Sparse Grid Approach to Accelerate Particle-In-Cell Technique: Application to the Hall Thruster E×B Instability

The Particle-In-Cell (PIC) technique couples a Lagrangian method to describe charged particles transport with Eulerian approach to resolve Maxwell’s equations. They are extensively used in the context of low temperature plasmas. For such applications, the self-induced magnetic field generated by charged particle currents is negligible and Maxwell’s equations reduce to Poisson’s equation. For accuracy and stability of explicit schemes, electrostatic PIC algorithm needs to resolve the Debye length and the inverse of plasma frequency, leading to severe constrains in term of grid spacing and timestep, respectively.