A conservative implicit PIC scheme for the hybrid kinetic-ion fluid-electron model on curvilinear meshes

The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach to model multi-scale problems in space and laboratory plasmas. However, current explicit schemes suffer from a number of key algorithmic issues related to the stable propagation of whistler waves, and finite-grid instabilities for cold ion beams due to non-conservation of discrete momentum or energy. Here, we present a novel particle-based non-linear hybrid algorithm that features discrete conservation of mass, momentum and energy. Recently, the basic algorithm has been extended to allow the efficient treatment of multi-scale problems in generalized curvilinear geometries, using a fluid moment-based preconditioner to accelerate convergence when stepping over fast normal modes. A number of test problems are presented to demonstrate the correctness of the implementation, the unique conservation properties, and the favorable stability properties of the new scheme.