Fundamental and harmonics of Thomson backscattered X-rays from an intense laser beam

We have formulated and obtained analytical expressions for Thomson backscattered X-ray radiation for an electron beam interacting with a linearly polarized electromagnetic undulator. The analytical expressions are valid for the fundamental and harmonics with arbitrarily large laser intensities. The formulation includes the effect of small angular misalignment between the laser pulse and the electron beam. This misalignment is found to increase the spectral width and distort the symmetry of the backscattered radiation.< >