  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.
