A possibility of realization of a new, of principle, physical phenomenon is shown. This is the phenomenon of energy equalization of charged particle beams in the time of their acceleration in the crossed undulative electric and magnetic undulation fields (EH-fields). The phenomenon predicted is referred to as the effective cooling effect. Main properties and features of the effect are studied. In particular, it is shown that it would be experimentally observed for the existing today level of acceleration technologies.

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