Longitudinal dynamics for electrons in the thermal wave model for charged particle beams

An extension of the longitudinal thermal wave model, including both radiation damping and quantum excitation (stochastic effect) is presented here. We show that, in the presence of the RF potential well, the longitudinal dynamics is governed by a 1-D Schrodinger-like equation for a complex wave function whose squared modulus gives the longitudinal bunch profile. Remarkably, the appropriate emittance scaling is naturally recovered, and the asymptotic equilibrium condition for the bunch length is found. These results open the possibility to apply the thermal wave model, already tested for protons, in a more accurate way to electrons