Kinetic theory of solitary waves on coasting beams in synchrotrons

A generalization of the Vlasov-Poisson system describing the collective dyn amics of stored, high-energy hadron beams under the influence of a complex wall impedance is derived in the highly relativistic beam limit gamma >>1. A coherent electric field structure E-z(r,z) is found to affect the beam dy namics in O(gamma(-2)), giving rise to an updated feedback between line den sity (respectively, beam current) and self-fields. Propagating solitary wav e solutions as special solutions of this system are obtained by the potenti al method known from plasma physics. Various parameter regimes are investig ated and wave structures are found which are characterized by notches (resp ectively, humps) in the resonant part of the distribution function. These c oherent waves typically travel with thermal velocities and below (kinetic s olitary waves) but also structures moving with larger phase velocities (hyd rodynamic solitons) are found. Dory's conjecture about mass conjugation is approved a posteriori in the purely reactive case but is found to be substa ntially altered in the strongly resistive case. Hydrodynamic Korteweg-de Vr ies solitons are shown to exist in the purely reactive case and for beams a bove transition energy and for weak space charge effects only. (C) 2000 Ame rican Institute of Physics. [S1070-664X(00)00508-5].