Thermal wave model for nonlinear longitudinal dynamics in particle accelerators

By using the recently proposed thermal wave model for relativistic charged particle beam propagation, a new approach for studying some nonlinear effects in accelerating machines is developed. By taking into account the interaction of a relativistic charged particle bunch with both RF and the self-induced wakes and neglecting the synchroton radiation emission, we show that the longitudinal dynamics is governed by a nonlinear Schrödinger equation for a complex wave function whose squared modulus is proportional to the longitudinal bunch density. This wave model, for which the diffraction parameter is represented here by the longitudinal emittance, is suitable to give a new description for the bunch instability and capable of reproducing the coherent instability conditions. Furthermore, we show that soliton-like solutions for the density profile are possible. © 1993.