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For a large class of problems the self-consistent simulation of charged particle beams in linear accelerators is necessary. Especially, in all low-energetic sections such as injectors the self-consistent interaction of particles and fields has to be taken into account. Well-known programs like the MAFIA TS Modules typically use the Particle-in-cell (PIC) method for beam dynamics simulations. Since they use a fixed computational grid which has to resolve the bunch adequately, they suffer from enormous memory consumption. Therefore and especially in the 3D case, only rather short sections can be simulated. A remedy to this limitation is the usage of a grid which refines itself in the vicinity of particles. For this purpose, a new code called SMOVE based on a time-adaptive grid is being developed. First promising results will be presented at the conference.
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