Interaction of free electrons with an intense focused laser pulse in Gaussian and conical axicon geometries

We calculate the dynamics and the radiation emitted from free electrons in an ultrashort pulsed laser focus. In a Gaussian focus, at low electron densities for which space charge is negligible, we find that ponderomotive forces limit the effective volume of radiation emission to a region that is much smaller than the focal waist and even significantly smaller than the fundamental wavelength. Constructive interference produces significant enhancements in the radiation emitted by the plasma for the lower harmonics, whereas destructive interference limits the radiation for the higher harmonics. We also investigate the radiation emitted by electrons in the focus of a conical axicon, an optical geometry that was proposed for laser-based electron accelerators [J. Appl. Phys. 54, 4285 (1983)]. This radiation may be a useful diagnostic in such accelerators. These studies are intended as a prelude to experiments with high-intensity ultrashort laser pulses.