Three-dimensional calculations using the quiet implicit PIC method

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:489500

Barnes, D C; Nebel, R A; Sovinec, C R; Nystrom, W D ^[1]

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1. Los Alamos National Lab., NM (United States)

Solution of the time-implicit moment equations for electron and ion species, combined with Maxwell`s equations, is the kernel of the moment-implicit particle method and of the quiet implicit PIC method, a generalized {delta}f method for electromagnetic plasma simulation. Previous implementations have used a variety of direct and iterative approaches for obtaining solutions to large sparse linear systems. These methods suffer from both excessive computational cost, sometimes negating the advantage of implicit time differencing; and from lack of convergence in some regimes of interest, rendering the method inapplicable. We describe a new formulation of the coupled problem, leading to a symmetric, positive definite system. We also show that this symmetric problem may be efficiently and reliably solved by a conjugate gradient method. A three-dimensional algorithm has been constructed, using a pseudospectral Fourier treatment of the poloidal and toroidal directions, and a finite difference treatment of the radial direction. The radially-dependent, poloidal and toroidal averaged operator is used as a preconditioner. Convergence is rapid, with a typical iteration count of 10 for 10{sup -5} convergence. New results of the two-fluid form of this code to an internal m = 1 internal kink mode will be presented. The algorithm`s ability to reproduce kinetic properties of plasmas is being tested with a one-dimensional code, which has recently been modified to permit periodic boundary conditions. When a nonuniform temperature distribution is imposed as an initial condition, the gradients axe reduced by long mean-free-path particles that stream parallel to the magnetic field. Tests of collisionless wave damping have also been conducted for the ion-cyclotron range of frequencies, and results axe compared with analytic predictions.

• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 489500
• Report Number(s): CONF-960354--
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ALGORITHMS
CONVERGENCE
MAXWELL EQUATIONS
PLASMA SIMULATION
TEMPERATURE DISTRIBUTION
THREE-DIMENSIONAL CALCULATIONS