The attosecond x_ray pulse trains emitted by a single electron intersecting with an intense Gaussian laser beam have been investigated theoretically and numeric ally by use of Thomson scattering of free electrons. The temporal and spatial ch aracteristics of the radiation are presented for different laser amplitude param eters a0 (1—10) and initial energies of the electron γ0(1 —100MeV). It is found that the durations of the pulse trains and individual pul se depend significantly upon the laser beam width and intensity, as well as the electron energy. Specifically, the individual pulse duration, the separation bet ween neighboring pulses, and the duration of the pulse profile are all proportio nal to 1/γ20. The emission power and energy are propo rtional to γ 60 and γ40, respectively. Whe n changing the laser amplitude a 0，the radiation power is proportional to a20, the individu al pulse duration to 1/a0, and the separation between pulses to a0. When keeping the laser amplitude while changing the beam w idth w0，the number of pulses in the profile, the duration of t he pulse profile, an d the emission energy are proportional to w0. If the laser powe r is fi xed while changing the beam width and intensity, the emission energy and profile duration of the emission pulse train are almost fixed. For a given laser amplit ude a0=1, a beam width w0 equal to 2 laser w avelengths, an d the initial electron energy of 10MeV，for example, the radiation profile of th e pulse trains has a duration of 14×10-3τ0, whic h is only a few attoseconds if the laser oscillation period τ0 is a few f emotoseconds.
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