Comparison of Delta Function and Gaussian Wakes for Longitudinal Tracking

The longitudinal motion of bunched beams in large storage rings has been simulated in synchrotron phase space, including the effects of wake-fields excited by the bunches themselves in the RF cavities. Using the delta-function wake-potential of the cavities requires a great deal of computing time and, in addition, the results depend on the number of superparticles considered. The computing time can be strongly reduced by using tables of wake potentials of a fixed bunch shape. We investigate the case where the distribution is assumed to be Gaussian. The validity and limitations of this model as function of the beam intensity are analysed by evaluation of higher moments of the distribution (variance, skewness, kurtosis). This shows that the assumption of the shape remaining Gaussian is insufficient and yields misleading results when the beam current is too high. This phenomenon appears to be related to the manifestion of turbulence in the beam.