A Resistive Theory of Bunch Lengthening

A new theory of bunch lengthening in electron storage rings is proposed. The equilibrium bunch length is that length which stabilizes the bunch against the onset of "fast" resistive instability, caused by the combination of many high frequency resonators such as vacuum flanges. The heat dissipated in these impedance sources follows immediately from the bunch length. It is found that the anomalous bunch length is determined by a scaling parameter g=(hVcos??s)/I. Data taken in SPEAR I and II, data in which g extends in value by more than three orders of magnitude, can be fit with an appropriate choice of high frequency, large width coupling impedance. The impedance functions for SPEAR I and II are taken to be the same, a reflection of the fact that the high frequency sources are chamber discontinuities rather than structures connected with the rf systems. A parameter search leads to an impedance characterized by a central frequency ~5 GHz, a width (FWHM) ~1.8 GHz and a peak impedance ~0.2 M??. The expected and observed higher mode resistance (i.e.heat dissipated) for SPEAR are compared and found to be in agreement. Predictions are given for PEP and PETRA.