• S. Franke, W. Ackermann, T. Weiland
  TEMF, TU Darmstadt, Darmstadt

The Vlasov equation describes the evolution of a particle density under the effects of electromagnetic fields. It is derived from the fact that the volume occupied by a given number of particles in the 6D phase space remains constant when only long-range interaction as for example Coulomb forces are relevant and other particle collisions can be neglected. Because this is the case for typical charged particle beams in accelerators, the Vlasov equation can be used to describe their evolution within the whole beam line. This equation is a partial differential equation in 6D and thus it is very expensive to solve it via classical methods. A more efficient approach consists in representing the particle distribution function by a discrete set of characteristic moments. For each moment a time evolution equation can be stated. These ordinary differential equations can then be evaluated efficiently by means of time integration methods if all considered forces and a proper initial condition are known. The beam dynamics simulation tool V-Code implemented at TEMF utilizes this approach. In this paper the numerical model, main features and designated use cases of the V-Code will be presented.