Geometric Particle-In-Cell discretizations of a plasma hybrid model with kinetic ions and mass-less fluid electrons

We explore the possibilities of applying structure-preserving numerical methods to a plasma hybrid model with kinetic ions and mass-less fluid electrons satisfying the quasi-neutrality relation. The numerical schemes are derived by finite element methods in the framework of finite element exterior calculus (FEEC) for field variables, Particle-In-Cell (PIC) methods for the Vlasov equation, and splitting methods in time based on an anti-symmetric bracket proposed. Conservation properties of energy, quasi-neutrality relation, positivity of density, and divergence-free property of the magnetic field are given irrespective of the used resolution and metric. Local quasi-interpolation is used for dealing with the current terms in order to make the proposed methods more efficient. The implementation has been done in the framework of the Python package STRUPHY [1], and has been verified by extensive numerical experiments.