Long-time numerical computation of electromagnetic fields in the vicinity of a relativistic source

We propose an implicit scheme for the calculation of electromagnetic fields in the vicinity of short electron bunches moving in a transversally bounded domain, as it has place in particle accelerators. The scheme is able to accurately model curved boundaries and does not suffer from dispersion in direction of motion. It is based on splitting the discrete curl operator in its transversal and longitudinal parts. Unlike previous conformal schemes the new method has a second order convergence without the need to reduce the maximal stable time step of the conventional staircase approach. This feature allows the usage of a moving mesh easily. Several numerical examples are presented and the algorithm is compared to other approaches.