A low-dispersion, exactly energy-charge-conserving semi-implicit relativistic particle-in-cell algorithm

Leap-frog based explicit algorithms, either energy-conserving or €œmomentum-conserving€, do not conserve energy discretely. Fully implicit algorithms can conserve discrete energy exactly (Lapenta and Stefano. POP 2011), which is desirable for long-term simulations, but introduce large dispersion errors in the light-wave modes, regardless of timestep sizes. This can lead to intolerable simulation errors where highly accurate light propagation is needed (e.g. laser-plasma interactions, LPI). In this study, we selectively combine the leap-frog and Crank-Nicolson methods to produce a low-dispersion, exactly energy-and-charge-conserving PIC algorithm. Specifically, we employ the leap-frog method for Maxwell equations, and the Crank-Nicolson method for particle equations. Such an algorithm admits exact global energy conservation, exact local charge conservation, and preserves the dispersion properties of the leap-frog method for the light wave. The algorithm has been implemented in a code named iVPIC, based on the VPIC code (https://github.com/losalamos/vpic) developed at LANL. We will present numerical results that demonstrate the properties of the scheme with sample test problems (e.g. Weibel instability run for 10^7 timesteps, and LPI applications).