Loading and Injection of Maxwellian Distributions in Particle Simulations

Existing and new particle loading and injection algorithms for particle simulations are analyzed to determine numerical accuracy and computational efficiency. Emphasis has been placed on loading and emission of Maxwellian, drifting Maxwellian, and cutoff Maxwellian velocity distributions. Once a velocity distribution has been inverted for loading or injection, time-centering of the position and velocity is necessary in order to maintain second-order accuracy. Here, the accuracy of these methods is determined and compared to three analytic test cases with spatially varying, time-dependent, and time-independent electric fields in a homogeneous magnetic field and a self-consistent crossed-field diode. The initial push is shown to be important in calculating the correct electric field at the boundary where particles are injected, in relaxing constraints on the time step, and in providing reliable field fluctuations due to particle statistics.