Stellarators using arrays of permanent magnets

A non-transitory computer-readable medium storing instructions for defining an array of permanent magnets for a stellarator, comprising:

• obtaining an initial arrangement of a plurality of permanent magnets positioned around a plasma having a plasma surface;
• optimizing dipole moment magnitudes and dipole moment orientation angles of each permanent magnet of the plurality of permanent magnets in the initial arrangement to provide a revised arrangement of the plurality of permanent magnets, wherein the optimization of the dipole moment magnitudes and dipole moment orientation angles comprises:
• generating an improved arrangement of the plurality of permanent magnets, wherein the improved arrangement is generated by computing a first numerical minimization of an error field on the plasma surface, where dipole moment magnitudes and dipole moment orientation angles are free and continuous parameters in the computation of the first numerical minimization, and where the dipole moment magnitude is constrained from exceeding a pre-defined maximum value,
• generating the revised arrangement, wherein the revised arrangement is generated by computing a second numerical minimization of a composite cost function that penalizes both the error field on the plasma surface and intermediate dipole moment magnitudes, wherein the computation of the second numerical optimization uses the generated improved arrangement as an initialization, and wherein each magnet of the plurality of magnets in the revised arrangement has either a zero dipole moment magnitude or a non-zero dipole moment magnitude, and where the non-zero dipole moment magnitude has a predetermined value;
• defining a set of allowable dipole moment orientation angles;
• and
• setting the dipole moment orientation angles of each of the permanent magnets having the non-zero dipole moment magnitudes in the generated revised arrangement to one of the dipole moment orientation angles in the defined set of allowable dipole moment orientation angles to provide the array of permanent magnets.

A system for defining an array of permanent magnets for a stellarator, the system comprising:

• (i) one or more processors, and (ii) one or more memories coupled to the one or more processors, the one or more memories to store computer-executable instructions that, when executed by the one or more processors, cause the system to perform operations comprising:
• obtaining an initial arrangement of a plurality of permanent magnets positioned around a plasma having a plasma surface;
• optimizing dipole moment magnitudes and dipole moment orientation angles of each permanent magnet of the plurality of permanent magnets in the initial arrangement to provide a revised arrangement of the plurality of permanent magnets, wherein the optimization of the dipole moment magnitudes and dipole moment orientation angles comprises:
• generating an improved arrangement of the plurality of permanent magnets, wherein the improved arrangement is generated by computing a first numerical minimization of an error field on the plasma surface, where dipole moment magnitudes and dipole moment orientation angles are free and continuous parameters in the computation of the first numerical minimization, and where the dipole moment magnitude is constrained from exceeding a pre-defined maximum value,
• generating the revised arrangement, wherein the revised arrangement is generated by computing a second numerical minimization of a composite cost function that penalizes both the error field on the plasma surface and intermediate dipole moment magnitudes, wherein the computation of the second numerical optimization uses the generated improved arrangement as an initialization, and wherein each magnet of the plurality of magnets in the revised arrangement has either a zero dipole moment magnitude or a non-zero dipole moment magnitude, and where the non-zero dipole moment magnitude has a predetermined value;
• defining a set of allowable dipole moment orientation angles;
• and
• setting the dipole moment orientation angles of each of the permanent magnets having the non-zero dipole moment magnitudes in the generated revised arrangement to one of the dipole moment orientation angles in the defined set of allowable dipole moment orientation angles to provide the array of permanent magnets.