Abstract
A novel method of 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. With reasonable laser parameters (laser flash energy about 10 J) one can decrease transverse beam emittances by a factor of about 10 per stage. The ultimate transverse emittances are much below those achievable by other methods. Beam depolarization during cooling is about 5%–15% for one stage. This method is especially useful for photon colliders and opens new possibilities for e+e colliders and x-ray free-electron lasers based on high-energy linacs.

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