Three-dimensional simulation of ultrarelativistic charged beams dynamics: study of initial and boundary conditions

We consider problems of initial and boundary conditions in the mathematical modeling of full three-dimensional charged beam dynamics applicable to colliders of new generation. In this case high values of relativistic factors ($10^3$–$10^6$) lead to high gradients of electromagnetic fields, requiring special attention to the computation of initial and boundary conditions. We present new methods for the computation of initial and boundary conditions, their analysis and comparison with standard methods. The algorithms presented are also applicable to other problems addressed by the particle-in-cell-method with high relativistic factors.