Effect of Proton Bunch Parameter Variation on AWAKE

In AWAKE, long proton bunches propagate through a plasma, generating wakefields through the self-modulation instability (SMI). The phase velocity of these wakefields changes during the first 4 m of propagation and growth of the SMI, after which it stabilizes at the proton bunch velocity. This means that the ideal injection point for electrons to be accelerated is after 4 m into the plasma. Using the PIC code OSIRIS, we study how small changes in the initial proton bunch parameters (such as charge, radial and longitudinal bunch length, etc) to be expected in the experiment affect the phase velocity of the wakefields, primarily by looking at the difference in the phase of the wakefields at the point of injection (along the bunch and along the plasma) when changing these parameters by a small amount (±5%). We also look for the region of optimal acceleration/focusing for electron injection. Ultimately, it is found that small changes in the initial proton bunch parameters are not expected to significantly impact electron injection experiments in the future.