The role of the Wigner function in charged-particle beam transport

The role of the Wigner function in the dynamics of charged particle beams in high-energy accelerating machines is discussed. This is done within the quantum-like description of the thermal wave model (TWM). A brief review of the numerical experiments showing satisfactory agreement between TWM and the particle tracking simulations is presented. A simple analysis in phase space in terms of the Wigner quasidistribution, showing that TWM is capable of reproducing the beam dynamics in the presence of the space charge effects, is put froward.