RADIATION DAMPING AND QUANTUM EXCITATION FOR LONGITUDINAL CHARGED-PARTICLE DYNAMICS IN THE THERMAL-WAVE MODEL

On the basis of the recently proposed thermal wave model (TWM) for par ticle beams, we give a description of the longitudinal charge particle dynamics in circular accelerating machines by taking into account bot h radiation damping and quantum excitation (stochastic effect), in the presence of a RF potential well. The longitudinal dynamics is governe d by a 1-D Schrodinger-like equation for a complex wave function whose squared modulus gives the longitudinal bunch density profile. In this framework, the appropriate r.m.s. emittance scaling law, due to the d amping effect, is naturally recovered, and the asymptotic equilibrium condition for the bunch length, due to the competition between quantum excitation (QE) and radiation damping (RD), is found. This result ope ns the possibility to apply the TWM, already tested for protons, to el ectrons, for which QE and RD are very important.