2022
Muir, Dean; Pfefferlé, David; Qu, Zhisong; Hole, Matthew; Hegland, Markus
Numerical Integration of Particle Orbits in Discontinuous Fields Using VENUS-LEVIS and SPEC Journal Article
In: Computer Physics Communications, vol. 271, pp. 108191, 2022, ISSN: 0010-4655.
Abstract | Links | BibTeX | Tags: discontinuous fields, full-orbit, numerical method, SPEC, VENUS-LEVIS
@article{muirNumericalIntegrationParticle2022,
title = {Numerical Integration of Particle Orbits in Discontinuous Fields Using VENUS-LEVIS and SPEC},
author = {Dean Muir and David Pfefferl\'{e} and Zhisong Qu and Matthew Hole and Markus Hegland},
doi = {10.1016/j.cpc.2021.108191},
issn = {0010-4655},
year = {2022},
date = {2022-02-01},
urldate = {2022-02-01},
journal = {Computer Physics Communications},
volume = {271},
pages = {108191},
abstract = {The orbit code VENUS-LEVIS is adapted to follow particles in plasma equilibria with discontinuous fields generated by the Stepped Pressure Equilibrium Code (SPEC). The latter is an implementation of the Multi-Region relaxed MHD model, which efficiently computes Taylor states in a series of nested toroidal volumes and supports the formation of magnetic islands and chaotic field regions. To adapt VENUS-LEVIS, an event location procedure is implemented in the existing numerical integrator, which ensures the particle sees the correct field along its trajectory, regardless of the discontinuities present in the Stepped Pressure Equilibrium model. The algorithm is tested in the case where the magnetic field is uniform in the upper and lower half-spaces but has a discontinuity in its direction (shear) on the plane z=0. Particle drifts due to the discontinuity are studied. The convergence properties of the numerical scheme are highlighted by the numerical accuracy, and conservation of the system's invariants, such as energy and momentum. Simulations and convergence studies using the SPEC-LEVIS interface in axisymmetric geometry are then presented. Finally, illustrative particle drifts due to the discontinuity are studied and explained: we examine drifts associated with the change in Larmor radius of passing particles with small excursion from flux surfaces.},
keywords = {discontinuous fields, full-orbit, numerical method, SPEC, VENUS-LEVIS},
pubstate = {published},
tppubtype = {article}
}
2021
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}
}
2020
Qu, Z. S.; Pfefferlé, D.; Hudson, S. R.; Baillod, A.; Kumar, A.; Dewar, R. L.; Hole, M. J.
Coordinate Parameterisation and Spectral Method Optimisation for Beltrami Field Solver in Stellarator Geometry Journal Article
In: vol. 62, no. 12, pp. 124004, 2020, ISSN: 0741-3335.
Abstract | Links | BibTeX | Tags: curvilinear coordinates, MHD equilibrium, numerical method, SPEC
@article{quCoordinateParameterisationSpectral2020,
title = {Coordinate Parameterisation and Spectral Method Optimisation for Beltrami Field Solver in Stellarator Geometry},
author = {Z. S. Qu and D. Pfefferl\'{e} and S. R. Hudson and A. Baillod and A. Kumar and R. L. Dewar and M. J. Hole},
doi = {10.1088/1361-6587/abc08e},
issn = {0741-3335},
year = {2020},
date = {2020-11-01},
urldate = {2020-11-01},
volume = {62},
number = {12},
pages = {124004},
publisher = {IOP Publishing},
abstract = {The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the stepped pressure equilibrium code (SPEC) is efficient when the domain is a hollow torus, but ill-conditioning of the discretised linear equations occurs in the (solid) toroid due to the artificially singular coordinate parameterisation near the axis. In this work, we propose an improved choice for the reference axis to prevent coordinates surfaces from overlapping. Then, we examine the parity and asymptotics of the magnetic vector potential near the axis and suggest the use of recombined and rescaled Zernike radial basis functions. The maximum relative error in the magnetic field of the Wendelstein 7-X geometry is shown to reach 10-9 at high resolution in a series of convergence tests and benchmarks against the boundary integral equation solver for Taylor states. The new method is also reported to significantly improve the accuracy of multi-volume SPEC calculations. A comparison between free-boundary SPEC and the analytical Dommaschk potential is presented with higher-than-usual Fourier resolution. It is illustrated that we are able to resolve low amplitude current sheets when an interface is placed where there is no flux surface in the analytic solution. This was previously concealed because of insufficient numerical resolution.},
keywords = {curvilinear coordinates, MHD equilibrium, numerical method, SPEC},
pubstate = {published},
tppubtype = {article}
}