|approved||axisymmetrictaylor.pdf||2016-04-07 19:47:32||Antoine Cerfon|
Author: Antoine J. Cerfon
Requested Type: Pre-Selected Invited
Submitted: 2016-02-13 12:35:53
Co-authors: M. O'Neil
Courant Institute of Mathematical Sciences NYU
251 Mercer St
New York, NY 10012
The Stepped Pressure Equilibrium Code (SPEC)  calculates three dimensional MHD equilibria by subdividing the plasma domain into regions which are in relaxed Taylor states and separated by ideal MHD interfaces. In the last few years, SPEC has had much success in interpreting experimental results as well as improving our understanding of outstanding theoretical questions pertaining to 3-D equilibria. It is likely to soon become a popular code for the study of stellarators and Resonant Magnetic Perturbation (RMP) physics in tokamaks.
We present a new algorithm for the calculation of Taylor states in toroidal and toroidal-shell geometries which can be directly applied to improve the speed and accuracy of SPEC. Our scheme relies on an integral representation for the force-free magnetic field which is associated with a generalized Debye source representation of Maxwell fields. This formulation of the problem immediately yields a well-conditioned second-kind integral equation, and has several advantages. First, the force-free equation curl B = mu B is satisfied exactly by construction. Second, the formulation is the same for both axisymmetric and non-axisymmetric geometries. Third, the code has low memory requirements, since only the boundary needs to be discretized. Fourth, the solver can be coupled with high-order quadrature rules and fast algorithms, such as fast multipole methods, to obtain overall rapid convergence of the solution.
We give several numerical examples demonstrating the performance of our solver for Taylor states in axisymmetric torii and toroidal shells, and detail the steps we are undertaking to construct a solver capable of handling non-axisymmetric geometries.
 S. R. Hudson, R. L. Dewar, G. Dennis, M. J. Hole, M. McGann, G. von Nessi and S. Lazerson, Physics of Plasmas 19, 112502 (2012)