Convergence Testing on the EPOCH Particle-in-Cell Code: How many particles are enough?

Particle-in-cell (PIC) simulations are a great tool to explore underlying physics in intense laser experiments and to model potential future experiments. However, PIC simulations can be very computationally expensive, taking hundreds of run-time hours even on state of the art supercomputers. Consequently, it is important to understand the most efficient way to perform a particular computation that still yields a sensible result. One important metric for the accuracy of a given PIC simulation is the extent that the particles and fields conserve energy. Numerical heating can occur if the resolution is too low or by using too few macroparticles per cell. In this work we use the EPOCH PIC code to simulate the interaction of an ultra-intense laser with a thin target in the Target Normal Sheath Acceleration regime. We conduct many of these simulations with different numbers of electron and ion particles per cell and analyze the results with correlation matrix techniques to determine suitable parameters for running an energy conserved simulation.