From Theoretical Foundation to Invaluable Research Tool: Modern Hybrid   Simulations
  In many plasmas, in particular in space science, protons govern much of the essential physics. Minority ions, suprathermal tails, and electrons at times account for additional details. However, electron effects usually appear on much smaller spatial and temporal scales. For more than two decades, scientists have refined computational models that concentrate on the dominating and larger-scale ion kinetic physics, while treating the much lighter electrons as a charge-neutralizing fluid. These physics-based, algorithmic model descriptions are called hybrid codes, which have established an invaluable position for themselves - clearly distinct from MHD calculations, but simpler and much more efficient than full-particle simulations. Here, the foundation and numerical details of hybrid codes are reviewed, and differences between existing algorithms are elucidated. 
D. Krauss-Varban