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Proton beam defocusing in AWAKE: comparison of simulations and measurements

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In 2017, AWAKE demonstrated the seeded self-modulation (SSM) of a 400 GeV proton beam from the Super Proton Synchrotron at CERN. The angular distribution of the protons deflected due to SSM is a quantitative measure of the process, which agrees with simulations by the two-dimensional (axisymmetric) particle-in-cell code LCODE to about 5%. The agreement is achieved in beam population scans at two selected plasma densities and in the scan of longitudinal plasma density gradient. The agreement is reached only in the case of a wide enough simulation box (several plasma wavelengths) that is closer to experimental conditions, but requires more computational power. Therefore, particle-in-cell codes can be used to interpret the SSM physics underlying the experimental data.