Multiple Timescale Calculations of Sawteeth and Other Global Macroscopic Dynamics of Tokamak Plasmas
Authors: S.C. Jardin, N. Ferraro, J. Breslau and J. Chen
Abstract:
The M3D-C1 [1] code is designed to perform 3D nonlinear magnetohydrodynamics (MHD) calculations of
a tokamak plasma that span the timescales associated with ideal and resistive stability as well as parallel
and perpendicular transport. This requires a scalable fully implicit time advance where the time step is
not limited by a Courant condition based on the MHD wave velocities or plasma flow but is chosen
instead to accurately and efficiently resolve the physics. In order to accomplish this, we make use of
several techniques to improve the effective condition number of the implicit matrix equation that is
solved each time-step. The split time advance known as the differential approximation [2] reduces the
size of the matrix and improves its diagonal structure. A particular choice of velocity variables and
annihilation operators approximately split the large matrix into 3 sub-matrices, each with a much
improved condition number. A final block-Jacobi preconditioner further dramatically improves the
condition number of the final matrix, allowing it to converge in a Krylov solver (GMRES) with a small
number of iterations. As an illustration, we have performed transport timescale simulations of a
tokamak plasma that periodically undergoes sawtooth oscillations [3]. We specify the transport
coefficients and apply a "current controller" that adjusts the boundary loop-voltage to keep the total
plasma current fixed. The short-time plasma response depends on the initial conditions, but the longtime
behavior depends only on the transport coefficients and the boundary conditions applied.
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Submitted to: Computational Science and Discovery (December 2011)
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Download PPPL-4717 (pdf 952 KB 19 pp)
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