Direct Measurement of Intra-beam
Scattering in Atomic Beam Sources
Z.Ye for the HERMES Target Group
DESY
16th International Spin Physics Symposium, SPIN 2004,
October 2004; ICTP, Trieste, Italy
 Introduction
 Measurement Principle
 Result from the HERMES-ABS
 Summary
Introduction
 Discrepancies between measured intensity and expected

HERMES ABS: 20% less than expected, Rest Gas Attenuation accounted
N.Koch, Ph.D Thesis, Univ. Erlägen-Nürnberg (1999)
Introduction
 Discrepancies between measured intensity and expected

HERMES ABS: 20% less than expected, Rest Gas Attenuation accounted

VEPP-3 ABS: 40% less than expected, IBS estimated ~20%
M.V.Dyug et. al, NIM A 495 (2002) 8-19
Introduction
 Discrepancies between measured intensity and expected

HERMES ABS: 20% less than expected, Rest Gas Attenuation accounted

VEPP-3 ABS: 40% less than expected, IBS estimated ~20%
 IBS could be the candidate to explain these discrepancies.
 However no direct measurement has been provided yet.
 Difficult to measure by detecting the scattered atoms
Introduction
 Discrepancies between measured intensity and expected

HERMES ABS: 20% less than expected, Rest Gas Attenuation accounted

VEPP-3 ABS: 40% less than expected, IBS estimated ~20%
 IBS could be the candidate to explain these discrepancies.
 However no direct measurement has been provided yet.
 Difficult to measure by detecting the scattered atoms.
 Using a set of high frequency transitions between the sextupole
magnets of the ABS, the IBS effect can be measured directly.
How to measure IBS
Intra-Beam Scattering (IBS) : Particles with different velocities in the
beam scatter on each other and get lost
How to measure IBS
Intra-Beam Scattering (IBS) : Particles with different velocities in the
beam scatter on each other and get lost
 The relative loss of density
d  due to IBS in a parallel beam is
proportional to beam density  , traveled distance dz , scattering
cross-section d , velocity spread  and reverse of the square
of mean velocity  2
d
  
  
 dz
2


.
How to measure IBS
Intra-Beam Scattering (IBS) : Particles with different velocities in the
beam scatter on each other and get lost
 The relative loss of density
d  due to IBS in a parallel beam is
proportional to beam density  , traveled distance dz , scattering
cross-section d , velocity spread  and reverse of the square
of mean velocity  2
 Varying the beam density while keeping the other parameters of the beam
unchanged, the IBS effect can be varied and measured
I1  I 0  1   IBS 
I2 
I0
2
  
 1  IBS 
2 

I3 
I0
2
  
 1  IBS 
2 

How to measure IBS
Intra-Beam Scattering (IBS) : Particles with different velocities in the
beam scatter on each other and get lost
 The relative loss of density
d  due to IBS in a parallel beam is
proportional to beam density  , traveled distance dz , scattering
cross-section d , velocity spread  and reverse of the square
of mean velocity  2
 Varying the beam density while keeping the other parameters of the beam
unchanged, the IBS effect can be varied and measured
I1  I 0  1   IBS 
I2 
I0
2
  
 1  IBS 
2 

I 2  I 3  I1
 IBS

I1
21   IBS 
I3 
I0
2
  
 1  IBS 
2 

Measuring IBS in an ABS
Using the HFTs between the sextupoles, certain fractions of the atoms in
the beam can be removed without affecting the other beam parameters
Measuring IBS in an ABS
Using the HFTs between the sextupoles, certain fractions of the atoms in
the beam can be removed without affecting the other beam parameters
Only the effect in the 2nd part of the ABS ( from the 2nd sextupole
subsystem to the target cell ) is measured.
Measuring IBS in the HERMES ABS
4 ABS injection modes using SFT2-4/WFT1-3 between the sextupoles
HFT empl.
states inj.
-
1 2
SFT2-4
1
WFT1-3
2
SFT2-4, WFT1-3
-
Measuring IBS in the HERMES ABS
4 ABS injection modes using SFT2-4/WFT1-3 between the sextupoles
 ABS intensity:
HFT empl.
states inj.
-
1 2
SFT2-4
1
WFT1-3
2
SFT2-4, WFT1-3
-
(1)
(1)
( 2)
( 2)
I  I 0  1   RGA  1   IBS   1   RGA  1   IBS  
 
