LG, CEDAR Optics Simulation 1 Generate rays according to momentum, mass, n-1, Pressure Uniform over length of counter, uniform over in Å Use fitted -dependence of n-1 for quartz, Helium, Hydrogen Track photons through all optics elements Apply cut at diaphragm Project ray through quartz window onto PM plane Possibility to analyse per ray or to simulate events formed by a number of rays, assuming  40 accepted photo-electrons from  250 photons produced All parameters are defined in data cards – easy to adapt

LG, CEDAR Optics Simulation 2

LG, CEDAR Optics Simulation 3 [A]QuartzHeliumHydrogen Refractive index at 20 o C, 1 atm

LG, CEDAR Optics Simulation 4 Some validations for CEDAR-N SituationR diaphr  diaphr Spot PM Monochromatic pencil beam K x 24 mm Monochromatic pencil beam  Monochromatic pencil beam protons Beam spot 10 mm  in each plane Beam divergence 0.1 mrad in each plane x24 mm Momentum spread 1% x24 mm ‘Nominal beam’ (1%, 0.1 mrad, 10 mm) x24 mm Cedar-N, bar of Helium, 75 GeV/c, diaphragm 10 mm PM plane at Z = 706 mm, diaphragm at 1251 mm, quartz window at 851 mm Monochromatic pencil beam K x 24 mm ‘Nominal beam’ (1%, 0.1 mrad, 10 mm) x24 mm For Hydrogen at 2.61 bar:

LG, CEDAR Optics Simulation 5 3 mm Ring at correct position  -K separation as expected:

LG, CEDAR Optics Simulation 6 8 Condensors “focus” the photons on the PM’s Simulation allows to calculate the image size and to optimise location of the photon detectors

LG, CEDAR Optics Simulation 7  [rad] R [mm] Same plot in (R,  ) coordinates

LG, CEDAR Optics Simulation 8 Event analysis for standard CEDAR Generate randomly 60 photoelectrons (for ‘nominal beam’) Count number of 6-,7- and 8-fold coincidences Derive from that an efficiency: Coincidence10 mm5 mm2 mm1 mm 6-fold fold fold May need some fine-tuning of # photo-electrons, but a-priori not completely unreasonable

LG, CEDAR Optics Simulation 9 Next steps Implement and test Cedar-W with N2 gas Test new algorithms with different light detectors Need to introduce realistic frequency spectrum? Optimise location of light detectors