Stability of High Beta Plasma Calculations by Monte Carlo Orbit Integration

CLAUS is a new non-variational eigenvalue solver, which is a modern implementation of the dispersion functional approach[1] based on the Vlasov-Maxwell model and developed specifically for high-β plasmas with analytically intractable particle orbits. Thermal and beam ions are represented by full kinetics; kinetic orbit integrals are handled by using Monte Carlo markers to evaluate unperturbed trajectories and are analytically continued by rational approximation via the AAA algorithm[2]. The electron response can be found through Monte Carlo calculations or through Ohm's Law, in which the model reduces to the Vlasov-Fluid approximation. Benchmarks against simple Alfven waves, lower hybrid drift instabilities, and kink instabilities are presented, demonstrating the correct implementation of this model and code. Application to realistic field-reversed configuration (FRC) plasmas show the presence of beam-driven compressional Alfven eigenmodes (CAEs) which saturate at relatively low amplitudes. The properties of these CAEs appear to be consistent with Mirnov measurements in the FRC experiments at TAE Technologies.

[1]Barnes, D C, et al. "Kinetic tilting stability of field‐reversed configurations." The Physics of fluids (1986).

[2]Nakatsukasa, Y, Olivier S, and Lloyd N. T. "The AAA algorithm for rational approximation." SIAM Journal on Scientific Computing (2018).