We report the observation and investigation of synchronous energy exchange between nonrelativistic electrons and the ponderomotive (beat) force of two counterpropagating intense pulsed ${\mathrm{CO}}_{2}$ laser beams, operating at different frequencies in a stimulated Compton-scattering scheme. The interaction occurred in the nonlinear (trapping) regime, the physics of which is the same as that which occurs in laser accelerators and efficiency-enhanced free-electron lasers (FEL's) with long wigglers. The experiment is a first demonstration of the principle of inverse FEL acceleration and electromagnetic pump FEL operation in the nonlinear (trapping) regime. It can also be described as a demonstration of a ``traveling beat-wave'' Kapitza-Dirac effect in the nonlinear regime. Two different mechanisms of enhanced energy transfer were observed---electron trapping and phase-area displacement. Experimental results and computer simulations of both mechanisms are presented.
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