Self field effects on the beam in storage rings

A high intensity beam (protons) moving in a storage ring creates sizable fields which act back on the particles. The influence of these self and mirror fields, excluding any additional RF fields, is taken into account to discuss the changing of a linear charge distribution. We describe the spatial deforming of the bunch in a first order approximation by a differential equation which is independent of any ring parameter. By a simple scaling law we can apply the solution to special ring dimensions. For a parabolic charge distribution we found an analytical solution for the time- and position-dependence of the charge density lambda(z,t) and of the particle momentum Δp/p (z,t). (orig.)