Long-range beam-beam interactions

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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!

Answers and Replies

mfb
Mentor
Electromagnetic forces, yes.

A smaller beam size at the collision point corresponds to a larger angular spread at the same emittance - and therefore a larger beam size once you are away from the interaction point. The bunch spacing in the LHC is 25 ns = 7.5 m, the next bunch crossing (where the beams should be well separated) is 3.25 m away - still well inside the detectors.

Electromagnetic forces, yes.

A smaller beam size at the collision point corresponds to a larger angular spread at the same emittance - and therefore a larger beam size once you are away from the interaction point. The bunch spacing in the LHC is 25 ns = 7.5 m, the next bunch crossing (where the beams should be well separated) is 3.25 m away - still well inside the detectors.
Thank you for your reply. I am not really sure I understand. By Gauss law, the electric field outside the beam (which is mainly a cylinder) should be the same no matter what the radius (width) of the beam is. Also what do you mean by angular spread?

mfb
Mentor
The forces are not the same across the beam - that is bad, and it is more prominent if the beams are wider. You can even get collisions from the overlap.
Also what do you mean by angular spread?
Their flight direction has a broader distribution.

The forces are not the same across the beam - that is bad, and it is more prominent if the beams are wider. You can even get collisions from the overlap.Their flight direction has a broader distribution.
You said "it is more prominent if the beams are wider". I agree with this and this is what I thought, too. But for HL-LHC the beam width will be reduced. Yet, they have to increase the crossing angle. Why increase the crossing angle if the beam width is reduced, hence the effects of long range correlation are smaller?

mfb
Mentor
But for HL-LHC the beam width will be reduced.
See post 2: At the interaction point the beam will be narrower, but outside it will be wider.