A Method for Obtaining 3D Charge Density Distribution of a Self-Modulated Proton Bunch

The Advanced Wakefield Experiment (AWAKE) at CERN is the first plasma wakefield accelerator experiment to use a proton bunch as driver. The long bunch undergoes seeded self-modulation (SSM) in a 10 m-long plasma. SSM transforms the bunch into a train of short micro-bunches that resonantly drive high-amplitude wakefields. We use optical transition radiation (OTR) and a streak camera to obtain time-resolved images of the bunch transverse charge density distribution in a given plane. In this paper we present a method to obtain 3D images of the bunch by scanning the OTR across the entrance slit of the streak camera. Reconstruction of the 3D distribution is possible because with seeding self-modulation is reproducible*. The 3D images allow for checking the axi-symmetry of SSM and for detecting the possible presence of the non-axi-symmetric hosing instability (HI).