Generation of uniform relativistic electron layer and linear and nonlinear coherent Thomson scattering*

A novel, multi-layer target [H.-C. Wu \textit{et al.}, PRL 104, 234801 (2010)] is proposed to generate uniform relativistic electron layers for coherent Thomson backscattering (CTS). A few-cycle laser pulse produces an electron layer from an ultrathin foil and then a second foil reflects the laser pulse, but lets the electrons pass through unperturbed. 2D-PIC simulations show that after interacting with the drive and reflected laser pulses, the electrons form a very uniform flyer that propagates in the direction of laser propagation. Such a flyer backscatters light with a full Doppler shift factor of $4\gamma ^2$. Nonlinear CTS theory for relativistic laser intensity shows that compared with linear CTS, a relativistically intense laser induces transverse motion of the electron layer and decreases the linear Doppler shift by a factor $1+a_0^2 $. Consequently, in order to obtain the same x-ray photon energy as linear CTS, the nonlinear case needs higher electron energy. Theory also shows that CTS efficiency reaches saturation when laser amplitude$a_0 >2$. PIC simulations show that a powerful x-ray pulse (1 keV, 10 attoseconds, and GW power) can be generated and that diffraction-limited focusing may boost the intensity to of order $10^{24}$W/cm$^2$.