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The first measurements of the Fourier coefficients ($V_{n\Delta}$) of theazimuthal distributions of charged hadrons emitted from photon-proton($\gamma$p) interactions at the LHC are presented. The data are extracted from68.8 nb$^{-1}$ of ultra-peripheral proton-lead (pPb) collisions at$\sqrt{s_\mathrm{NN}}$ = 8.16 TeV using the CMS detector. The high energy leadions produce a flux of photons that can interact with the oncoming proton. This$\gamma$p system provides a set of unique initial conditions with multiplicitylower than in photon-lead collisions but comparable to recent electron-positronand electron-proton data. The $V_{n\Delta}$ coefficients are presented inranges of event multiplicity and transverse momentum ($p_\mathrm{T}$) and arecompared to corresponding hadronic minimum bias pPb results. For a givenmultiplicity range, the mean $p_\mathrm{T}$ of charged particles is smaller in$\gamma$p than in pPb collisions. For both the $\gamma$p and pPb samples,$V_{1\Delta}$ is negative, $V_{2\Delta}$ is positive, and $V_{3\Delta}$consistent with 0. For each multiplicity and $p_\mathrm{T}$ range,$V_{2\Delta}$ is larger for $\gamma$p events. The $\gamma$p data are consistentwith model predictions that have no collective effects.

Two-particle azimuthal correlations in $\gamma$p interactions using pPb collisions at $\sqrt{s_\mathrm{NN}}$ = 8.16 TeV