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We present the results of numerical simulations and experimental studiesabout the effects of resonant and random excitations on proton losses,emittances, and beam distributions in the Large Hadron Collider (LHC). Inaddition to shedding light on complex nonlinear effects, these studies areapplied to the design of hollow electron lenses (HEL) for active beam halocontrol. In the High-Luminosity Large Hadron Collider (HL-LHC), a considerableamount of energy will be stored in the beam tails. To control and clean thebeam halo, the installation of two hollow electron lenses, one per beam, isbeing considered. In standard electron-lens operation, a proton bunch sees thesame electron current at every revolution. Pulsed electron beam operation(i.e., different currents for different turns) is also considered, because itcan widen the range of achievable halo removal rates. For an axially symmetricelectron beam, only protons in the halo are excited. If a residual field ispresent at the location of the beam core, these particles are exposed totime-dependent transverse kicks and to noise. We discuss the numericalsimulations and the experiments conducted in 2016 and 2017 at injection energyin the LHC. The excitation patterns were generated by the transverse feedbackand damping system, which acted as a flexible source of dipole kicks. Protonbeam losses, emittances, and transverse distributions were recorded as afunction of excitation patterns and strengths. The resonant excitations inducedrich dynamical effects and nontrivial changes of the beam distributions, which,to our knowledge, have not previously been observed and studied in this detail.We conclude with a discussion of the tolerable and achievable residual fieldsand proposals for further studies.

Resonant and random excitations on the proton beam in the Large Hadron Collider for active halo control with pulsed hollow electron lenses