Laser cooling of electron beams at linear colliders

A method for electron beam cooling is considered which can be used for linear colliders. The electron beam is cooled during collision with a focused powerful laser pulse. The ultimate transverse emittances are much lower than those achievable by other methods. This method is especially useful for high-energy photon colliders. In this paper we review and analyze limitations in this method, discuss a new method of obtaining very high laser powers required for the laser cooling, radiation conditions and finally present a possible scheme for the laser cooling of electron beams.