TY - JOUR

T1 - Combined plasma-coil optimization algorithms

AU - Henneberg, S. A.

AU - Hudson, S. R.

AU - Pfefferlé, D.

AU - Helander, P.

PY - 2021/4/3

Y1 - 2021/4/3

N2 - Combined plasma-coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria for multiregion relaxed magnetohydrodynmics (MRxMHD) is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi-free-boundary optimization, and the free-boundary (coil) optimization. These are described using the MRxMHD energy functional, the Biot-Savart integral, the coil-penalty functional and the virtual casing integral and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma-coil optimization algorithms, we emphasize the importance of the stability matrix.

AB - Combined plasma-coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria for multiregion relaxed magnetohydrodynmics (MRxMHD) is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi-free-boundary optimization, and the free-boundary (coil) optimization. These are described using the MRxMHD energy functional, the Biot-Savart integral, the coil-penalty functional and the virtual casing integral and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma-coil optimization algorithms, we emphasize the importance of the stability matrix.

KW - fusion plasma

UR - http://www.scopus.com/inward/record.url?scp=85105585487&partnerID=8YFLogxK

U2 - 10.1017/S0022377821000271

DO - 10.1017/S0022377821000271

M3 - Article

AN - SCOPUS:85105585487

JO - Journal of Plasma Physics

JF - Journal of Plasma Physics

SN - 0022-3778

M1 - 905870226

ER -