Canonical variables based numerical schemes for hybrid plasma models with kinetic ions and massless electrons

We study the canonical variables based numerical schemes of a hybrid model with kinetic ions and mass-less electrons. Two equivalent formulations of the hybrid model are presented with the vector potentials in different gauges and the distribution functions depending on canonical momentum (not velocity), which constitutes a pair of canonical variables with the position variable. Particle-in-cell methods are used for the distribution functions, and the vector potentials are discretized by the finite element methods in the framework of finite element exterior calculus. Splitting methods are used for the time discretizations. It is illustrated that the second formulation is numerically superior and the schemes constructed based on the anti-symmetric bracket proposed have better conservation properties and lower noise level, although the filters can be used to improve the schemes of the first formulation.