Artificial Collisions, Entropy and Emittance Growth in Computer Simulations of Intense Beams

Artificial collisions during particle tracking with selfconsistent space charge lead to diffusion-like, numerical effects. The artificial collisions generate a stochastic noise spectrum. As a consequence the entropy and the emittance can grow along periodic focusing structures. The growth rates depend on the number of simulation macro-particles and on the space charge tune shifts. For long-term tracking studies the numerical diffusion can lead to incorrect beam loss predictions. In our study we present analytical prediction for the numerical friction and diffusion in 2D simulations. For simple focusing structures we derive a relation between the friction coefficient and the entropy growth. The scaling of the friction coefficient with the macro-particle number and the space charge tune shift is obtained from 2D simulations and compared to the analytic predictions.