Fast Algorithms for the Tracking of Electron Beams∗

The simulation of the motion of a particle beam in linear colliders requires fast and robust numerical algorithms. The following approach to simulate the effect of nonlinear space charge forces on the dynamics of space charge dominated electron beams has been realized in the tracking code Q [9]. The related tracking algorithm has to solve the relativistic equations of motion for a large number of time steps and unknowns. The underlying physical model uses a grid– based method for the field calculations which allows the consideration of far more macroparticles than other methods. The numerical convergence studies presented in this paper show the robustness of the tracking algorithm and coincide with theoretical results. Further, several techniques for the construction of a fast adapted multigrid solver for the determination of the nonlinear space charge forces are investigated.