  Compton scattered x-rays can be generated using a configuration consisting of
a single, ultra-intense laser pulse, and a shaped gas target. The gas target
incorporates a hydrodynamically formed density spike, which nonlinearly
scatters the incident pump radiation, to produce a counter-propagating
electromagnetic wiggler. This self-generated wiggler field Compton scatters
from electrons accelerated in the laser wakefield of the pump radiation. The
nonlinear scattering mechanism in the density spike is examined theoretically
and numerically in order to optimize the Compton scattered radiation. It is
found that narrow-band x-rays are produced by moderate intensity pump radiation
incident on the quarter-critical surface of the density spike, while high
fluence, broadband x-rays are produced by high intensity pump radiation
reflected near the critical surface.
