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In 2017, AWAKE demonstrated the seeded self-modulation (SSM) of a 400 GeVproton beam from the Super Proton Synchrotron (SPS) at CERN. The angulardistribution of the protons deflected due to SSM is a quantitative measure ofthe process, which agrees with simulations by the two-dimensional(axisymmetric) particle-in-cell code LCODE. Agreement is achieved for beampopulations between $10^{11}$ and $3 \times 10^{11}$ particles, various plasmadensity gradients ($-20 \div 20\%$) and two plasma densities ($2\times 10^{14}\text{cm}^{-3}$ and $7 \times 10^{14} \text{cm}^{-3}$). The agreement isreached only in the case of a wide enough simulation box (at least five plasmawavelengths).

Proton beam defocusing in AWAKE: comparison of simulations and measurements