Fluid description of the longitudinal instability in high current coastingbeams

The longitudinal instability of an intense coasting beam in the ESR (Experi mentier-Speicherring) [G. Rumolo , Nucl. Instrum. Methods A415, 411 (1998)] has been investigated far away from the stability boundary for several val ues of the machine impedance. Experiments have clearly shown the growth of the slow wave, generation of higher harmonics, asymmetric wave steepening, and saturation. A one-dimensional fluid model has been successfully employe d to explain the growth of the slow wave as well as the nonlinear steepenin g and the harmonic generation. Taking into account the effects of the initi al momentum spread of the beam through a modified space charge impedance, t he model predicts with high accuracy the rise time and the frequency shift of the unstable wave. Subsequently, nonlinear convective effects are shown to give rise to wave steepening and harmonic generation. Predictions of the fluid model are compared to experimental data and with those obtained unde r a full kinetic model as well as from the particle-in-cell code PATRIC [I. Hofmann, Z. Naturforsch. 87a, 939 (1982)]. (C) 1999 American Institute of Physics. [S1070-664X(99)02511-2].