Hyperbolicity of a Hermite-Laguerre moment model for the plasma edge in slab geometry

Simulating effects at the micro scale of the plasma edge in magnetic confinement fusion devices requires a numerically stable and efficient mathematical model. Particle dynamics can be modeled by a kinetic equation, which is difficult to solve due to the high dimensionality of the phase space. In this paper we derive a moment model for a reduced drift-kinetic equation to elucidate the question of hyperbolicity of the system, which is necessary to create a numerically stable model. The system matrix of an infinite set of moment equations is derived, after which the hyperbolicity of the model is investigated through the characteristic polynomial of said matrix. Hyperbolicity regions of the models are calculated and loss of hyperbolicity is shown to occur in scenarios relevant to magnetic confinement fusion. A regularization procedure that makes the system globally hyperbolic is used to overcome the loss of hyperbolicity leading to a stable moment model hierarchy for plasma edge simulations.