Abstract
A new construction of a free-electron laser using induced betatron oscillations to increase the FEL gain or efficiency is proposed. Induced betatron oscillations are driven by an additional space-periodic magnetic field with a period close to that of electron betatron oscillations in an undulator magnetic field. The induced oscillation amplitude proves to be sensitive to electron energy variation. In the result one more mechanism causing electron grouping in a ponderomotive wave takes place. This mechanism can cause the increase of the gain in a small-signal regime or the realization of an amplification regime close to an autoresonance when FEL efficiency grows essentially.
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