Fluid description of the longitudinal instability in high current coasting beams

The longitudinal instability of an intense coasting beam in the ESR (Experimentier–Speicherring) [G. Rumolo et al., Nucl. Instrum. Methods A415, 411 (1998)] has been investigated far away from the stability boundary for several values 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 employed to explain the growth of the slow wave as well as the nonlinear steepening and the harmonic generation. Taking into account the effects of the initial momentum spread of the beam through a modified space charge impedance, the 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 under a full kinetic model as well as from the particle-in-cell code PATRIC [I. Hofmann, Z. Naturforsch. 87a, 939 (1982)].