Theory of the transverse gradient wiggler

We develop analytical models for the operation of gain-expanded transverse gradient wigglers in the low, medium, and high optical intensity regimes. The first two are Raman regimes in which the optical wave and transverse betatron oscillations grow simultaneously. They differ from one another only in the nature of the saturation mechanism. The third or high intensity regime is a trapped particle regime physically very similar to the regime of high extraction variable parameter wigglers.