Abstract
By applying a nonperturbative quantum electrodynamic theory, we study ponderomotive resonances when an electron beam is scattered by a standing photon wave. Our study shows that the ponderomotive parameter u p , the ponderomotive energy per laser-photon energy, for each of the two traveling laser modes possesses a minimum value ћω/(m e c 2). Ponderomotive resonances occur only when the ratio of the laser photon energy to the electron rest-mass energy is a fraction, where the denominator is twice the square of a positive integer and the numerator is the total ponderomotive number, which is also a positive integer.
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