Effective luminosity simulation for PANDA experiment A.Smirnov, A.Sidorin, D.Krestnikov, R.Pivin Joint Institute for Nuclear Research 141980, Dubna, Russia PANDA Meeting, ITEP, October 22, 2008

Luminosity of PANDA experiment (high-luminosity mode) Pbar production / annihilation rate, s^-1 (r) 1e7 Cross-section of p - pbar, barn (b) 0,05 Maximum luminosity, cm^-2 s^-1 (L_m = r / b) 2e32 Hydrogen density, cm^-3 4,26e22 Pellet size (diameter), mm 0,028 Pellet flux radius, mm 1,25 Distance between pellets, mm 5 Effective target density, cm^-2 (n) 4e15 Revolution period, sec (T) 2e-6 Proton number (N) 1e11 Average luminosity, cm^-2 s^-1 (L_a = N * n / T)

BETACOOL application over the world (since 1995) TSL, Uppsala MSL, Stockholm JINR, Dubna ITEP, Moscow ITMP, Sarov BINP, Novosibirsk FZJ, Jülich GSI, Darmstadt Erlangen Univ. MPI, Heidelberg CERN, Geneva München Univ. Fermilab, Batavia BNL, Upton Tech-X, Boulder RIKEN, Wako NIRS, Chiba Kyoto Univ. Hiroshima Univ. Beijing Univ. IMP, Lanzhou

New algorithm is being developed BETACOOL overview General goal of the BETACOOL program is to simulate long term processes (in comparison with the ion revolution period) leading to variation of the ion distribution function in 6 dimensional phase space. New algorithm is being developed It calculates the luminosity variation via real pellet distribution and the beam profiles SO In the case of pellet target simulation the existing algorithm is based on assumption that during one step of the integration a large number of the pellets cross the beam.

Average luminosity calculation x s Pellet flux Number of events: 1) Integration over betatron oscillation 2) Integration over flux width 3) Number of turns per integration step Real models of interaction with pellet Number of events for model particle Particle probability distribution

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 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

Vacuum conditions of COSY experiment Pellet target area Vacuum conditions inside COSY storage ring are not constant because of the pellet collector

Effective luminosity calculation Pellet distribution Pellet distribution Ion beam profile

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

Effective luminosity calculation Short time-scale luminosity (signals from each pellet) Average luminosity Detector limit Long time-scale luminosity (average luminosity) Average luminosity Effective luminosity Average luminosity is the total integral from pellet signals. Detector limit is defined by the detector design (here average luminosity corresponds to 2e32 and detector limit is chosen 3e32 cm^-2 s^-1) Effective luminosity is the integral of pellet signals below the detector limit.

Designed parameters for PANDA (high-luminosity mode) Momentum, GeV/c 9 RMS momentum spread 1e-4 Transverse emittance (RMS normalized) 0,4 Average luminosity, cm^-2 s^-1 2e32 Detector limit, cm-2 s^-1 3e32 Effective target density, cm^-2 4e15 Pellet velocity, m/s 60 Pellet flux radius, mm 1,25 Pellet size (diameter), mkm 28 Distance between pellets, mm 5

Detector limit, cm^-2 s^-1 Effective to average luminosity ratio for different detector limit (high-luminosity mode) Inerpellet distance, mm  Pellet size (diameter), mkm 2,00E+32 3,00E+32 5,00E+32 1,00E+33 0,25 10 0,908074 1 2 20 7,73E-01 0,943172 5 28 4,29E-01 5,56E-01 7,32E-01 9,70E-01 Detector limit, cm^-2 s^-1 Designed parameters

Detector limit, cm^-2 s^-1 Effective to average luminosity ratio for different detector limit (high-resolution mode) Inerpellet distance, mm Pellet size (diameter), mkm Detector limit, cm^-2 s^-1 2,00E+31 3,00E+31 5,00E+31 1,00E+32 2,00E+32 0,25 10 0,765097 0,916092 1,006607 0,998266 1,001888 2 20 3,79E-01 0,561785 0,768713 1 0,99372 5 28 1,89E-01 2,63E-01 3,86E-01 6,32E-01 9,79E-01

Summary Effective luminosity is very sensitive on the pellet size in the case of high-luminosity mode. For designed pellet size 28 mkm and detector limit 50% over average luminosity 2e32 cm^-2 s^-1 the effective luminosity is about 50% of average one. To avoid this problem the pellet size should be less than 20 mkm with distance between pellets 2 mm. Insignificance increasing of the detector limit does not bring large improvement. In the case of high-resolution mode the detector limit is much higher than average luminosity and effective luminosity equal average one.