Luminosity for q-Gaussian distribution functions in the transverse plane, for identical beams colliding head-on
-See Mathematica notebook for the solution of the luminosity integrals: Lumiqgauss.nb
-See Python script for the impact of the tails on the luminosity, for various cases, together with the validation when comparing to Gaussian luminosities: Lumi_qGaussian_cases.ipynb
The analytical luminosity calculation for q-Gaussian distribtuions (see https://arxiv.org/pdf/1806.07317.pdf) is based on:
-q-Gaussian sigmas of the distributions
-on some integrals that are functions of the parameter q of the q-Gaussian distribution
-> the 2 beams are assumed to be equal for simplicity...better if each beam is treated separately
-> needs to be improved by adding the contribution of xing
Useful links
- "Impact of Non-Gaussian Beam Profiles in the Performance of Hadron Colliders" by S.Papadopoulou: https://arxiv.org/pdf/1806.07317.pdf
- BE seminar presentation by S.Papadopoulou: https://indico.cern.ch/event/881753/attachments/1975298/3287453/BEseminar_stef.pdf
- "LUMINOSITY MEASUREMENTS AND CALCULATIONS": by K. Potter: https://cds.cern.ch/record/261063/files/p117.pdf
- "HOW GOOD IS THE R.M.S. AS A MEAS;JRE OF BEAM SIZE ? " by Hereward: http://cds.cern.ch/record/2048980/files/CERN-MPS-DL-69-15.pdf