Publications

Resolution requirements for energy conservation in kinetic plasma simulations

Bennett, Nichelle L.; Welch, Dale R.

The kinetic codes used to model the coupled dynamics of electromagnetic fields and charged particle transport have requirements for spatial, temporal, and charge resolution. These requirements may vary by the solution technique and scope of the problem. In this report, we investigate the resolution limits in the energy-conserving implicit particle-in-cell code CHICAGO. This report has the narrow aim of determining the maximum acceptable grid spacing for the dense plasmas generated in models of z-pinch target gases and power-flow electrode plasmas. In the 2D sample problem, the plasma drifts without external forces with velocity of 10 cm/µs. Simulations are scaled by plasma density to maintain uniform strides across the plasma and from the plasma to the boundaries. Additionally, the cloud-in-cell technique is used with 400 particles per cell and Δt = 0.85× the Courant limit. For the linear cloud distribution, the criterion for conserving energy is ΔE/E_tot < 0.01 for 50,000 time steps. The grid resolution is determined to crudely be Δx ≲ 3l_s, where l_s is the electron collisionless skin depth. For the second-order cloud distribution the criterion is ΔE/E_tot < 0.005 yielding Δx ≤ 15l_s. These scalings are functions of the chosen v_d, Δt, particles-per-cell, and number of steps.