Simulation study of betatron radiation in AWAKE Run 2 experiment

The spectroscopy of betatron radiation from the focusing plasma column can work as a powerful non-invasive beam diagnostic method for plasma wakefield acceleration experiments such as the AWAKE. In this paper, the effects of radial size mismatch and off-axis injection on the beam dynamics, as well as the spectral features of the betatron radiation emitted by the witness electron bunch in the quasi-linear proton-driven plasma wakefield are studied. It is shown that the evolution of the critical betatron photon energy and the overall photon angular distribution can effectively reveal the initial injection conditions of the witness electron bunch. The possibility of using this method for the diagnostics of the seed electron bunch in the proton self-modulation stage of AWAKE Run 2 is also discussed.