1. Simulation of Luminosity Variation
in Experiments with a Pellet Target
A.Smirnov, A.Sidorin
(JINR, Dubna, Russia)

2. Contents Luminosity. Ring, beam and target parameters
Luminosity variation in experiment with a pellet target
Beam heating and cooling
Stabilization of the beam emittance: tilt of the electron beam
Compensation of ionization energy loss: barrier RF bucket
The processes to be simulated
Short-term luminosity variation
Detector limitations and effective luminosity

3. Maximum achievable luminosity
The antiproton loss rate in the ring
If the antiproton storage efficiency stor is about 100%
Upper limit of the mean luminosity
Experiment with an Internal target
limitation for antiproton number
Choice of the target type

4. Antiproton life-time in the ring
1. Single scattering on acceptance angle
This process does not limit the target density if
~ 610-6
or A > 40 mmmrad
2. Ionization energy loss
The energy loss are distributed according to
At E = 8 GeV, Emax = 42 MeV

5. Ring acceptance on the momentum deviation
Effective cooling of the antiprotons
Stochastic cooling time in the first approximation
does not depend on the deviation
Electron cooling is effective at p/p < 10-3
2. Mean energy loss compensation using RF
At reasonable RF amplitude the longitudinal acceptance is
p/p ~ 10-3

6. FAIR: Pellet target L  107/5·10-26 = 2·1032 cm-2 s-1 life > 104 s
Expected antiproton production rate is about 107 1/s
The reaction cross-section is about 50 mbarn
The limit for mean luminosity:
L  107/5·10-26 = 2·1032 cm-2 s-1
High Energy Storage Ring:
The ring circumference is about 574 m, revolution period is 2 s
life > 104 s
N  1011
  4·1015 cm-2
Pellet target

7. Luminosity of PANDA experiment (high-luminosity mode)
Pbar production / loss rate, s-1
1·107
Cross-section of p - pbar, barn
0,05
Mean 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
Peak luminosity, cm-2 s-1

8. 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

9. 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

10. The effects leading to the beam heating
1. Scattering on residual gas atoms is negligible if
nrg < 109 cm-3
2. Longitudinal heating due to scattering in the target
High resolution mode (HR) p ~ 10-4

11. The effects leading to the beam heating
3. Transverse heating due to scattering in the target
4. Intra-beam scattering
In the thermal equilibrium between longitudinal and transverse degrees
of freedom in HR (if transverse and longitudinal cooling rates are the same)
It is necessary to stabilize the beam emittance at some reasonable level At
IBS is negligible

12. Beam cooling
1. At stochastic cooling one can adjust longitudinal and transverse cooling times
independently
2. At electron cooling the cooling times have comparable values for all
degrees of freedom
D.Reistad et. al., Calculations on high-energy electron cooling in the HESR,
Proceedings of COOL 2007, Bad Kreuznach, Germany
Intentional misalignment (tilt) of the electron beam
is most attractive for stabilization of the emittance value.

13. Tilt of the electron beam
When the misalignment angle reaches
a certain threshold value the ions start to oscillate with
a certain value of betatron amplitude.
Transverse plane
Beam profiles
Simulations with BETACOOL

14. Compensation of ionization energy loss: barrier RF bucket
Compensation of mean energy loss by RF decreases sufficiently
requirements to the cooling power
VRF
p/p
s-s0 t V0 T2 T1 1 2
max ~ V ~ 5 kV

15. The processes to be simulated
1. Interaction with the pellet target based on realistic scattering models
2. Intra-beam scattering at arbitrary ion distribution
3. Stochastic cooling, taking into account nonlinearity of the force
at large amplitudes
4. Electron cooling at electron beam misalignment
5. Longitudinal motion at arbitrary shape of the RF voltage
To provide benchmarking
Simulations using independent codes (BETACOOL, MOCAC)
Comparison with experiments (ESR and COSY)
Longitudinal motion in Barrier RF buckets,
Investigation of electron cooling with electron beam misalignment,
Short term luminosity variation with the WASA pellet target

16. 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

17. 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

18. 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

19. 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 (2008 and 2009 runs) was used
COSY
Parameters of COSY experiment

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

21. Investigations of electron cooling at COSY 7-11 April 2010
New fast (~ 40 ms) Ionization Profile Monitor
Measurements of longitudinal component of the cooling force,
Investigation of chromatic instability
Possibility to work with Barrier Buckets

22. 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

23. 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

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

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

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

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

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

29. Conclusions
The choice of the target density depends on the ring acceptance. More strong limitation leading to necessity of the pellet target is RF voltage amplitude
Horizontal beam size at the target has to be stabilized at optimum value (transverse overcooling the beam leads to increase the momentum spread due to IBS and large luminosity variations)
Vertical beam size determines short-scale luminosity variation and optimum value has to be about inter pellet distance)
Current parameters of the beam and target can be optimized.
The code development has to be prolonged as well as experimental study at COSY