The AWAKE experiment at CERN  recently demonstrated the world's first acceleration of electrons in a proton-driven plasma wakefield accelerator . Such accelerators show great promise for a new generation of linear e-p colliders using GV/m accelerating fields. Effectively driving a wakefield in AWAKE requires 100-fold self-modulation of the 12 cm Super Proton Synchrotron (SPS) proton beam using a plasma-driven process which must be carefully controlled to saturation [3,4]. Previous works have modeled this process assuming cylindrical symmetry of the transverse space and momentum profiles of the proton bunch. In this work, 3D particle-in-cell simulations are used to investigate the self-modulation of non-round beams. Implications of such effects for effectively sustaining resonant wakefields are discussed.
 P. Muggli et al. (AWAKE Collaboration), Plasma Physics and Controlled Fusion, 60(1) 014046 (2017)
 M. Turner et al. (AWAKE Collaboration), Phys. Rev. Lett. 122, 054801 (2019)
 E. Adli et al. (AWAKE Collaboration), Phys. Rev. Lett. 122, 054802 (2019)
 E. Adli et al. (AWAKE Collaboration), Nature 561, 363–367 (2018)