Numerical simulations for a hybrid model of kinetic ions and mass-less fluid electrons in canonical formulations

Abstract

We study the structure-preserving discretizations of a hybrid model with kinetic ions and mass-less electrons. Different from most existing works in the literature, we conduct the discretizations based on two equivalent formulations with vector potentials in different gauges, and the distribution functions depend on canonical momentum (not velocity). Particle-in-cell methods are used for the distribution functions, and vector potentials are discretized by finite element methods in the framework of finite element exterior calculus. Splitting methods are used for time discretizations. For the first formulation, filters are used to reduce the noises from particles and are shown to improve the numerical results significantly. The schemes of the second formulation show good stability and accuracy because of the use of symplectic methods for canonical Hamiltonian systems. Magnetic fields obtained from the vector potentials are divergence-free naturally. Some numerical experiments are conducted to validate and compare the two discretizations.

Energy conserving particle-in-cell methods for relativistic Vlasov–Maxwell equations of laser-plasma interaction

“…The action integral and Poisson bracket of AN-VP have been proposed and applied into numerical discretizations in [12,10,11]. When we take quasi-neutral limit for scheme (7), we get sub-step…”

“…Recently some structure-preserving methods have been proposed in [31,13] for F-VP. Structure-preserving methods of the AN-VP are proposed based on variational or Hamiltonian formulations in [12,10,11]. In this work, we focus on MB-VP, propose the action integral and Hamiltonian structure firstly, then construct structure-preserving methods.…”