Scattering of a few-cycle laser pulse by a single relativistic electron

The scattering of a single relativistic electron with few-cycle plane wave laser pulse with intensity of about \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I=1.38\times 10^{14}\,\text{ W/cm }^{2}$$\end{document} is theoretically and numerically analyzed in the linear regime, and the radiated energy spectra of electron shows that zeptosecond X-ray pulses can be supported. The influences of the initial carrier-envelope phase offset \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi _0$$\end{document} of the incident few-cycle laser pulses are studied, and the results demonstrate that a single zeptosecond pulse can be produced from scattering by using a single-cycle laser pulse with fixed initial carrier-envelope phase offset \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi _0 =\pi /2$$\end{document}. It is discovered that the influence of the initial carrier-envelope phase \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi _0$$\end{document} on the spectrum of the radiation is apparent for low and high frequency of the spectrum, but there is no influence of the central part of the spectrum.