Unit 2 - Luminosity of a collider and specification of the magnets in the interaction region

<!--HTML--><p>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.&nbsp;</p> <p>In this unit we&nbsp;will review the definition of luminosity, and the equation giving the luminosity as a function of the beam parameters. Moreover, we will make&nbsp; a summary of the&nbsp;main physical barriers limiting&nbsp;luminosity.</p> <p>We then discuss the details of the optics around the interaction point, showing the principle of beam size reduction through a triplet of quadrupoles. 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 then explain for the experimental magnets is more convenient to have large sizes and smaller field.</p> <p>We conclude by applying the equations to the case of LHC, to HL-LHC, and discussing the cases of a&nbsp;&nbsp;higher energy collider in the LHC tunnel (HE LHC), and of a 100 TeV collider with 16 T magnets (FCC).</p>