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 Nuclear and Particle Physics Nuclear and Particle Physics Help Forum Sep 24th 2018, 02:43 AM #1 Junior Member   Join Date: Sep 2018 Posts: 1 Bunch collision frequency Hey guys, so I am asked to prove that the luminosity of two colliding beams, where the bunches are described by Gaussians, is: L = f*Nb*N1*N2/(4*pi*sigma_x*sigma_y) (see eq. 16 in link: https://cds.cern.ch/record/941318/files/p361.pdf) Where f=revolution frequency (I imagine this is the time it take for a bunch to go around the synchrotron/cyclotron/device), Nb=number of bunches per beam, N1 and N2=number of particles per bunch in beam 1 and beam 2 respectively, and sigma_x and sigma_y are the variances in x and y for the Gaussian. The bunches are described by the distribution p(x,y,z)=C*exp(-x²/(2*sigma_x²)-y²/(2*sigma_y²)-z²/(2*sigma_z²)). I calculate the overlap integral and get that the luminosity in one collision is: L_collision = N1*N2/(8*pi*sigma_x*sigma_y) I am almost certain that this is correct. However, to get the total luminosity, they then multiply this by f*Nb*2 !!! Could someone explain where this comes from? In my opinion, if we were to multiply L_collision by the total number of collisions in the device, we should multiply it by f*2*Nb², or simply by Nb if we are only considering the collisions at a specific point in the device. Thanks in advance.  Tags bunch, collision, frequency Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post hyungjko Waves and Sound 1 Feb 7th 2013 12:33 PM christina Kinematics and Dynamics 4 Nov 22nd 2009 10:35 AM porterp74 Waves and Sound 2 Jul 6th 2009 04:14 PM ramiro Advanced Mechanics 1 Mar 15th 2009 06:43 PM dsptl Periodic and Circular Motion 1 Nov 9th 2008 01:56 PM