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v3.3.3-pre
This unit belongs to the first part of the course, which is focussed on the main equations ruling the energy and the luminosity of a particle collider, and to the derivation of the magnet specifications.
In this unit we will review the definition of luminosity, and the equation giving the luminosity as a function of the beam parameters. Moreover, we will make a summary of the main physical barriers limiting luminosity in a collider.
We then briefly discuss the equations that are related to the size and to the field in experimental magnets. We then explain for the experimental magnets is more convenient to have large sizes and smaller field. When the bunch spacing is smaller than the longitudinal size of the experiment, one has to open a crossing angle to avoid parasitic collisions. We derive the main equations for the crossing angle, and the impact on the reduction of luminosity via the geometric reduction factor.
We then discuss the details of the optics around the interaction point, focussing on the case of a "quadrupole first" with a triplet of quadrupoles as in the LHC. We will derive (1) the relation between the magnet aperture and the size of the beam in the interaction point and (2) the relation between the triplet integrated gradient and the beam energy and the experiment size.
We conclude by applying the equations to the case of LHC, to HL-LHC, and discussing the cases of a 100 TeV collider with 16 T magnets (FCC).