Hyper Boris integrators for particle-in-cell simulation

We propose a family of numerical solvers for the nonrelativistic Newton-Lorentz equation in particle-in-cell (PIC) simulation.The new solver extends the standard 4-step Boris procedure, which has second-order accuracy in time, in several ways.First, we repeat the 4-step procedure n times, using an n-times smaller timestep (Delta_t/n).To speed up the calculation, we derive a formula for the arbitrary subcycling number n.Second, prior to the 4-step procedure, we apply Boris-type gyrophase corrections to the electromagnetic field.In addition to the magnetic field, we amplify the electric field in an anisotropic manner to achieve higher-order (N=2,4,6... th order) accuracy.Third, combining these two methods, we propose a family of high-accuracy particle solvers, the hyper Boris solvers.The n-cycle Nth-order solver gives a numerical error of ~ (Delta_t/n)N at affordable computational cost.