Analysis of a mixed semi-implicit/implicit algorithm for low-frequency two-fluid plasma modeling

A temporally staggered algorithm for advancing solutions of the two-fluid plasma model is analyzed with von Neumann’s method and with differential approximation. The implicit leapfrog algorithm [C.R. Sovinec et al., J. Phys. Conf. Series 16 (2005) 25–34] is found to be numerically stable at arbitrarily large time-step when the advective, Hall, and gyroviscous terms are temporally centered in their respective advances and the coefficient of the semi-implicit operator meets the criterion found for basic hyperbolic systems. Numerical instability with forward or backward differencing of advection is evident as an ill-posed equation in the differential approximation for a simplified system. At large time-step, the accuracy of the algorithm is comparable to that of the Crank–Nicolson method for all plane waves except the parallel mode that is sensitive to the ion cyclotron resonance. An implementation reproduces theoretical results on the transition from resistive magnetohydrodynamics to two-fluid reconnection in a sheared-slab linear tearing mode. A nonlinear three-dimensional computation in toroidal geometry shows an increasing exponentiation rate of kinetic energy as magnetic reconnection from an internal kink mode changes from current-sheet to ‘X-point’ geometry.