Lattice Boltzmann Scheme for Drift Diffusion Equations in Cold Plasma Applications

Abstract This paper presents a Lattice Boltzmann Method (LBM) tailored for solving drift-diffusion equations in cold plasma applications. The proposed scheme is aimed to be a first step to address the challenges of simulating cold plasmas, characterized by non-equilibrium conditions and complex interactions among electrons, ions, and electric fields. By employing a parabolic scaling and simplifying assumptions, the method ensures computational efficiency while maintaining accuracy. Validation is performed through numerical test cases. While promising, future work will focus on incorporating energy dynamics and handling variable diffusion coefficients to enhance the method’s applicability in diverse plasma scenarios.