Kinetic theory of solitary waves on coasting beams in synchrotrons

A generalization of the Vlasov-Poisson system describing the collective dynamics of stored, high-energy hadron beams under the influence of a complex wall impedance is derived in the highly relativistic beam limit γ≫1. A coherent electric field structure Ez(r,z) is found to affect the beam dynamics in O(γ-2), giving rise to an updated feedback between line density (respectively, beam current) and self-fields. Propagating solitary wave solutions as special solutions of this system are obtained by the potential method known from plasma physics. Various parameter regimes are investigated and wave structures are found which are characterized by notches (respectively, humps) in the resonant part of the distribution function. These coherent waves typically travel with thermal velocities and below (kinetic solitary waves) but also structures moving with larger phase velocities (hydrodynamic solitons) are found. Dory's conjecture about mass conjugation is approved a posteriori in the purely reactive case but is found to be substantially altered in the strongly resistive case. Hydrodynamic Korteweg-de Vries solitons are shown to exist in the purely reactive case and for beams above transition energy and for weak space charge effects only. © 2000 American Institute of Physics.