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Exactly what procedures are followed to increase the luminosity of a particle collider? Say when LHC increases its luminosity, does it increase the number of protons per bunch? If yes, then how?

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Luminosity is literally the number of particles, so yes, putting in more of them increases the luminosity.

I think you are perhaps confusing the luminosity of a particular experiment with the maximum luminosity the accelerator can handle. The former is just how much stuff they put in, the later is a function of the design itself.

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