Indirect self-modulation instability measurement concept for the AWAKE proton beam

AWAKE, the Advanced Proton-Driven Plasma Wakefield Acceleration Experiment, is a proof-of-principle R&D experiment at CERN using a 400GeV/c proton beam from the CERN SPS (longitudinal beam size σz=12cm) which will be sent into a 10m long plasma section with a nominal density of ≈7×1014atoms/cm3 (plasma wavelength λp=1.2mm). In this paper we show that by measuring the time integrated transverse profile of the proton bunch at two locations downstream of the AWAKE plasma, information about the occurrence of the self-modulation instability (SMI) can be inferred. In particular we show that measuring defocused protons with an angle of 1mrad corresponds to having electric fields in the order of GV/m and fully developed self-modulation of the proton bunch. Additionally, by measuring the defocused beam edge of the self-modulated bunch, information about the growth rate of the instability can be extracted. If hosing instability occurs, it could be detected by measuring a non-uniform defocused beam shape with changing radius. Using a 1mm thick Chromox scintillation screen for imaging of the self-modulated proton bunch, an edge resolution of 0.6mm and hence an SMI saturation point resolution of 1.2m can be achieved.