Longitudinal space charge effects near transition

Experimental and numerical studies of the longitudinal beam dynamics in the Small Isochronous Ring (SIR) at Michigan State University revealed a fast, space-charge driven instability that did not fit the model of the negative mass instability. This paper proposes a simple analytical model explaining these results. Also, the paper compares the model to result s of experimental and numerical studies of the longitudinal beam dynamics in SIR.