Artificial collisions, entropy and emittance growth in computer simulations of intense beams

Artificial collisions during particle tracking with self-consistent 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. In our study we present analytical predictions 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