A.Smirnov, A.Sidorin, D.Krestnikov Effective Luminosity Simulation for PANDA Experiment at FAIR A.Smirnov, A.Sidorin, D.Krestnikov (JINR, Dubna, Russia)

Luminosity of PANDA experiment (high-luminosity mode) Pbar production / loss rate, s-1 1·107 Cross-section of p - pbar, barn 0,05 Maximum luminosity, cm-2 s-1 2·1032 Hydrogen density, Atom/cm3 4,26·1022 Pellet size (diameter), mm 0,028 Pellet flux radius, mm 1,25 Distance between pellets, mm 5 Effective target density, cm-2 4·1015 Revolution period, sec 2·10-6 Antiproton number 1·1011 Mean luminosity, cm-2 s-1

Maximum achievable luminosity =107/5·10-26 = 2·1032 cm-2 s-1 limit for mean luminosity From the other hand limitation for antiproton number life > 104 s N ~ 1011  ~ 4·1015 cm-2

Pellet target  = <>thickness Frozen hydrogen density,  Atoms/cm3 4.261022 The pellet radius, rp m 15 The pellet flux radius, rf mm 1.5 Mean distance between pellets, <h> 5 Mean target density <> 1.71016 Mean distance between pellets Flux radius Pellet diameter  = <>thickness

Areal density for Gaussian beam (pellet is in the beam centre) Peak/mean Effective density  in cm  = 1 mm,  = 4·1015 cm-2, Peak/mean = 2.5

Physical models of Internal target Longitudinal degree of freedom Gaussian model Real (Urban) model ; ; n1, n2 – number of excitation events to different atomic energy levels n3 – number of ionization events x – uniform random number Eloss – mean energy loss, x – Gaussian random Estr – energy fluctuations (straggling) N N DP/P0 DP/P0 DP/P0+Estr DP/P DP/P Eloss Eloss

Transverse degree of freedom Gaussian model Real (plural) model q – rms scattering angle x – Gaussian random numbers c – screening angle N – number of scattering events x – uniform random numbers target target qstr

Average luminosity calculation with BETACOOL code x s Pellet flux for each model particle Number of events: 1) Integration over betatron oscillation 2) Integration over flux width 3) Number of turns per integration step Number of events for model particle Particle probability distribution Realistic models of interaction with pellet Urban + plural scattering

Parameters of COSY experiment WASA@COSY experiment Deuterium beam Momentum, GeV/c 1.2 Energy, MeV/u 177 Particle number 2×1010 Horizontal emittance,  mm mrad 1 Vertical emittance 0.5 Initial momentum spread 2×10-4 Deuterium target Pellet radius, mm 15 Pellet flux radius, mm 2.5 Mean distance between pellets, mm 10 Deuterium density, atom/cm-3 6×1022 COSY Circumference, m 183.4728 Momentum slip factor,  0.533 Horizontal acceptance,  m rad 2.2E-5 Vertical acceptance,  m rad 1E-5 Acceptance on momentum deviation ±1.2×10-3 For benchmarking BETACOOL code data from COSY experiment (June 08 run) was used WASA @ COSY Parameters of COSY experiment

Experiments without barrier bucket h = 8 mm d = 0.03 mm The beam momentum spread can be calculated from measured frequency spread

Signals from detectors Green and yellow lines are signals from pellet counter Black line is number of particles Other colour lines are signals from different detectors Simulation of particle number on time Simulation of long scale luminosity on time

Designed parameters for PANDA (high-luminosity mode) Momentum, GeV/c 9 RMS momentum spread 1·10-4 Transverse emittance (RMS normalized) 0,4 Average luminosity, cm-2 s-1 2·1032 Detector limit, cm-2 s-1 3·1032 Effective target density, cm-2 4·1015 Pellet velocity, m/s 60 Pellet flux radius, mm 1,25 Pellet size (diameter), µm 28 Distance between pellets, mm 5

Effective luminosity calculation Pellet distribution Pellet distribution Ion beam profile

Short scale luminosity variations Experiment h = 8 mm d = 0.03 mm Simulation h = 0.2 mm d = 0.01 mm

Two variants of detector limit Top cut y Average luminosity Average luminosity Full cut y Effective luminosity x

Effective to average luminosity ratio for different detector limit (high-luminosity mode) Top cut Full cut

Effective to average luminosity ratio for different detector limit (high-resolution mode) Top cut Full cut

Conclusions In the case of high-resolution mode if the detector limit is much higher than average luminosity and effective luminosity equals average one. In the case of high-luminosity mode the effective luminosity is very sensitive to the pellet size. For designed pellet size of 28 µm and detector limit 50% over average luminosity of 2·1032 cm-2 s-1 - with top cut regime the effective luminosity is about 50% of average one - with full cut regime – less than 20%