We study the canonical momentum based discretizations of a hybrid model with kinetic ions and mass-less electrons. Two equivalent formulations of the hybrid model are presented, in which the vector potentials are in different gauges and the distribution functions depend on canonical momentum (not velocity). 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, although the filters can be used to improve the schemes of the first formulation.

翻译：本文研究了针对具有动力学离子和无质量电子的混合模型的正则动量离散化方法。提出了该混合模型的两种等价形式，其中矢势采用不同规范，分布函数取决于正则动量（而非速度）。分布函数采用粒子云网格方法求解，矢势则在有限元外微分框架下通过有限元方法离散。时间离散化采用分裂方法。研究表明，第二种形式在数值上更具优势，且基于所提出的反对称括号构造的数值格式具有更优的守恒性质，尽管滤波器可用于改进第一种形式对应格式的性能。