High-order implicit particle-in-cell method for plasma simulations at solid densities

A high-order implicit multidimensional particle-in-cell (PIC) method is developed for simulating plasmas at solid densities. The space-time arrangement is based on Yee and a leapfrog algorithm for electromagnetic fields and particle advancement. The field solver algorithm completely eliminates numerical instabilities found in explicit PIC methods with relaxed time step and grid resolution. Moreover, this algorithm eliminates the numerical cooling found in the standard implicit PIC methods by using a pseudo-electric-field method. The particle pusher algorithm combines the standard Boris particle pusher with the Newton-Krylov iteration method. This algorithm increases the precision accuracy by several orders of magnitude when compared with the standard Boris particle pusher and also significantly decreases the iteration time when compared with the pure Newton-Krylov method. The code is tested with several benchmarks, including Weibel instability, and relativistic laser plasma interactions at both low and solid densities.