding coils 230 of the plurality of surrounding coils is not interconnected with any of the shaped coils 212. In other words, no surrounding coil 230 is interconnected with any of the other planar surrounding coils 230 or any of the other shaped coils 212, as depicted in FIG. 2A, FIG. 2B, and FIG. 5. In some embodiments, each of the surrounding coils 230 is supported by a structural component 231. In some embodiments, the structural component 231 and the magnetic field shaping unit 210 may be coupled to another structural member 540 that responds to unbalanced forces and torques.

[0075] In some embodiments, the surrounding coil does not exhibit the N-fold rotational symmetry of the toroidal field (TF) coil. If the surrounding coil were N-fold rotational symmetry as in the prior art TF coil, the planar shaped coil would require an irreducible amount of current length (amperes*meters) to correct this field. If the surrounding coil could be non-N-fold rotational symmetric, the current length requirement of the planar shaped coil could be significantly reduced. It is believed that such requirements could be reduced by nearly a factor of 10 by allowing the surrounding coil to be more favorably positioned.

[0076] In some embodiments, the stellarator of the present disclosure includes from about 3 to about 150 surrounding coils. In other embodiments, the stellarator of the present disclosure includes from about 3 to about 100 surrounding coils. In still other embodiments, the stellarator of the present disclosure includes from about 3 to about 75 surrounding coils. In further embodiments, the stellarator of the present disclosure includes from about 3 to about 50 surrounding coils. In still further embodiments, the stellarator of the present disclosure includes from about 3 to about 25 surrounding coils. Even further embodiments, the stellarator of the present disclosure includes from about 3 to about 15 surrounding coils. Even further embodiments, the stellarator of the present disclosure includes from about 3 to about 10 surrounding coils. In some embodiments, the spacing between each surrounding coil can range from about 10 cm to about 1 m.

[0077] The forming coil 212 and the surrounding coil 230 may include one or more superconducting materials. A superconductor is a material that achieves superconductivity. Superconductivity occurs when a material exceeds a critical temperature (T c Superconductivity is the property of certain materials to conduct direct current (DC) electricity without energy loss when cooled below a certain temperature (called superconductivity). Electric current in a superconductor can continue indefinitely. Exemplary superconducting materials include Nb-Ti, Nb3Sn, MgB2, LaBaCuO x , LSCO (e.g., La 2-x Sr x CuO4, etc.), YBCO (e.g. YBa2Cu3O x or YBa2Cu3O7), REBCO, bismuth-based copper oxide superconductors (BSCCO) (Bi2Sr2CaCu2O8 (Bi-2212) and Bi2Sr2Ca2Cu3O 10 (including Bi-2223), TBCCO (e.g., Tl2Ba2Ca2Cu3O 10 or Tl m Ba2Ca n-1 Cu n O 2n+m+2+δ ), HgBa2Ca2Cu3O x, and other mixed-valence copper oxide perovskite materials. In some embodiments, the forming coil and the surrounding coil may be included on the same material. In other embodiments, the forming coil and the surrounding coil may be included on different materials.

[0078] 2D and 2E, in some embodiments, the stellarator of the present disclosure further includes 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 saddles are planar. In some embodiments, the control coils and / or saddles are non-planar. In some embodiments, the control coils and / or saddles are superconducting. In some embodiments, the control coils and / or saddles are non-interconnected, specifically, they are not interconnected with any of the disclosed coils (e.g., surrounding coils, shaping coils) or with any of the others of the plasma axis. In some embodiments, the control coils and / or saddle coils are disposed between the plasma boundary and the magnetic field shaping system. In some embodiments, the control coils and / or saddle coils are disposed on the non-plasma axis facing side, outwardly of the magnetic field shaping system. The control coils are coils that are included as a contingency for unexpected sources of error. These errors may arise from errors in the assembly of the magnet system or from unexpected plasma physics. Before measuring the error, the appropriate current in the control coil is not known. During normal operation of the stellarator, when the stellarator and plasma are operating at their respective design points, the control current has zero current. The design of the stellarator magnetic field does not include the contribution from the control coil.

