Classical and Quantum-like approaches to charged-particle fluids in a quadrupole

A classical description of the dynamics of a dissipative charged-particle fluids in a quadrupole- like device is developed. It is shown that the set of the classical fluid equations contains the same information as a complex function satisfying a Scrodinger-like equantions in which the Planck's constant is replaced by the time-varying emittance, which is related to the time-varying temperature of the fluid. . Within this framework the dynamics of an electron bunch in a storage ring in the presence of radiation damping and quantum exication is recovered.