  We present the results of numerical simulations and experimental studies
about the effects of resonant and random excitations on proton losses,
emittances, and beam distributions in the Large Hadron Collider (LHC). In
addition to shedding light on complex nonlinear effects, these studies are
applied to the design of hollow electron lenses (HEL) for active beam halo
control. In the High-Luminosity Large Hadron Collider (HL-LHC), a considerable
amount of energy will be stored in the beam tails. To control and clean the
beam halo, the installation of two hollow electron lenses, one per beam, is
being considered. In standard electron-lens operation, a proton bunch sees the
same electron current at every revolution. Pulsed electron beam operation
(i.e., different currents for different turns) is also considered, because it
can widen the range of achievable halo removal rates. For an axially symmetric
electron beam, only protons in the halo are excited. If a residual field is
present at the location of the beam core, these particles are exposed to
time-dependent transverse kicks and to noise. We discuss the numerical
simulations and the experiments conducted in 2016 and 2017 at injection energy
in the LHC. The excitation patterns were generated by the transverse feedback
and damping system, which acted as a flexible source of dipole kicks. Proton
beam losses, emittances, and transverse distributions were recorded as a
function of excitation patterns and strengths. The resonant excitations induced
rich 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 fields
and proposals for further studies.
