Computer Simulation of the Electron-Bunch Widening as Due to Self-Bunching

Several theories1-10 have been proposed to explain anomalous bunch lengthening and widening in particle storage rings.11-13 All these theories either assume a modification of the accelerating potential well or a high frequency self-bunching mechanism similar to the one proposed for proton bunches.8,10,14,15 Some of the theories assume interaction between several modes of self-bunching which leads then to "turbulence". In most cases it is possible to derive a stability condition in terms of bunch current and impedance, but then the assumption is made that the bunch will blow up its width to a value which matches the stability condition. To check how valid is this assumption we carried out a computer simulation of the beha-viour of a high-intensity electron bunch. We adopted a very special case of impedance model which is a constant and real impedance for any frequency. In this case the space charge effect is simply proportional to the local current.