2021
1.
Henneberg, S. A.; Hudson, S. R.; Pfefferlé, D.; Helander, P.
Combined Plasma– Coil Optimization Algorithms Journal Article
In: Journal of Plasma Physics, vol. 87, no. 2, 2021, ISSN: 0022-3778, 1469-7807.
Abstract | Links | BibTeX | Tags: coil design, optimisation, SPEC, variational calculus
@article{hennebergCombinedPlasmaCoil2021,
title = {Combined Plasma\textendash Coil Optimization Algorithms},
author = {S. A. Henneberg and S. R. Hudson and D. Pfefferl\'{e} and P. Helander},
doi = {10.1017/S0022377821000271},
issn = {0022-3778, 1469-7807},
year = {2021},
date = {2021-04-01},
urldate = {2021-04-01},
journal = {Journal of Plasma Physics},
volume = {87},
number = {2},
publisher = {Cambridge University Press},
abstract = {Combined plasma\textendash 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\textendash 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\textendash coil optimization algorithms, we emphasize the importance of the stability matrix.},
keywords = {coil design, optimisation, SPEC, variational calculus},
pubstate = {published},
tppubtype = {article}
}
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.