Principle of a correction of the long-range beam-beam effect in LHC using electromagnetic lenses

Due to the small bunch spacing, the beams in LHC collide not only in the four experimental points but experience more than one hundred 'near-misses'. They occur on either side of the collision points in places where the beam separation is in the range of 7 to 13 sigma. These so-called 'long-range'interactions are more and more recognized to be a drastic mechanism leading to beam blow-up or beam loss even-though the tunes of the particles are under control. We show in this note that, contrary to the head-on-beam interaction, a simple non linear model of the long-range interactions can be devised. This model suggests a rather simple correction principle by electromagnetic lenses, basically a wire, which correct with a good accuracy simultaneously the linear and non-linear perturbations. The correction of the average perturbation over all the bunches seems not demanding. An exact correction of the so-called PACMAN bunches may be done at a frequency an order of magnitude lower than the bunch frequency and is being evaluated.