ij
ij
(1 / 2 )
st
nd
 RGA
/ IBS : intensity loss due to RGA (IBS) in the 1 (2 ) part of the ABS.
 ij
 ji
: transition efficiency of an atom in state j become as an atom in
state i after the HFTs between the sextupoles.
: transmission probability of an atom through the ABS which is in
state j before and in state i after the HFTs between sextupoles
  ji
Measuring IBS in the HERMES ABS
4 ABS injection modes using SFT2-4/WFT1-3 between the sextupoles
HFT empl.
states inj.
-
1 2
SFT2-4
1
WFT1-3
2
SFT2-4, WFT1-3
-
 ABS intensity:
(1)
(1)
( 2)
( 2)
I  I 0  1   RGA  1   IBS   1   RGA  1   IBS  
 
ij
  ij
ij
 Nucleon magnetic moment is much smaller than electron magnetic moment:
( 2)
( 2)
( 2)
 IBS
 x  2 IBS
 2 IBS
,1  2
,1
,2
 Injection mode with ideally no atoms injected:
( 2)
 IBS
, no state  0
Measuring IBS in the HERMES ABS
4 ABS injection modes using SFT2-4/WFT1-3 between the sextupoles
I I
1
2
I
I
12
12
HFT empl.
states inj.
-
1 2
SFT2-4
1
WFT1-3
2
SFT2-4, WFT1-3
-
 I no state

x
 
21  x 
Measuring IBS in the HERMES ABS
4 ABS injection modes using SFT2-4/WFT1-3 between the sextupoles
I I
1
2
I
I
12
12
HFT empl.
states inj.
-
1 2
SFT2-4
1
WFT1-3
2
SFT2-4, WFT1-3
-
 I no state

x

21  x 
x I no state
 12
2 I

Measuring IBS in the HERMES ABS
4 ABS injection modes using SFT2-4/WFT1-3 between the sextupoles
I I
1
2
I
I
12
12
HFT empl.
states inj.
-
1 2
SFT2-4
1
WFT1-3
2
SFT2-4, WFT1-3
-
 I no state

x

21  x 
x I no state
 12
2 I


     4  W13  S 24  W13  S24 ij   ij 
 ij

 

i
ii
0
1 x 2
1 x
Results with the HERMES ABS
ABS intensity measured by Breit-Rabi Polarimeter, which measures
the hyperfine populations of a sample atomic beam from the target cell
HFT empl.
-
states inj.
1 2
BRP meas. intensity
66.5 +/- 0.3 kHz
SFT2-4
1
41.8 +/- 0.2 kHz
WFT1-3
2
38.2 +/- 0.3 kHz
SFT2-4, WFT1-3
-
10.9 +/- 0.1 kHz
Results with the HERMES ABS
ABS intensity measured by Breit-Rabi Polarimeter, which measures
the hyperfine populations of a sample atomic beam from the target cell
HFT empl.
states inj.
1 2
-
BRP meas. intensity
66.5 +/- 0.3 kHz
SFT2-4
1
41.8 +/- 0.2 kHz
WFT1-3
2
38.2 +/- 0.3 kHz
SFT2-4, WFT1-3
-
10.9 +/- 0.1 kHz
( 2)
x   IBS
 8.4  1.6%
,1  2
Results with the HERMES ABS
ABS intensity measured by Breit-Rabi Polarimeter, which measures
the hyperfine populations of a sample atomic beam from the target cell
Measurements with SFT2-4 and WFT1-3 between the sextupoles:
( 2)
x   IBS
 8.4  1.6%
,1  2
Also did with SFT and retuned MFT1-3 (negative gradient field)
x  7.5  1.4% neglecting  MFT   24 23 1  12  2
Results with the HERMES ABS
ABS intensity measured by Breit-Rabi Polarimeter, which measures
the hyperfine populations of a sample atomic beam from the target cell
Measurements with SFT2-4 and WFT1-3 between the sextupoles:
( 2)
x   IBS
 8.4  1.6%
,1  2
Total IBS in the HERMES ABS 20-25%
Summary
 A method to directly measure the IBS effect in an ABS by
using a set of transitions between sextupoles is introduced.
 Results using the HERMES ABS are presented. The results
explain well the discrepancy between the measured intensity
and the expected one.
 The study confirms further that the IBS effect is relevant for
ABSs and has to be taken into account in the design of future
high intensity ABSs.
IBS in VEPP-3ABS
M.V.Dyug et. al, NIM A 495 (2002) 8-19
 Intensity is smaller than expected, IBS is roughly estimated to be 20%.
Fig 9 Intensity of the focused deuterium
beam versus the currents through the
coils of the magnets.
Fig 10 Calculated density near the beam
axis along the ABS.
IBS in the HERMES-ABS
Z.Ye, Intra-Beam Scattering from Monte Carlo, under preparation
IBS in the HERMES-ABS
N.Koch, Ph.D Thesis, Univ. Erlagen-Nuernberg, DESY-Thesis-1999-015
 Rest Gas Attenuation was measured and calculated by MC simulation.
Meas. Intensity
6.4 1016 s 1
Calculated (n=2)
7.5  1016 s 1
Calculated (n=5)
1.5 1017 s 1
I ( )  I 0 cos n ( )
High Frequency Transition
 The effect of a HFT which exchanging atoms in state a and b , on the
hyperfine populations of the hydrogen atoms can be described by a 4 4
matrix ab :
new
old
ni
  ab ij  ni
j
 For example, for a strong field transition (SFT) 2-4:
0
1

