Quantum-like description of modulational instability and Landau damping in the longitudinal dynamics of high-energy charged-particle beams

Within the framework of the thermal wave model (TWM), a quantum-like description of longitudinal coherent instabilities of high-energy charged-particle beams in the presence of non-negligible resistive part of the coupling impedance is presented. It is shown that, similarly to previous quantum-like investigations in which only a purely reactive impedance was considered, the longitudinal coherent instability can be described in terms of a modulational instability associated with the nonlinear Schrödinger equation (NLSE) also in the present case. In addition, by using the Wigner transform to carry out the analysis in phase-space, the role of Landau damping is considered in connection with the above instability, showing that TWM is capable of reproducing all the results of the conventional theory of the coherent instability as well as of predicting new results (in particular, the possible existence of a quantum-like Landau damping), connected with the crucial role of thermal noise introduced by the emittance in the resonance condition between waves and particles in the beam. This new result generalizes the present conventional theory of the longitudinal coherent instability and may be related to the very recent new phenomena observed in the context of nonlinear collective particle beam dynamics. © 1999 American Institute of Physics. © 1999 American Institute of Physics