[0079] 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 magnetic field shaping units and, optionally, the one or more surrounding coils. In some embodiments, the one or more controllers are adapted to control a subset of the shaping coils disposed on a surface of the magnetic field shaping units. In some embodiments, the 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 sources that may be configured to increase or decrease current through the surrounding coils and / or the subset of the shaping coils. In some embodiments, the one or more controllers include a switching system that may be configured to connect the one or more power sources to a particular subset of the surrounding coils and / or the shaping coils.

[0080] Embodiments of the subject matter and operations described in this disclosure can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed herein and their structural equivalents, or in one or more combinations thereof.Embodiments of the subject matter described herein can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a computer storage medium for execution by, or for controlling the operation of, a data processing apparatus.

[0081] In some embodiments, the controller includes a processor and a non-transitory computer-readable storage medium operably coupled to the processor. The computer storage medium may be or may 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. Furthermore, the computer storage medium is not a propagating signal, but the computer storage medium may be a source or destination of computer program instructions encoded in an artificially generated propagating signal. The computer storage medium may also be or may 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 device on data stored in one or more computer-readable storage devices or received from other sources. In some embodiments, the non-transitory computer-readable storage medium includes instructions that, when executed by the processor, cause the processor to adjust the magnetic field strength generated by one or more coils to contain a plasma within the magnetic field.

[0082] How to design a stellarator In some embodiments, a method is provided for designing a stellarator using shaping and surrounding coils. As seen in FIG. 6, the method 600 includes determining 610 a continuous surface dipole or surface current potential distribution that produces any magnetic field required to confine the plasma using surface currents, given an optimized plasma target and surrounding coil array as in Merkel 1987 (Merkel, P. 1987. Nuclear Fusion 27(5):867.) or Landreman 2017 (Landreman, Matt. 2017. Nuclear Fusion 27(5):867.) 57(4):(046003). The method may also include receiving parameters and then defining a configuration of the shaped coil by discretizing the continuous surface dipole or current potential distribution (620). Non-limiting examples of parameters that may be received are the resolution of the surface to be discretized into the coil, a cutoff current below which the coil is removed from the design, and / or a maximum coil linear dimension. The method may also include modeling (630), e.g., via simulation, the reconstructed plasma and comparing characteristics of the reconstructed model plasma to the optimized plasma target (640). In some embodiments, the reconstructed model plasma is modeled using a free boundary plasma solver.

[0083] In some embodiments, the method may include optimizing the target plasma characteristics and magnetic field coil requirements through an iterative process. After the comparing step 640, the method may include adjusting (650) parameters used to define (determine) the shaping coil configuration, and then repeating (625) the defining (620), generating (630), and comparing (640) steps until an acceptable comparison is achieved. Iteratively define the shaping coil configuration, generate a reconstructed model plasma, compare the characteristics, and adjust the parameters used to define the shaping coil configuration.

[0084] After the comparing step 640, the method may include defining (660) forces on a subset of the coils, such as any of the surrounding coils and / or any of the shaped coils, or any subset thereof. Once the forces on the subset of coils are defined, the method may also include designing (670) one or more structural members 540 and / or structural components 231 to be responsive to the forces on the subset of coils.

[0085] All U.S. patents, U.S. patent application publications, U.S. patent applications, foreign patents, foreign patent applications, and / or non-patent publications referred to in this application and / or listed in this application Data Sheet are incorporated herein by reference in their entirety. Aspects of the embodiments can be modified, if desired, to employ concepts from the various patents, applications, and publications to provide yet further embodiments.

[0086] Although the present disclosure has been described with reference to certain exemplary embodiments, it should be understood that many other modifications and embodiments may be devised by those skilled in the art that fall within the spirit and scope of the principles of the present disclosure. More specifically, reasonable variations and modifications may be made in the components and / or configurations of the combined configuration of the subject matter within the scope of the foregoing disclosure, the drawings, and the appended claims without departing from the spirit of the present disclosure. In addition to variations and modifications of the components and / or configurations, alternative uses will also be apparent to those skilled in the art.

