An Explicit, Energy Conserving, 2nd Order in Time Particle In Cell Algorithm

We have developed a new energy conserving Particle In Cell method that is based on second order in time versions of the Maxwell-Ampere equation and the Lorentz force law. Taking inspiration from Noether's theorem, the method has been constructed to be completely symmetric in time on three discrete time steps, which simplifies the calculation of the Lorentz force. The method also uses a spatially symmetric combination of field to particle interpolation and current weighting that is based on a variant of the charge conserving Villasenor Buneman algorithm. The method thus does not exhibit artificial grid heating when the Debye length is not resolved, and should be useful for simulations of cold dense plasmas, such as those can arise on cathode surfaces and from pulsed laser ionization.