1. 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

2. 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)

3. 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

4. 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.

5. Average luminosity calculationx 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

6. Parameters of COSY experiment
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
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
COSY
Parameters of COSY experiment

7. Experiments without barrier bucket
The beam momentum spread can be calculated from measured frequency spread

8. 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

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

10. Effective luminosity calculation
Pellet distribution
Pellet distribution
Ion beam profile

11. 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

12. 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.

13. 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

14. 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

15. 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

16. 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.