Compact spectral characterization of 10-500 MeV $\gamma $-rays from the Texas Petawatt Laser-Driven Plasma Accelerator

GeV ($\gamma_{\mathrm{e}}$ \textgreater 2000) electron bunches from petawatt-laser-driven plasma accelerators can be converted to tunable, narrowband or to broadband continuum $\gamma $-ray (h$\nu $ \textgreater 10 MeV) pulses by Thomson backscattering (TBS) or bremsstrahlung, respectively. Inserting a plasma mirror (PM) near the accelerator exit converts electrons to $\gamma $-rays compactly and inexpensively, in a TBS/bremsstrahlung mixture determined by PM thickness, material and location. Characterizing the $\gamma $-ray spectra accurately is a challenge, usually addressed with bulky pair production/Compton spectrometers. Here, we spectrally characterize PM-generated TBS/bremsstrahlung $\gamma $-rays from 1-2 GeV Texas-Petawatt-Laser-accelerated electron bunches using a compact stack calorimeter, to record energy-dependent particle showers generated by incoming $\gamma $-rays. An iterative Bayesian algorithm, based on a calorimeter response matrix built from GEANT4 simulations, reconstructs TBS and bremsstrahlung contributions for each shot, as PM and electron parameters vary. ~The method should be widely applicable to plasma-accelerator-based radiation with MeV photon energies.