Progress in the study of mesh refinement for particle-in-cell plasma simulations and its application to heavy ion fusion

The numerical simulation of the driving beams in a heavy ion fusion power plant is a challenging task, and, despite rapid progress in computer power, one must consider the use of the most advanced numerical techniques. One of the difficulties of these simulations resides in the disparity of scales in time and in space which must be resolved. When these disparities are in distinctive zones of the simulation region, a method which has proven to be effective in other areas (e.g. fluid dynamics simulations) is the Adaptive-Mesh-Refinement (AMR) technique. We follow in this article the progress accomplished in the last few months in the merging of the AMR technique with Particle-In-Cell (PIC) method. This includes a detailed modeling of the Lampel-Tiefenback solution for the one-dimensional diode using novel techniques to suppress undesirable numerical oscillations and an AMR patch to follow the head of the particle distribution. We also report new results concerning the modeling of ion sources using the axisymmetric WARPRZ-AMR prototype showing the utility of an AMR patch resolving the emitter vicinity and the beam edge