Longitudinal instability analysis for the IPNS upgrade

The proposed 1-MW spallation neutron source upgrade calls for a 2-GeV rapidly-cycling synchrotron (RCS) with an intensity of 1.04×10¹⁴ protons per pulse. Due to the high intensity, the potential exists for collective instabilities. Emphasis is placed on controlling these by (a) minimizing the machine impedance by using a contour-following RF shield and (b) maximizing the momentum spread to make use of Landau damping. The coupling impedance is estimated and is dominated by space charge effects. It is found that the longitudinal microwave stability limit can be exceeded unless the momentum spread is sufficient. A longitudinal tracking code was developed to simulate injection and acceleration, including the effects of space charge and other sources of impedance. With the aid of the simulation, and under the assumptions of the instability theory, we arrive at an RF voltage profile and beam injection parameters which avoid both the instability and beam loss through the entire cycle. The limitations of the analysis are explored