Transcript Document

Simulation of Luminosity Variation
in Experiments with a Pellet Target
A.Smirnov, A.Sidorin
(JINR, Dubna, Russia)
1
Contents
1. Luminosity. Ring, beam and target parameters
2. Luminosity variation in experiment with a pellet target
3. Beam heating and cooling
4. Stabilization of the beam emittance: tilt of the electron beam
5. Compensation of ionization energy loss: barrier RF bucket
6. The processes to be simulated
7. Short-term luminosity variation
8. Detector limitations and effective luminosity
2
Maximum achievable luminosity
The antiproton loss rate in the ring
dN
dN
dN

  stor
dt reaction dt other loss
dt production
If the antiproton storage efficiency stor is about 100%
L
 dN

dN
dN
/  

 /
dt reaction
dt
dt
production
other
loss


Upper limit of the mean luminosity
L
dN
/
dt production
Experiment with an Internal target
L  N    f rev
N 
dN
1

dt production   f rev
limitation for antiproton number
dN
dN
N


dt reaction dt other loss  life

1
f rev life
N
dN
  life
dt reaction
Choice of the target type
3
Antiproton life-time in the ring
1. Single scattering on acceptance angle
This process does not limit the target density if
2
 rp  1
 ss  4  2  2  
    acc
2
r


1
p
2
 acc
 4  2 
~ 610-6
   
or A > 40 mmmrad
2. Ionization energy loss
The energy loss are distributed according to
g E  
E max 
Emax  I I
Emax
1
E2
At E = 8 GeV, Emax = 42 MeV
2me c 2  2  2
m m 
1  2 e   e 
M M 
2
p
 1  102
p max
4
Ring acceptance on the momentum deviation
1. 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
5
FAIR:
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
N  4  1029 cm2
life > 104 s
N  1011
  4·1015 cm-2
Pellet target
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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
Hydrogen density, Atom/cm3
2·1032
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
2·1032
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Pellet target
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>
mm
5
Mean target density <>
Atoms/cm3
1.71016
4 3
rp
  32 
r f h
 = <>thickness
Flux radius
Mean distance
between pellets
Pellet
diameter
8
 eff ,mean 

Areal density for Gaussian beam
2  x
rf

rf
 x2
2 r  x exp 
2
2

x

2
f
2

dx

rp2  x 2
2
 x2
y
 eff ,max 
2 r  x  y exp 

2
2



2 x y  rp  r 2  x 2
2

2

x
y

p
(pellet is in the beam centre)

rp
2
p
2
1 1 0
2
16
7.999
16
11 0

dydx


8
8 1 0
15
6
Peak/mean
Effective density
6 1 0
15
R atio(   )
 ( )
4
4 1 0
15
2
2 1 0
15
0
0
1.067
0
0 .0 5
4
51 0
0 .1

0 .1 5
0 .2
0 .2
 in cm
0
0
0.05
0.05
0.1

0.15
0.2
0.2
 = 1 mm,  = 4·1015 cm-2, Peak/mean = 2.5
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The effects leading to the beam heating
1. Scattering on residual gas atoms is negligible if
Cnrg  
nrg < 109 cm-3
2. Longitudinal heating due to scattering in the target
1
 long

 p2
 p2 Trev
2

2
p
2
   E str

 
2
   1 E
E
2
str
 2 
 E max 1  
2

 MeV cm2  Z P2 ZT
  0.1535
eff
 2
g

A


T
High resolution mode (HR) p ~ 10-4
1
 cool ,||

1
 t arg et,||
 2  1.55s 1
10
The effects leading to the beam heating
3. Transverse heating due to scattering in the target
1
 t arget,
2
 * rms

2Trev
rms ~ 5 108
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)
Ti ,  m c  
2
2
2

 Ti ,||  m c2  2 p2

1
 IBS
 p 
     ~ 1010   m  rad
  
2
~ 50 s 1
It is necessary to stabilize the beam emittance at some reasonable level
At
 ~ 107   m  rad,  *  10 m IBS is negligible
11
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.
12
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
13
Compensation of ionization energy loss:
barrier RF bucket
Compensation of mean energy loss by RF decreases sufficiently
requirements to the cooling power
VRF
V0
t
T2
T1
p/p
1
2
s-s0
V0T1 
T0 cp0 
2Ze
 A2,max
max ~ 10-3
V ~ 5 kV
14
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
15
Physical models of Internal target
Longitudinal degree of freedom
Gaussian model
2
2
2
 p 
   Eloss

