A two-dimensional model to simulate collisional effects in high-intensity beams

The collisional effects in a high-intensity coasting beam have been analyzed by using a simulation code which provides the direct numerical integration of Hamilton equations of motion for a 2D systems of charged particles confined by a linear field. Scaling law for the relaxation time towards thermodynamic equilibrium as a function of the beam parameters (number of particles, space-charge strength, emittances, tunes) is proposed on the basis of the Landauʹs collisional theory. Furthermore, a preliminary study of the interplay between collisional effects and nonlinear phenomena in the case of Montague resonance for a static working point near to the resonance and for a slow crossing of the resonance is presented.