Charged-particle beam transport: Quantum-like description versus classical description

The Thermal Wave Model seems to provide a realistic quantum-like description of charged particle beam optics. It is proven that, for a multipole potential, the classical and the quantum-like description are in agreement up to the second-order distribution function moment equations. The discrepancy are due to higher-order moments which are experimentally hardly measurable. This result is supported by a recent numerical investigation where the phase-space distributions produced by a standard tracking code has been compared with the natural candidates for such a distribution in the quantum-like model, namely the Wigner function, and the Husimi function.