  

;
2
p


1
E


 loss 
2
Real (Urban) model
2
2
 p 
   E str

  

2
p


1
 E

 str 
 p 
 p 
 p 

  
    

p
p
p



 str

 loss
Eloss – mean energy loss,  – Gaussian random
Estr – energy fluctuations (straggling)
n3
I
i 1 1  gi
E  n1I1  n2 I 2  
E
max
; g  E I
max
n1, n2 – number of excitation events to
different atomic energy levels
n3
– number of ionization events

– uniform random number
N
N
P/P0
P/P0
P/P0+Estr
Eloss
P/P
Eloss
P/P
16
Transverse degree of freedom
Gaussian model

x 
 1
2
2
str
Real (plural) model
  1


xi   
 1  cos2 
i 

  1 
N
y 

 2
2
2
str
  1


yi   
 1  sin 2 
i 

  1 
N
 – rms scattering angle
 – Gaussian random numbers
target
 – screening angle
N – number of scattering events
 – uniform random numbers
target
str
17
Average luminosity calculation
with BETACOOL code
s
for each model particle
Number of events:
1) Integration over betatron
oscillation
2) Integration over flux width
3) Number of turns per integration
step
Pellet flux
Number of events for model
particle
x
Particle
probability
distribution
Realistic models of interaction
with pellet
Urban + plural scattering
18
WASA@COSY experiment
Deuterium beam
Momentum, GeV/c
1.2
Energy, MeV/u
177
Particle number
2×1010
Horizontal emittance,  mm mrad
Vertical emittance
For benchmarking BETACOOL
code data from COSY experiment
(2008 and 2009 runs) was used
1
0.5
Initial momentum spread
2×10-4
Deuterium target
Pellet radius, m
15
Pellet flux radius, mm
2.5
Mean distance between pellets,
mm
10
Deuterium density, atom/cm-3
6×1022
WASA @ COSY
COSY
Circumference, m
183.4728
Momentum slip factor, 
0.533
Horizontal acceptance,  m rad
2.2E-5
Vertical acceptance,  m rad
Acceptance on momentum
deviation
1E-5
±1.2×10-3
Parameters of
COSY
experiment
19
Experiments without
barrier bucket
h = 8 mm
d = 0.03 mm
p 1  f

p  nf0
The beam momentum spread
can be calculated from
measured frequency spread
20
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
0.0003
Friction force, eV/cm
0.00025
0.0002
0.00015
0.0001
0.00005
0
0.0E+00 2.0E+06 4.0E+06 6.0E+06 8.0E+06 1.0E+07 1.2E+07 1.4E+07 1.6E+07
Proton velocity, cm/s
Possibility to work with Barrier Buckets
21
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
22
Designed parameters for PANDA
(high-luminosity mode)
Momentum, GeV/c
RMS momentum spread
Transverse emittance (RMS normalized)
9
1·10-4
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
Pellet flux radius, mm
60
1,25
Pellet size (diameter), µm
28
Distance between pellets, mm
5
23
Effective luminosity calculation
Pellet distribution
Flux radius
Pellet
distribution
Mean distance
between pellets
Pellet
diameter
Ion beam profile
24
Short scale luminosity variations
Experiment
h = 8 mm
d = 0.03 mm
Simulation
h = 0.2 mm
d = 0.01 mm
25
Two variants of detector limit
Detector limit
Top cut
y
Average luminosity
Average luminosity
Full cut
y
Effective luminosity
x
26
Effective to average luminosity ratio for different
detector limit (high-luminosity mode)
Top cut
1.2
2.00E+32
.
1.2
1
3.00E+32
effective luminosity
effective luminosity
.
Full cut
1
5.00E+32
0.8
1.00E+33
0.6
0.4
0.2
0
10
15
20
pellet size
25
30
2.00E+32
3.00E+32
5.00E+32
0.8
1.00E+33
0.6
0.4
0.2
0
10
15
20
25
30
pellet size
27
Effective to average luminosity ratio for different
detector limit (high-resolution mode)
Top cut
.
1.2
2.00E+31
3.00E+31
5.00E+31
1.00E+32
2.00E+32
1
0.8
0.6
0.4
0.2
0
10
15
20
pellet size
25
30
1.2
effective luminosity
effective luminosity
.
Full cut
2.00E+31
3.00E+31
5.00E+31
1.00E+32
2.00E+32
1
0.8
0.6
0.4
0.2
0
10
15
20
25
30
pellet size
28
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
29