Tracking of electron beams with numerically determined space charge forces

A tracking algorithm for the description of electron beams using grid-based space charge fields is compared to a method based on point-to-point calculations. The charged particles´ equations of motion are solved with a fifth-order embedded Runge-Kutta method using the concept of macroparticles. The space charge forces are determined in the bunch´s restframe with a multigrid-method