AWAKE is a proton-driven plasma wakefield experiment under way at CERN that recently demonstrated the successful acceleration of injected electrons . Underpinning the experiment is the fact that the long proton bunches (~6-12 cm) used to drive the wakefields undergo a self-modulation process, which in practice corresponds to a seeded instability . The resulting train of microbunches (with lengths of the order of the plasma wavelength) is able to excite the wakefields resonantly.
In this work we use particle-in-cell (PIC) simulations to study the effects of small shot-to-shot fluctuations of the initial proton bunch parameters on the amplitude and phase of the wakefields resulting from a seeded self-modulation (SSM) process . We demonstrate that the effects on the wakefield properties are small after saturation of the SSM. In particular, the phase variations correspond to much less than a quarter wakefield period, making deterministic injection of electrons (or positrons) into the accelerating and focusing phase of the wakefields in principle possible. We further use the wakefields from the simulations and a simple test electron model to estimate the same effects on the maximum final energies of electrons injected along the plasma, which are also found to be below the initial variations of $\pm$5%. Lastly, we discuss the optimal injection conditions for electrons that lead to the most energy gain.
 The AWAKE collaboration, Nature 561, 363-367 (2018)
 N. Kumar, A. Pukhov, and K. V. Lotov, Phys. Rev. Lett. 104, 255003 (2010)
 M. Moreira, J. Vieira, and P. Muggli, Phys. Rev. Accel. Beams 22, 031301 (2019)
|Working group||Laser-driven electron acceleration|