Problems of multi-TeV photon colliders

A high energy photon collider (gamma-gamma, gamma-electron) based on backward Compton scattering of laser light is a very natural supplement to e+e- a linear collider and can significantly enrich the physics program. The region below about one 0.5-1 TeV is very convenient from a technical point of view: wave length of the laser should be about 1 micron, i.e. in the region of most powerful solid state lasers, collision effects do not restrict the gamma-gamma luminosity. In the multi-TeV energy region the situation is more complicated: the optimum laser wave length increases in proportionally with the energy, the required flash energy also increases due to nonlinear effects in the Compton scattering; bunch trains are shorter (for warm high gradient linacs), this leads to higher backgrounds; the collision effects (coherent pair e+e- pair creation) restrict the luminosity. These problems and possible solutions are discussed in this paper. A method of laser focusing is considered which allows the decrease of the required laser flash energy and the practical elimination of the problem of nonlinear effects in Compton scattering; a way to reduce collision effects and obtain ultimate gamma-gamma luminosities at multi-TeV photon colliders is suggested.