ABSTRACT
Abstract. Ln order to simulate the beam dynamics in particle accelerators the Ensemble Model has been developed [1 ,2]. The Model divides a particle beam in a set of sub-beams or Ensembles. Besides the motion of the macroparticle center in phase space an internal motion inside Ensemble is considered. Within linear approximation for acting forces one can possible to build a compact self-consistent model based on 6 first-and 21 second order moments of the distribution function. This reduces the number of required macroparticles drastically. It was shown [3], that even with one Ensemble the simulation of the beam sizes and correlations in photoinjector yields good agreement with conventional beam dynamics codes, while the Ensemble Model bas demonstrated significant advantage in computation time. Ln contrary to the conventional macroparticles the sizes and correlations of the Ensemble change in accordance with gradients of applied forces. The space charge model for the Single Ensemble Model (SEM) is based on the homogeneously charged ellipsoid (known as K-V distribution [4]). Such an approach, being very efficient for the SEM, has significant difficulties for application to Multi Ensemble Model (MEM). As an alternative approach the 6D Gaussian distribution has been considered, and Multi-Centered Gaussian Expansion for the space charge force calculation has been studied [5]. The V-Code, based on the Ensemble Model, has been developed for the on-line beam dynamics simulations [3,6,7].
