Parallel algorithm for solution of problems of charged particle dynamics by the use of load balance

We present new solution methods for dynamics of counter charged beams in accelerators and plasma electrons dynamics in a trap with inverse magnetic mirrors and multipole magnetic walls. The models are based on the particle-in-cell method. These problems require extremely large computations and can be solved by the use of powerful supercomputers only. A modification of the euler-lagrangian decomposition is implemented in order to achieve full and balanced load of computational nodes in case of highly nonuniform particle distribution in space and time.