Analysis of effect of macro-particle number on phase space distribution of charged particle beam using particle pair transformation

To describe a charged particle beam in an accelerator, macro-particle method is widely used in numerical simulation. In order to analyze the effect of number of macro-particles on the resolution in the phase space distribution, particle pair transformation, which is a transformation to reduce the number of macro-particles, was defined. The particle pair transformation was applied to two dimensional uniform circular distribution, Using the transformation, the resolution in the virtual phase space distributions, x-E_x and y-E_y, which are calculated from the static electric field caused by the particle distribution, was analyzed. In the analysis, random algorithm and quasi-random algorithm were used to generate the initial particle distributions. The random algorithm occasionally generates a particle pair, whose distance is extremely short, and it causes strong electric field. It increases the virtual emittance in x-E_x and y-E_y spaces. When the number of macro-particles was reduced by the particle pair transformation, the average particle distance was extended and made even, and the virtual emittance converged for both the random and the quasi-random algorithms. (author)