 0 1   24
S 24  
0
0

0 
24



0  24 
1
0 

0 1   24 
0
0
where  24 is the transition efficiency of SFT2-4.
 Transition efficiencies larger than 98% for the HFT units used in the
ABS and BRP for the HERMES experiment has been reported.
Sextupole Magnet
 The probability for a hydrogen atom to be transmitted by the sextupole
magnet system can be described by a 4 4 matrix:
State
1
2
3
4
1
0.45
0.45
0.033
0.047
2
0.45
0.45
0.03
0.043
3
0.009
0.0085
0
0
4
0.013
0.013
0
0
 Row refer to the hyperfine states in the first sextupole subsystem, while
columns refer to the hyperfine states in the second sextupole subsystem.
For example, a hydrogen atom in state 2 interchanged to state 4 by an
ideal SFT 2-4 (  24  1 ) between the two sextupole subsystems has an
absolute probability  24  0.043 to enter the target cell.
Measurement with SFT2-4/WFT1-3
Meas. No.
1
HFT empl. states inj.
-
1 2
ABS Beam Intensity



(1)
(1)

I 1  I 0  1   RGA
 1   IBS
1  
( 2)
IBS , 1  2
   

   ij
44 ij
ij


(1)
(1)

I 2  I 0  1   RGA
 1   IBS
2
SFT2-4
1
1      S
( 2)
IBS , 1


24 ij
  ij
ij


(1)
(1)
I 3  I 0  1   RGA
 1   IBS

3
4
WFT1-3
SFT2-4
&
WFT1-3
2
1  
( 2)
IBS , 2
   W

   ij
13 ij
ij


(1)
(1)
I 4  I 0  1   RGA
 1   IBS

No state
1 
( 2)
IBS , no state
   W
13
ij
 S 24 ij   ij
Measurement with SFT2-4/MFT1-3
Meas. No.
1
HFT empl. states inj.
-
1 2
ABS Beam Intensity



(1)
(1)

I 1  I 0  1   RGA
 1   IBS
1  
( 2)
IBS , 1  2
   

   ij
44 ij
ij


(1)
(1)

I 2  I 0  1   RGA
 1   IBS
2
SFT2-4
1
1      S
( 2)
IBS , 1


24 ij
  ij
ij


(1)
(1)
I 3  I 0  1   RGA
 1   IBS

3
4
MFT1-3
SFT2-4
&
MFT1-3
1
1  
( 2)
IBS , 2
   M

   ij
13 ij
ij


(1)
(1)
I 4  I 0  1   RGA
 1   IBS

No state
1 
( 2)
IBS , no state
   M
ij
13
 S 24 ij   ij