Coherent Thomson backscattering from laser-driven relativistic   ultra-thin electron layers
  The generation of laser-driven dense relativistic electron layers from ultra-thin foils and their use for coherent Thomson backscattering is discussed, applying analytic theory and one-dimensional particle-in-cell simulation. The blow-out regime is explored in which all foil electrons are separated from ions by direct laser action. The electrons follow the light wave close to its leading front. Single electron solutions are applied to initial acceleration, phase switching, and second-stage boosting. Coherently reflected light shows Doppler-shifted spectra, chirped over several octaves. The Doppler shift is found to be proportional to \gamma_x^2=1/(1-\beta_x^2), where \beta_x is the electron velocity component in normal direction of the electron layer which is also the direction of the driving laser pulse. Due to transverse electron momentum p_y, the Doppler shift by 4*\gamma_x^2=4*\gamma^2/(1+(p_y/mc)^2) ~= 2*\gamma is significantly smaller than full shift of 4*\gamma^2. Methods to turn p_y -> 0 and to recover the full Doppler shift are proposed and verified by 1D-PIC simulation. These methods open new ways to design intense single attosecond pulses. 
J\"urgen Meyer-ter-Vehn and Hui-Chun Wu