Simulation of hollow beams with cancellation of steady state nonlinear space-charge

A technique is described for making multi-particle computer simulations of coherent instability consistent with conventional bunched-beam longitudinal instability theory. The argument behind the technique exposes an oversight of instability theory: the response of the phase-space distribution to the nonlinear steady state wakefields is neglected. As an example, the technique is applied to a beam with the steady-state space-charge fields artificially cancelled. The computer simulations presented are seen to agree with mode-coupling theory. Beam and machine parameters are taken from the proposed TRIUMF-KAON Accumulator, which is a high current proton storage ring.<>