Hello! I am reading about HL-LHC upgrades and they introduce ##\beta^*## which is directly related to the transverse size of the beam. Now they say that in order to increase the luminosity you need to reduce ##\beta^*##, which makes sense as a reduced volume means higher particle density so increased number of collisions, so increased luminosity. However they mention than at the interaction points, the crossing angle need to be increased, if ##\beta^*## is reduced, in order to avoid long-range beam-beam interactions. The crossing angle is the angle, at the interaction point, between the 2 pipes in which the protons go in different direction. Can someone explain to me what these long-range beam-beam interactions are (are they just electromagnetic forces between the 2 beams?) and why a reduced beam width would increase the effect of long-range beam-beam interactions. Thank you!