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

2. 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

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

4. 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

5. 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

6. 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
n – 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

7. 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

8. Average luminosity calculation with BETACOOL codex 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

9. 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

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

11. 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

12. 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

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

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

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

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

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

18. 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%