Numerical simulation of electromagnetic turbulence in tokamaks

Abstract

Nonlinear two‐ and three‐fluid equations are written for the time evolution of the perturbed electrostatic potential, densities, vector potential, and parallel ion motion of collisional and trapped electron plasmas in tokamak geometry. The nonlinear terms arise from the Ẽ×B₀ convection (d̃/dt=∂/∂t+ṽ_E ⋅ ∇_⊥) and magnetic flutter [∇̃_∥=∇_∥+(B_⊥/B₀) ⋅ ∇_⊥]. Simplified two‐dimensional (k_⊥) mode coupling simulations with a fixed average parallel wavenumber (k_∥=1/Rq) and curvature drift [ω_g=(L_n/R)ω_* ] characteristic of outward ballooning are performed. Homogeneous stationary turbulent states of the dissipative drift and interchange modes from 0≤β<β_crit for both the collisional and trapped electron plasmas are obtained. Transport coefficients associated with E×B and magnetic motions are calculated. The problem of simulating plasmas with high viscous Reynolds number is treated with an absorbing mantle at the largest wavenumbers. The results are summarized by comparison to simple mixing length rules: ñ/n₀∼1/k_⊥L_n, B̃/B₀ ∼(β/2) ⋅ q ⋅ ñ/n₀, D_E∼γ/k²_⊥.