Filter Pack X-ray Spectrum Reconstruction for Betatron Streaking Experiment

For laser wakefield acceleration, single-shot diagnostic techniques are used to obtain the betatron X-ray spectrum. One method is the use of a filter pack in front of an X-ray camera to calculate the critical energy of a synchrotron-like spectrum. The pack is made of strips, each with varying thicknesses of aluminum and copper. To recover the spectrum, the spatial intensity profile is normalized by taking the background from the empty spaces between the strips and interpolating to recover the profile. A critical energy is guessed, and transmission data is calculated. The guess is adjusted to minimize the sum of the squares of the residuals between the real and calculated values, and this final value is taken to be the true critical energy. In betatron streaking experiments, the wakefield follows a curved trajectory as it travels through a transverse density gradient. Emitted X-rays “streak” across the camera, so the spectrum can be retrieved as the emission angle changes, representing the evolution of the critical energy with time.