  In work is considered average transverse dynamics of an electron beam in the
autoresonant laser. It is shown, that in approach of the given external
electromagnetic wave (small gain free electron laser) transverse emittance of a
beam of the charged particles decreases. This for the first time found out
effect can be used for cooling beams of various accelerators of the charged
particles. In the field of particle energy about 100 in the mass energy units,
beam energy losses are negligible. This method of charge beams cooling may be
applied to electron, muon and various heavy particle beams.