Claims

1. It is a stellarator, (a) A magnetic shaping coil system comprising one or more magnetic shaping units that define a gap adapted to confine a plasma, wherein each magnetic shaping unit is (i) One or more structural mounting elements, and (ii) A magnetic field forming coil system comprising one or more planar forming coils disposed on the surface of one or more structural mounting elements, (b) A stellarator comprising a plurality of planar surrounding coils that surround the magnetic field shaping coil system.

2. The stellarator according to claim 1, wherein the stellarator includes approximately 3 to approximately 100 planar surrounding coils.

3. The stellarator according to claim 1, wherein the stellarator comprises at least four planar surrounding coils.

4. The stellarator according to claim 1, wherein the plurality of planar surrounding coils include one or more superconducting materials.

5. The stellarator according to claim 1, wherein the plurality of planar surrounding coils are not interconnected with one another.

6. The stellarator according to claim 1, wherein the stellarator comprises at least four magnetic field shaping units.

7. The stellarator according to claim 1, wherein the surface of one or more structural mounting elements faces the gap.

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

9. The stellarator according to claim 8, wherein the one structural mounting element is wedge-shaped.

10. The stellarator according to claim 1, wherein each of the one or more magnetic field shaping units comprises two or more structural mounting elements.

11. The stellarator according to claim 1, wherein one or more planar molded coils are not interconnected with one another.

12. The stellarator according to claim 1, wherein the shape of each of the one or more planar molded coils is substantially rectangular, substantially rectangular with rounded corners, or substantially circular.

13. The stellarator according to claim 1, wherein each of the one or more magnetic field shaping units comprises about 5 to about 100 shaping coils.

14. The stellarator according to claim 1, wherein each of the one or more magnetic field shaping units comprises about 5 to about 50 shaping coils.

15. The stellar according to claim 1, wherein one or more molded coils include a superconducting material.

16. The stellarator according to claim 1, further comprising one or more controllers.

17. The stellarator according to claim 1, further comprising one or more control coils and / or one or more saddle coils.

18. The stellarator according to claim 17, wherein one or more control coils and / or one or more saddle coils are communicably coupled to a controller.

19. The stellarator according to claim 1, wherein each of the one or more molding coils does not individually surround the plasma.

20. It is a stellarator, (a) A magnetic shaping coil system comprising one or more magnetic shaping units that define a gap adapted to confine a plasma, wherein each magnetic shaping unit is (i) One or more structural mounting elements, and (ii) A magnetic field forming coil system comprising one or more forming coils disposed on the surface of one or more structural mounting elements, (b) A stellarator comprising a plurality of surrounding coils that surround the plasma and the magnetic field forming coil system, wherein one or more forming coils and the plurality of surrounding coils contain one or more superconducting materials. In some embodiments, each of the one or more forming coils disposed on the surface of one or more structural mounting elements does not surround the plasma.

21. The stellarator according to claim 20, wherein each of the one or more molded coils is planar.

22. The stellarator according to claim 20, wherein the shape of each of the one or more molded coils is substantially rectangular, substantially rectangular with rounded corners, or substantially circular.

23. The stellarator according to claim 20, wherein each of the one or more magnetic field forming units comprises about 5 to about 100 forming coils.

24. The stellarator according to claim 20, wherein each of the one or more magnetic field shaping units comprises about 5 to about 50 shaping coils.

25. The stellarator according to claim 20, wherein one or more planar molded coils are not interconnected with one another.

26. The stellarator according to claim 20, wherein each of the one or more magnetic field shaping units comprises one structural mounting element.

27. The stellarator according to claim 26, wherein the one structural mounting element is wedge-shaped.

28. The stellarator according to claim 20, wherein each of the one or more magnetic field shaping units comprises two or more structural mounting elements.

