Quantumlike corrections and semiclassical description of charged-particle beam transport

It is shown that the standard classical picture of charged-particle beam transport in paraxial approximation may be conveniently replaced by a Wigner-Like picture in a semiclassical approximation. In this effective description, the classical phase-space equation for electronic rays is replaced by a von Neumann-like equation, where the transverse emittance plays the role of (h) over bar. Relevant remarks concerning the quantumlike corrections for an arbitrary potential in comparison with the standard classical description of the beam transport are given