Simulation of Space Charge Dynamics in High Intensive Beams on Hybrid Systems

The method for construction of analytical expressions for electric and magnetic fields for some set of the distributions of the charge density is described. These expressions are used for symbolic computation of the corresponding electric and magnetic fields generated by the beam during the evolution in accelerators. Here we focus on the use of the matrix form for Lie algebraic methods for calculating the beam dynamics in the presence of self-field of the beam. In particular, the corresponding calculations are based on the predictor-corrector method. The suggested approach allows not only to carry out numerical experiments, but also to provide accurate analytical analysis of the impact of different effects with the use of ready-made modules in accordance with the concept of Virtual Accelerator Laboratory. To simulate the large number of particle distributed resources for computations are used. Pros and cons of using described approach on hybrid systems are discussed. In particular, the investigation of overall performance of the predictor-corrector method is made.