PHASE-SPACE VORTICES IN UNBUNCHED BEAMS IN SYNCHROTRONS

A self-consistent theory of notches in coasting beam distributions is presented. These vortex-type structures in phasespace demand a kinetic description and are found e.g. in cases of large wall resistivities. They are nonlinear from the outset, even at arbitrary small amplitudes , and appear in the thermal range of the distribution function of beam particles, where linear wave theory would predict strong Landau dampi ng. This points out an unusual character of these modes and sheds new light on the spectrum of small amplitude perturbations of the Vlasov-P oisson system, as they lie outside the realm of linear wave theories a nd their nonlinear descendants.