  In 2017, AWAKE demonstrated the seeded self-modulation (SSM) of a 400 GeV
proton beam from the Super Proton Synchrotron (SPS) 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. Agreement is achieved for beam
populations between $10^{11}$ and $3 \times 10^{11}$ particles, various plasma
density 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 is
reached only in the case of a wide enough simulation box (at least five plasma
wavelengths).
