April 15-17

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Author: Dhairya Malhotra
Requested Type: Pre-Selected Invited
Submitted: 2019-02-22 16:00:33

Co-authors: A.J. Cerfon, L.M. Imbert-Gerard, M. O'Neil

Contact Info:
Courant Institute NYU
251 Mercer Street WWH 1008
New York, NY   10012-1
US

Abstract Text:
We present BIEST (Boundary Integral Equation Solver for Taylor states), a new numerical solver for the fast and accurate computation of fixed-boundary stepped-pressure equilibria in stellarators.

BIEST decomposes the calculation of stepped-pressure equilibria into the same two iterative steps as the SPEC solver (Stepped Pressure Equilibrium Code) [1] does: 1) The location of ideal MHD barriers is prescribed, and Taylor states are computed in the different regions separated by ideal MHD barriers; 2) the location of the ideal MHD barriers is moved in order to satisfy force balance. However, BIEST computes Taylor states in a fundamentally different way from SPEC. Specifically, in BIEST Taylor states are reformulated in terms of boundary integral equations, in which the unknowns to be computed are only defined on the ideal MHD barriers. This approach has several advantages: 1) the number of unknowns is greatly reduced as compared to SPEC, thus reducing the memory requirements; 2) BIEST avoids issues with the coordinate singularity which occurs when parameterizing the volume of genus-one domains; 3) the nature of the integral equations in BIEST leads to favorable conditioning as compared to volume based discretization schemes.

We tested the performance of BIEST for several stellarator geometries (W7-X, QAS3), and numerically confirmed the favorable comparison with SPEC, in terms of both accuracy (BIEST reaches 9-digit accuracy without encountering conditioning issues) and speed (factor of 3 to 10 speedup as compared to SPEC).


[1] S.R. Hudson, R.L. Dewar, G. Dennis, M.J. Hole, M. McGann, G. von Nessi, S. Lazerson, Computation of multi-region relaxed magnetohydrodynamics equilibria, Phys. Plasmas 19 (2012) 112502

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