Symplectic particle-in-cell methods for hybrid plasma models with Boltzmann electrons and space-charge effects
This work addresses numerical stability and accuracy issues in plasma physics simulations for researchers in computational physics, though it appears incremental as it builds on existing hybrid models and methods.
The paper tackles the development of symplectic particle-in-cell methods for hybrid plasma models with Boltzmann electrons and space-charge effects, resulting in numerical methods that preserve geometric structure and energy, as demonstrated through experiments on finite grid instability, Landau damping, and nonlinear ion waves.
We study the geometric particle-in-cell methods for an electrostatic hybrid plasma model. In this model, ions are described by the fully kinetic equations, electron density is determined by the Boltzmann relation, and space-charge effects are incorporated through the Poisson equation. By discretizing the action integral or the Poisson bracket of the hybrid model, we obtain a finite dimensional Hamiltonian system, for which the Hamiltonian splitting methods or the discrete gradient methods can be used to preserve the geometric structure or energy. The global neutrality condition is conserved under suitable boundary conditions. Moreover, the results are further developed for an electromagnetic hybrid model proposed in [Vu H X. J Comput Phys, 124(2):417-430]. Numerical experiments of finite grid instability, Landau damping, and resonantly excited nonlinear ion waves illustrate the behaviour of the proposed numerical methods.