Direct Measurement of Intra-beam Scattering in Atomic Beam Sources

Direct Measurement of Intra-beam Scattering in Atomic Beam Sources

Z.Ye for the HERMES Target GroupDESY

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)


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



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



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



The relative loss of density due to IBS in a parallel beam is proportional to beam density , traveled distance , scattering

cross-section , velocity spread and reverse of the square

of mean velocity

.

d

dzd

2

dzd

2





of mean velocity

Varying the beam density while keeping the other parameters of the beam unchanged, the IBS effect can be varied and measured

IBSII 101

21

20

2IBSI

I

21

20

3IBSI

I

d

dzd

2





of mean velocity

Varying the beam density while keeping the other parameters of the beam unchanged, the IBS effect can be varied and measured

IBSII 101

21

20

2IBSI

I

21

20

3IBSI

I

d

dzd

2

IBS

IBS

I

III

121

132

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

HFT empl. states inj.

-

SFT2-4

WFT1-3

SFT2-4, WFT1-3 -

4 ABS injection modes using SFT2-4/WFT1-3 between the sextupoles

21

1

2


ABS intensity:

: intensity loss due to RGA (IBS) in the 1st (2nd) part of the ABS.

: transition efficiency of an atom in state become as an atom in

state after the HFTs between the sextupoles.

: transmission probability of an atom through the ABS which is in

state before and in state after the HFTs between sextupoles


-

SFT2-4

WFT1-3

SFT2-4, WFT1-3 -


21

1

2

)1()1( 11 IBSRGA ij

jiij )2()2( 11 IBSRGA I 0I )2/1(/ IBSRGA

ij

jii

j

ij


ABS intensity:

Nucleon magnetic moment is much smaller than electron magnetic

moment:

Injection mode with ideally no atoms injected:


-

SFT2-4

WFT1-3

SFT2-4, WFT1-3 -


21

1

2

)1()1( 11 IBSRGA ij

ijij )2()2( 11 IBSRGA I 0I

)2(2,

)2(1,

)2(21, 22 IBSIBSIBS x

0)2(, statenoIBS



-

SFT2-4

WFT1-3

SFT2-4, WFT1-3 -

21

1

2

21

2121

I

IIII stateno

x

x

12




-

SFT2-4

WFT1-3

SFT2-4, WFT1-3 -

21

1

2

21

2121

I

IIII stateno

x

x

12 212

I

Ix stateno




-

SFT2-4

WFT1-3

SFT2-4, WFT1-3 -

21

1

2

21

2121

I

IIII stateno

x

x

12 212

I

Ix stateno

x

x

1

21

0241324134

iii

ijijijSWSW


Results with the HERMES ABS

HFT empl. states inj. BRP meas. intensity

- 66.5 +/- 0.3 kHz

SFT2-4 41.8 +/- 0.2 kHz

WFT1-3 38.2 +/- 0.3 kHz

SFT2-4, WFT1-3 - 10.9 +/- 0.1 kHz

21

1

2

ABS intensity measured by Breit-Rabi Polarimeter, which measures the hyperfine populations of a sample atomic beam from the target cell

Results with the HERMES ABS

HFT empl. states inj. BRP meas. intensity

- 66.5 +/- 0.3 kHz

SFT2-4 41.8 +/- 0.2 kHz

WFT1-3 38.2 +/- 0.3 kHz

SFT2-4, WFT1-3 - 10.9 +/- 0.1 kHz

21

1

2

ABS intensity measured by Breit-Rabi Polarimeter, which measures the hyperfine populations of a sample atomic beam from the target cell

%6.14.8)2(21, IBSx

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

%6.14.8)2(21, IBSx

%4.15.7 x 21 122324 MFT

Also did with SFT and retuned MFT1-3 (negative gradient field)

neglecting

Measurements with SFT2-4 and WFT1-3 between the sextupoles:

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

Total IBS in the HERMES ABS 20-25%

%6.14.8)2(21, IBSx

Measurements with SFT2-4 and WFT1-3 between the sextupoles:

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-3ABSM.V.Dyug et. al, NIM A 495 (2002) 8-19 Intensity is smaller than expected, IBS is roughly estimated to be 20%.

Fig 10 Calculated density near the beam

axis along the ABS.

Fig 9 Intensity of the focused deuterium

beam versus the currents through the

coils of the magnets.

IBS in the HERMES-ABSZ.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

Calculated (n=2)

Calculated (n=5)

116104.6 s116105.7 s

117105.1 s

)(cos)( 0 nII

High Frequency Transition The effect of a HFT which exchanging atoms in state and , on

the hyperfine populations of the hydrogen atoms can be described by a

matrix :

For example, for a strong field transition (SFT) 2-4:

where 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.

j

oldiijab

newi nn

a b

ab44

2424

242424

100

0100

010

0001

S

24

Sextupole Magnet The probability for a hydrogen atom to be transmitted by the sextupole

magnet system can be described by a matrix:

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 interchanged to state by an ideal SFT 2-4 ( ) between the two sextupole subsystems has an absolute probability to enter the target cell.

44

State

0.45

0.45

0.009

0.013

0.033 0.45

0.45

0.0085

0.03

0

0.013 0

0.047

0.043

0

0

1 2 3 4

1

2

3

4

2 4124

043.024

Measurement with SFT2-4/WFT1-3

Meas. No. HFT empl. states inj. ABS Beam Intensity

1

2

3

4

No state

-

SFT2-4

WFT1-3

SFT2-4

&

WFT1-3

21

1

2

)2(21,1 IBS

)2(1,1 IBS

)2(2,1 IBS

)2(,1 statenoIBS

ij

ijij 44

)1()1(0

1 11 IBSRGAII

)1()1(0

2 11 IBSRGAII

)1()1(0

3 11 IBSRGAII

)1()1(0

4 11 IBSRGAII

ij

ijijS 24

ij

ijijW 13

ij

ijijSW 2413

Measurement with SFT2-4/MFT1-3

Meas. No. HFT empl. states inj. ABS Beam Intensity

1

2

3

4

No state

-

SFT2-4

MFT1-3

SFT2-4

&

MFT1-3

21

1

1

)2(21,1 IBS

)2(1,1 IBS

)2(2,1 IBS

)2(,1 statenoIBS

ij

ijij 44

)1()1(0

1 11 IBSRGAII

)1()1(0

2 11 IBSRGAII

)1()1(0

3 11 IBSRGAII

)1()1(0

4 11 IBSRGAII

ij

ijijS 24

ij

ijijM 13

ij

ijijSM 2413

Direct Measurement of Intra-beam Scattering in Atomic Beam Sources

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