Effect of a resonant excitation on the evolution of the beam emittance and halo population

Collimation with hollow electron beams or lenses (HEL) is currently one of the most promising concepts for active halo control in HL-LHC. In previous studies it has been shown that the halo can be efficiently removed with a hollow electron lens. Equally important as an efficient removal of the halo, is to demonstrate that the core stays unperturbed. In the case of an ideal hollow electron lens without bends, the field at the location of the beam core vanishes and the core remains unperturbed. In reality, the field at the beam core does not vanish entirely due to imperfections in the electron beam profile and the electron lens bends necessary to guide the electron in and out of the proton aperture. In particular, in the case of a pulsed operation of the electron lens the non-vanishing residual field induces noise on the proton beam. To identify the most sensitive pulsing patterns for the resonant mode and derive tolerances on the profile imperfections, a first MD was carried out of which the first results are presented in this note.