29. The stellarator according to claim 20, wherein the plurality of surrounding coils surround the plasma confined within the gap.

30. The stellarator according to claim 20, wherein the stellarator includes approximately 3 to approximately 100 surrounding coils.

31. The stellarator according to claim 20, wherein the stellarator comprises at least four surrounding coils.

32. The stellarator according to claim 20, wherein the plurality of surrounding coils include one or more superconducting materials.

33. The stellarator according to claim 20, wherein the planar surrounding coils are not interconnected with one another.

34. The stellarator according to claim 20, further comprising one or more control coils and / or one or more saddle coils.

35. The stellarator according to claim 34, wherein one or more control coils and / or one or more saddle coils are communicably coupled to a controller.

36. It is a stellarator, (a) A gap and a structure adapted to confine a plasma having a plasma axis, (b) A plurality of planar formed coils, wherein an array comprising the plurality of planar formed coils surrounds the plasma axis, but any individual planar formed coil of the plurality of planar formed coils does not surround the plasma axis, (c) A stellarator comprising a plurality of planar surround coils, wherein each individual planar surround coil of the plurality of surround coils surrounds the plasma axis.

37. The stellarator according to claim 36, wherein the plurality of planar molded coils are not interconnected with one another.

38. The stellarator according to claim 37, wherein the plurality of planar molded coils are not interconnected with any of the plurality of surrounding coils.

39. The stellarator according to claim 36, wherein multiple planar surrounding coils are not interconnected with one another.

40. The stellarator according to claim 39, wherein the plurality of planar surrounding coils are not interconnected with any of the plurality of planar molded coils.

41. The stellar according to claim 36, wherein the plurality of molded coils include one or more superconducting materials.

42. The stellarator according to claim 36, wherein the plurality of surrounding coils include one or more superconducting materials.

43. The stellarator according to claim 36, wherein both the plurality of surrounding coils and the plurality of planar formed coils contain one or more superconducting materials.

44. The stellarator according to claim 36, comprising one or more control coils and / or one or more saddle coils.

45. The stellarator according to claim 44, wherein the one or more control coils and / or the one or more saddle coils are not superconducting coils.

46. The stellarator according to claim 36, wherein the shape of each of the one or more planar molded coils is substantially rectangular, substantially rectangular with rounded corners, or substantially circular.

47. The stellar according to claim 36, wherein the stellar comprises approximately 10 to approximately 10,000 molded coils.

48. The stellarator according to claim 36, wherein the stellarator comprises approximately 100 to approximately 2,000 molded coils.

49. The stellarator according to claim 36, wherein the stellarator includes approximately 3 to approximately 100 planar surrounding coils.

50. The stellarator according to claim 36, wherein the stellarator comprises at least four planar surrounding coils.

51. The stellarator according to claim 36, wherein the plasma is a deuterium plasma.

52. It is a stellarator, (a) A void adapted to confine plasma, comprising at least two surfaces, (b) at least two planar formed coils, wherein the first of the at least two planar formed coils is in close proximity to the first of the at least two surfaces but does not enclose the void, and the second of the at least two planar formed coils is in close proximity to the second of the at least two surfaces but does not enclose the void, (c) A stellarator comprising a plurality of planar surround coils, wherein each individual planar surround coil of the plurality of surround coils surrounds the plasma axis.

53. The stellarator according to claim 52, wherein at least two of the surfaces are on the opposite side of the confined plasma.

54. The stellarator according to claim 52, wherein the at least two planar molded coils are not interconnected with one another.

55. The stellarator according to claim 54, wherein the at least two planar molded coils are not interconnected with any of the plurality of surrounding coils.

56. The stellarator according to claim 52, wherein multiple planar surrounding coils are not interconnected with one another.

57. The stellarator according to claim 56, wherein the plurality of planar surrounding coils are not interconnected with any of the at least two planar shaped coils.

