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In this paper, the Thomson scattering interacting with periodic magnitude laser pulse is studied numerically and theoretically based on classical radiant theory. By using MATLAB simulation, we find that radiant energy spectrum of electron proves that relativistic electron colliding with the periodic magnitude pulse of laser can obtain the narrow second ray pulse. The implications of original carrier envelope phase of incident periodic scale pulse of laser on spatial radiant characteristics, temporal spectral characteristics and spectral characteristics of Thomson scattering radiant of electrons under periodic scale pulse of laser are investigated. Results prove that radiant accumulates in an area of the cone centered in backward radiant direction and that each radiant power is optimal in backward direction. It is also found that single-period pulse of laser scattering with a fixed original carrier envelope phase shift can produce a single oblique second pulse. As incident pulse of laser is close to a single period pulse, the emission spectra of electrons indicate a radiant pulse duration of oblique seconds of x-rays. In addition, implication of original carrier envelope phase on radiant spectrum is equally significant for the high and low frequencies of spectrum, has no implication on central part of spectrum. From the above conclusions, we can conclude that implication of original carrier envelope phase on energy spectrum makes radiant very relevant for characterizing pulse of laser of periodic magnitude or for determining degree of synchronization between electrons and pulse of laser.
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