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, although the filters can be used to improve the schemes of the first formulation.

翻译：本文研究了基于正则变量的混合模型数值方案，该模型包含动理学离子与无质量电子。针对不同规范下的矢势以及依赖于正则动量（而非速度）的分布函数，提出了两种等价的混合模型表述，其中正则动量与位置变量构成一对正则变量。采用粒子网格方法处理分布函数，并基于有限元外微积分框架运用有限元方法对矢势进行离散化。时间离散采用分裂格式。研究表明，第二种表述在数值上更具优势，基于所提出的反对称括号构建的数值格式具有更优的守恒特性和更低的噪声，尽管滤波器可用于改进第一种表述的数值格式性能。