Particle-In-Cell Method and Smoothness-Losing Solutions

A benchmark problem that models the breaking of relativistic plasma oscillations is proposed for testing particle-in-cell methods. It is shown that the TSC version is capable of reproducing the breaking effect, while the CIC version is not. Failed attempts of modeling lead to a gradient catastrophe observed on the axis of symmetry of the domain, which contradicts the corresponding theoretical results. These failures are caused by the resonant growth of the error over time at one of the algorithm’s stages. The proposed testing method is suitable for an arbitrary one-dimensional particle-in-cell method.