About the Particle-in-Cell Method and Solutions That Lose Smoothness

To test various versions of the particle-in-cell method, a benchmark problem simulating the breaking effect of relativistic plasma oscillations is proposed. It is shown that the breaking effect can be realized using the TSC version of the method, but not using the CIC version. Unsuccessful modeling attempts lead to the observation of a gradient catastrophe directly on the symmetry axis of the domain, which contradicts the corresponding theoretical results. The cause of these failures is the resonant growth of the error over time at one of the algorithm stages. The proposed testing method is suitable for an arbitrary one-dimensional version of the particle-in-cell method.