This paper presents a study of the possible ordering of charged hadrons in the azimuthal angle relative to the beam axis in high-energy proton-proton collisions at the Large Hadron Collider (LHC). A spectral analysis of correlations between longitudinal and transverse components of the momentum of the charged hadrons, driven by the search for phenomena related to the structure of the QCD field, is performed. Data were recorded with the ATLAS detector at center-of-mass energies of root s = 900 GeV and root s = 7 TeV. The correlations measured in a kinematic region dominated by low-p(T) particles are not well described by conventional models of hadron production. The measured spectra show features consistent with the fragmentation of a QCD string represented by a helixlike ordered gluon chain.