Injecting a Kapchinskij-Vladimirskij distribution into a proton synchrotron

Recently it has been suggested that the Kapchinskij-Vladimirskij (KV) distribution (1959) may be of practical interest for high intensity machines in that it may provide the maximum space charge limit for such a machine. One can make a plausible argument that the maximum beam intensity is obtained for a distribution for which all particles have the same tune, at least when the resonance is approached. Therefore, the following steps should be taken: first, reduce the chromaticity of the accelerator ring as much as possible, and second, make the betatron frequencies independent of amplitude, i.e., make the focusing forces linear. One way to make the focusing forces linear is to start with external focusing forces which are linear, and then make the space charge forces also linear by using a KV distribution. The authors describe two injection scenarios which produce a KV distribution (if we neglect beam-beam interactions during the injection process.) Simulations of these injection scenarios verify that the resulting distribution produces a uniform circular beam in xy-space. A simulation code was written which also includes the space charge interactions between the 500 injected turns in the proposed scenarios; the results are given. The space charge forces have a substantial effect on the resulting distribution