58. The stellarator according to claim 52, wherein the at least two planar molded coils include one or more superconducting materials.

59. The stellarator according to claim 52, wherein the plurality of surrounding coils include one or more superconducting materials.

60. The stellarator according to claim 52, wherein both the plurality of surrounding coils and the at least two planar shaped coils each contain one or more superconducting materials.

61. The stellarator according to claim 52, further comprising one or more control coils and / or one or more saddle coils.

62. The stellarator according to claim 61, wherein the one or more control coils and / or the one or more saddle coils are not superconducting coils.

63. The stellarator according to claim 52, wherein the shape of each of the at least two planar formed coils is substantially rectangular, substantially rectangular with rounded corners, or substantially circular.

64. The stellarator according to claim 52, wherein the stellarator includes approximately 3 to approximately 100 planar surrounding coils.

65. The stellarator according to claim 52, wherein the stellarator comprises at least four planar surrounding coils.

66. It is a stellarator, (a) Multiple structural supports, (b) One or more magnetic field shaping units operably connected to the plurality of structural supports, each magnetic field shaping unit comprising one or more planar surface mount molding coils, (c) A stellarator comprising a plurality of planar encircling coils, wherein the plurality of structural supports, the one or more magnetic field shaping units, and the plurality of encircling coils collectively define a gap adapted for confining a plasma therein.

67. The stellar according to claim 66, wherein the stellar includes approximately 3 to approximately 100 planar surrounding coils.

68. The stellarator according to claim 66, wherein the stellarator comprises at least four planar surrounding coils.

69. The stellarator according to claim 66, wherein the plurality of planar surrounding coils include one or more superconducting materials.

70. The stellarator according to claim 66, wherein the plurality of planar surrounding coils are not interconnected with one another.

71. The stellarator according to claim 66, wherein the stellarator comprises at least four magnetic field shaping units.

72. The stellarator according to claim 66, wherein each of the one or more planar surface-mount molded coils is not interconnected with one another.

73. The stellarator according to claim 66, wherein the shape of each of the one or more planar surface-mount molded coils is substantially rectangular, substantially rectangular with rounded corners, or substantially circular.

74. The stellarator according to claim 66, wherein each of the one or more magnetic field forming units comprises about 5 to about 100 planar surface-mount molded coils.

75. The stellarator according to claim 66, wherein each of the one or more magnetic field forming units comprises about 5 to about 50 planar surface-mount molded coils.

76. The stellar according to claim 66, wherein the one or more planar surface-mount molded coils include a superconducting material.

77. The stellarator according to claim 66, further comprising one or more controllers.

78. The stellarator according to claim 66, further comprising one or more control coils and / or one or more saddle coils.

79. The stellarator according to claim 78, wherein one or more control coils and / or one or more saddle coils are communicably coupled to a controller.

80. The stellar according to claim 66, wherein each of the one or more molding coils does not individually surround the plasma.

81. A method for designing a stellarator comprising one or more planar coils and an array of surrounding coils, (a) With respect to the stellarator, (i) to obtain the configuration of a target plasma and (ii) an array of surrounding coils, (b) Using surface current or surface current potential, determine a continuous surface dipole distribution that generates one or more magnetic fields to confine the target plasma, (c) Receiving one or more parameters selected from the surface resolution, cutoff current, and / or maximum coil linear dimension of the coil, (d) A method comprising defining the configuration of one or more planar coils by discretizing the determined continuous surface dipole distribution based on one or more received parameters.

82. The method of claim 81, further comprising generating a model of the plasma confined by the configuration of one or more planar coils and the array of surrounding coils.

83. The method according to claim 82, wherein generating the model of the plasma includes using a free boundary plasma solver.

84. The method of claim 81, further comprising optimizing the target plasma by iteratively defining the configuration of one or more planar coils.

85. The method according to claim 81, further comprising defining the force acting on one or more planar coils.

86. The method according to claim 85, further comprising designing a mechanical support to respond to the force applied to one or more planar coils.

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