The Gaussian approximation for a purely inductive wake function

The equilibrium bunch length in electron storage rings with a purely inductive localized wake function has been studied, assuming the Gaussian approximation of the distribution function in phase space. The localized wake describes more general cases, even uniformly distributed wakes, described by the Haissinski equation. The comparison of our results with those obtained from Haissinski equation shows good agreement and helps understanding the validity of the Gaussian approximation.