Angular streaking of betatron X-rays in a transverse density gradient laser-wakefield accelerator

In a plasma with a transverse density gradient, laser wavefront tilt develops gradually due to phase velocity differences in different plasma densities. The wavefront tilt leads to a parabolic trajectory of the plasma wakefield and hence the accelerated electron beam, which leads to an angular streaking of the emitted betatron radiation. In this way, the temporal evolution of the betatron X-ray spectra will be converted into angular "streak," i.e., having a critical energy-angle correlation. An analytical model for the curved trajectory of a laser pulse in a transverse density gradient is presented. This gives the deflection angle of the electron beam and the betatron X-rays as a function of the plasma and laser parameters, and it was verified by particle-in-cell simulations. This angular streaking could be used as a single-shot diagnostic technique to reveal the temporal evolution of betatron X-ray spectra and hence the electron acceleration itself.