Extension of the Ingenious Electrostatic Model to Electromagnetic Model for Large-Scale Plasma Simulation with Self-Consistent Electron Dynamics

Abstract

An ingenious model for large-scale electromagnetic (EM) plasma simulations is proposed. By introducing a dielectric tensor ε with enlarged permittivity elements ε∗ » ε0 to Poisson equation, ∇· (ε∇φ) = −ρ (ε0 is the permittivity of free space, φ is electrostatic potential and ρ is charge density), the Debye length is artificially elongated and the large-scale system can be numerically treated even for including the self-consistent electron dynamics [T. Takizuka et al., Plasma Fusion Res.13, 1203088 (2018)]. In cylindrical coordinates (R, θ, Z) for three-dimensional tokamak simulations, a toroidal element εθθ is chosen much larger than poloidal elements εRR = εZZ = ε∗, and a toroidal mesh size Δθ can be set much larger than poloidal mesh sizes ΔR,Z. Resultantly the total mesh number becomes reasonably small and computation cost can be reduced. EM responses are also simulated using a modified Darwin model for Ampere's law, ∇2 A = −μ0(J − ε∂∇φ/∂t)(A is magnetic vector potential, J is current density, and μ0 is the permeability of free space), where light-speed EM waves are neglected. This modification is consistent with the charge-density continuity.