Rate Redistribution In Dispersive Electron Cooling

It is known that dispersive coupling can be applied to realize three-dimensional cooling in stochastic cooling and laser cooling. In electron cooling, the transverse cooling rate is usually smaller than the longitudinal one, especially for high-energy beams. We find that dispersion can also be introduced into electron cooling (dispersive electron cooling) to redistribute the cooling rate between the longitudinal and transverse planes. In this paper, we present an analytical model to explain and estimate the rate redistribution in dispersive electron cooling, in which both ion dispersion and electron dispersion are included. It demonstrates that a small horizontal dispersion of the ions can enhance the horizontal cooling at the expense of longitudinal cooling, and the electron dispersion is also of benefit to this effect. We also find that this redistribution effect will be more significant when there is a large difference between the horizontal and longitudinal cooling rates, which will be of great significance for high-energy electron cooling in the future.