2021
2.
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.
2018
1.
Hudson, S R; Zhu, C; Pfefferlé, D; Gunderson, L
Differentiating the shape of stellarator coils with respect to the plasma boundary Journal Article
In: Physics Letters A, vol. 382, no. 38, pp. 2732 - 2737, 2018, ISSN: 0375-9601.
Abstract | Links | BibTeX | Tags: coil design, MHD equilibrium, stellarator
@article{hudson-2018,
title = {Differentiating the shape of stellarator coils with respect to the plasma boundary},
author = {S R Hudson and C Zhu and D Pfefferl\'{e} and L Gunderson},
doi = {https://doi.org/10.1016/j.physleta.2018.07.016},
issn = {0375-9601},
year = {2018},
date = {2018-09-29},
journal = {Physics Letters A},
volume = {382},
number = {38},
pages = {2732 - 2737},
abstract = {The task of designing the geometry of a set of current-carrying coils that produce the magnetic field required to confine a given plasma equilibrium in stellarators is expressed as a minimization principle, namely that the coils minimize a suitably defined error expressed as a surface integral, which is recognized as the quadratic-flux. A penalty on the coil length is included to avoid pathological solutions. A simple expression for how the quadratic-flux and coil length vary as the coil geometry varies is derived, and an expression describing how this varies with variations in the surface geometry is derived. These expressions allow efficient coil-design algorithms to be implemented, and also enable efficient algorithms for varying the shape of the plasma surface in order to simplify the coil geometry, and a numerical illustration of this is given.},
keywords = {coil design, MHD equilibrium, stellarator},
pubstate = {published},
tppubtype = {article}
}
The task of designing the geometry of a set of current-carrying coils that produce the magnetic field required to confine a given plasma equilibrium in stellarators is expressed as a minimization principle, namely that the coils minimize a suitably defined error expressed as a surface integral, which is recognized as the quadratic-flux. A penalty on the coil length is included to avoid pathological solutions. A simple expression for how the quadratic-flux and coil length vary as the coil geometry varies is derived, and an expression describing how this varies with variations in the surface geometry is derived. These expressions allow efficient coil-design algorithms to be implemented, and also enable efficient algorithms for varying the shape of the plasma surface in order to simplify the coil geometry, and a numerical illustration of this is given.