  In a hybrid plasma solver (particle ions, fluid mass-less electrons) regions
of vacuum, or very low charge density, can cause problems since the evaluation
of the electric field involves division by charge density. This causes large
electric fields in low density regions that can lead to numerical
instabilities. Here we propose a self consistent handling of vacuum regions for
hybrid solvers. Vacuum regions can be considered having infinite resistivity,
and in this limit Faraday's law approaches a magnetic diffusion equation. We
describe an algorithm that solves such a diffusion equation in regions with
charge density below a threshold value. We also present an implementation of
this algorithm in a hybrid plasma solver, and an application to the interaction
between the Moon and the solar wind. We also discuss the implementation of
hyperresistivity for smoothing the electric field in a PIC solver.
