Charge conservation in electromagnetic PIC codes; spectral comparison of Boris/DADI and Langdon-Marder methods Original Research Article

Non-charge conserving current collection algorithms for electromagnetic PIC plasma simulations may cause errors in Gaussʹs law. These errors arise from violations of the charge continuity equation, ∇ · J = −ϵπ/ϵt, which is turn cause errors in the irrotational part of E. Two techniques for reducing these errors are examined and compared: a modified Marder correction which corrects electric fields locally and primarily affects short wavelengths, and a Boris divergence correction, which solves Poissonʹs equation to correct the electric fields so that Gaussʹs law is enforced globally. The effect of each method on the spectrum of the error is examined. Computational efficiency and accuracy of the two techniques are compared: neither method is clearly superior. Cases examined include corrections in electromagnetic relativistic beam simulations, and a hot thermal plasma. In addition, the spectral comparison provides insight into the behavior of the schemes applied.