A quasi-neutral electromagnetic hybrid model with drift-kinetic electrons and fully kinetic ions

In this work, we propose a hybrid model that combines drift-kinetic electrons with fully kinetic ions under the quasi-neutrality assumption, discretized using a geometric particle-in-cell framework on dual-grids. The model advances the perturbed electromagnetic fields $E$ and $B$ directly, rather than the scalar and vector potentials. The parallel electric field $E_\parallel$ is obtained from Ohm's law. The perpendicular electric field $E_\perp$ is computed from Amp\`ere's law by extracting the $E_\perp$-dependent component of the drift-kinetic electron current. The quasi-neutrality constraint eliminates high-frequency light waves and Langmuir waves from the system. Temporal discretization is performed using low-storage Runge--Kutta schemes. In this quasi-neutral hybrid model, the right-hand polarized wave branch exhibits a whistler-like dispersion relation, which imposes a stringent timestep constraint. To address this, we develop a novel implicit-explicit splitting scheme for Faraday's law that significantly relaxes the timestep stability restriction. The model is validated in slab geometry by reproducing cold plasma wave branches, ion Bernstein waves, compressional and shear Alfv\'en waves, and ion acoustic waves.