Analytical particle pusher for electrostatic particle-in-cells including electric field shear

Particle-in-Cell (PIC) is a widely adopted methodology that enables plasma simulations from first principles. Classical PIC codes utilize the Boris-Buneman scheme for the solution of the Newton-Lorentz equation in the phase space. However, the required time step is constrained by the CFL condition in time due to the need to resolve the particle's gyromotion in the presence of a magnetic field. Here we analyze a new particle pusher based on an analytical solution obtained by solving the Newton-Lorentz equation in presence of a uniform magnetic field, including a linear gradient electric field oriented at an arbitrary angle with respect to the magnetic field vector. One key benefit of using the analytic pusher is a relaxation of the time step constraint because the gyromotion does not have to be resolved explicitly. Although the computational cost per timestep for analytic pusher is higher than Boris, the computational cost for the whole simulation is lower due to less stringent requirements on the time step. The implementation of the analytic pusher in the hybrid plasma PIC code, hPIC2, will be presented using test particle problems and PIC simulation of a Chodura sheath formation. Additionally, we compare the performance of the new pusher against the standard Boris-Buneman scheme.