Sausage mode stability boundaries: enumeration and verification

An axially symmetric sausage mode instability has been observed using particle simulation codes to propagate beams with a high degree of current neutralization. In this report the stability boundaries in terms of the magnitude and location of the return current are delineated for beams with square, Gaussian, and Bennett radial current profiles using the theoretical analysis of others. For the case in which the return current is held fixed as the beam propagates, a detailed comparison is made between the theoretical predictions and the results of the RINGFAST single disk particle simulation code. Agreement between theory and code results is good although the code results do show a slightly larger than predicted unstable region