Lattice Boltzmann model for collisionless electrostatic drift wave turbulence obeying Charney–Hasegawa–Mima dynamics

Abstract

A lattice Boltzmann method (LBM) approach to the Charney-Hasegawa-Mima (CHM) model for adiabatic drift wave turbulence in magnetised plasmas is implemented. The CHM-LBM model contains a barotropic equation of state for the potential, a force term including a cross-product analogous to the Coriolis force in quasigeostrophic models, and a density gradient source term. Expansion of the resulting lattice Boltzmann model equations leads to cold-ion fluid continuity and momentum equations, which resemble CHM dynamics under drift ordering. The resulting numerical solutions of standard test cases (monopole propagation, stable drift modes and decaying turbulence) are compared to results obtained by a conventional finite difference scheme that directly discretizes the CHM equation. The LB scheme resembles characteristic CHM dynamics apart from an additional shear in the density gradient direction. The occurring shear reduces with the drift ratio and is ascribed to the compressible limit of the underlying LBM.

The collisional drift wave instability in steep density gradient regimes

“…In contrast to the OB approximated model, we observe sheared and localised growth of the initial perturbation in the steep background density regime. This is in qualitative agreement with the previously reported NOB shearing effect of DWs of [50]. The radial location of the strongest growth coincides approximately with the maximum of the absolute background density gradient |∂ x n G |.…”