High Energy Photon Colliders. *

Using the laser backscattering method at future linear colliders one can obtain γγ and γe colliding beams (photon colliders) with energy and luminosity comparable to that in ee collisions. This option has been included in the pre-conceptual designs of linear colliders and in work on a Technical Design Report which is in progress. The physics motivation for photon colliders is quite clear. The proof of its technical feasibility and the search for the best solutions is of first priority now. A key element of a photon collider is a laser with high peak power and repetition rate. One very promising way to overcome this problem is the optical cavity approach which is discussed in this paper. A very high γγ luminosity could be achieved by further decreasing the beam emittances. This will be very challenging. One possible way is laser cooling of electron beams. This method is discussed in my second talk at this symposium. The solution to the first problem is vital for photon colliders and provides an interesting physics program. Solution of the second problem makes photon colliders a very powerful instrument for study of matter, the best for study of many phenomena. How to achieve these goals is the subject of this talk.