The electron movement based on the multi-photon nonlinear Compton scattering with the extra-intense stationary laser field is discussed by using KMR (Kroll-Morton-Rosenbluth) theory.We find that there exists only an evolution from periodicity to non-periodicity of the un-captured electron phase orbits after the energy exchange between the electron beam and laser fields.With the increase of the absorbed photon number n by an electron, this evolution will be more and more faster, while it is rapidly decreased with the enhancement of the collision non-flexibility ξ of the electrons and photons; When the electrons are captured by the laser fields, the evolution is finished, the electrons will stably transport,and the photons dont give up the energy to these electrons.
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