Abstract
The motion of an electron can be strongly influenced by the radiation emitted by the electron during the interaction with petawatt class lasers focused to small spot sizes. In order to study this problem we have numerically integrated the equation of motion of a single electron interacting with an intense electromagnetic wave and calculated the backscattered spectra. Large differences are found between the case where damping is included and not included. In particular, the first harmonic of the backscattered radiation is downshifted and the overall amplitude of the spectra is smaller than in the case with no damping. An analytical expression for the downshift is obtained and found to agree fairly well with the numerical calculations.
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