Effect of Solenoid in Quadrupole Magnet on
Electron Cloud Instability
11th KEKB Accelerator Review Committee (2006.03.21)
H. Fukuma, J.W. Flanagan, T. Kawamoto, T. Morimoto,
K. Oide, T. Tobiyama, F. Zimmermann
1. Introduction
2. Flat cable solenoid system
3. Experiment
4. Effect on luminosity
5. Simulations
6. Summary

1. Introduction
The electron cloud instability(ECI) at KEKB LER is largely mitigated by thesolenoid field applied to the vacuum chambers in drift space.
However, the blowup is still observed when the bunch spacing is reducedto 3.27 rf buckets or shorter.
A question is where the remaining electron clouds are.
The electron clouds may be accumulated in a quadrupole field because
the magnetic field is zero at the center of the magnet.
To investigate the electron clouds in the quadrupole magnet, a solenoid
made of a flat cable was developed and installed in 88 quadrupole magnets
which are 25% of the quadrupole magnets in arc sections.
If the remaining electron clouds are mainly in the quadrupole magnet andthe solenoid can affect the electron cloud in the quadrupole, the effect of
the solenoid on the ECI may be observed.

Expected electron density if the electrons in the quadrupole
are the primary cause of the ECI.
A condition where the strong head-tail instability occurs.
( K. Ohmi and F. Zimmermann, Phys. Rev. Lett.,85, 3821 (2000))2γν s∫ ρ ⋅ ds > πr βe y€ρ : the cloud density,s : the obit length,νs : the synchrotron tune,βy : the average vertical beta function.

Total length of quadrupole magnets is 218m which is 7.2% ofthe circumference.
Average ρ in the quadrupole > 7.4 1012 m-32. Flat cable solenoid system
As we do not want to split the quadrupole magnet to wind the solenoid, anda gap between a vacuum chamber and poles of the quadrupole is only about
2mm, a flat cable was used as the solenoid.
The flat cable was attached to connectors so as to make a loop of a wire.
•Flat cable : ECO-OKIFLEX-SN4 (Non-halogen cable)
Thickness of the cable : 0.98 mm
Wire pitch : 1.27 mm
Wire resistance : 222 ohm/km(5 ohm for a piece with the connector)
Maximum current : 2.1 A
Temperature rise (@current 2 A, room temp. 24ºC)
18 ºC(cable), 33ºC(connector)•Power supply : KENWOOD 5A, 300V
•Field strength : 17Gauss@2A

A piece of the solenoid

Installation
CircuitEight pieces of the solenoid were set in a quadrupole.
The solenoids were installed in 88 quads among 461
quadrupoles.
Location of the solenoids was near the entrance ofeach arc because of easy wiring work of DC cables.

QQ

Q
2AQ

2AV

10 Qs

10 Qs
Tsukuba

12 Qs

12 Qs
Nikko

Oho
12 Qs

12 Qs
Fuji
10 Qs

10 Qs

3. Experiment
Procedure :Measure the sideband of the dipole oscillation and the vertical beam
size with turn-on or -off of the solenoids in the quadrupoles.
The appearance of the sideband is related to the ECI.
The blowup of the vertical beam size caused by the ECI is
our main concern.
The dipole oscillation was measured by the BOR(Bunchoscillation Recorder).
The vertical beam size was measured by the interferometer.
Fill pattern 8/50/2, 4/80/3(# of trains/ # of bunches in a train/ bunch spacing in unit of rf bucket)

1) Experimental conditions
Betatron tune : (νH, νV) = (45.522, 43.623)
Chromaticity : (ξH, ξV) = (2.1, 6.5)
Vertical feedback gain : -14.6dB
RF voltage : 8 MV (νs = 0.024)
Solenoid : turn-on except for the solenoids in the quadrupoles
The beam conditions were chosen so as to avoid the low injection rate,
the dipole oscillation and the beam size blowup by the coupling
resonance.
(In physics operation,
Betatron tune=(45.506, 43.531), Chromaticity = (2.1, 4.8),
Vertical feedback gain = -18.6dB)
Above conditions were maintained throughout the experiment.

2) Sideband
The Fourier power spectrum of each bunch is calculated individually.

a) Overlapped spectrum of all bunches (averaged over trains)
8/50/2(2 bucket spacing)
450mA(1.13mA/bunch)sidebandSolenoid on

betatron tune

Solenoid off

8/50/2(2 bucket spacing)
400mA(1mA/bunch)

betatron tune

Solenoid on

Solenoid off

sideband4/80/3(3 bucket spacing)
450mA(1.4mA/bunch)sidebandSolenoid on

Solenoid off

betatron tune

4/80/3(3 bucket spacing)
400mA(1.25mA/bunch)sidebandSolenoid onbetatron tune

Solenoid off

There is no clear difference in the peak position and the height of the sideband
with or without the solenoid field in the quadrupoles.

b) Sideband along the train (J.W. Flanagan)

Solenoids ON, 2-bucket spacing

Solenoids ON, 3-bucket spacing

tailheadtune
Solenoids OFF, 2-bucket spacing

betatron tune sideband

Solenoids OFF, 3-bucket spacing

Sideband peak size (2 bucket spacing)
Q sols. on
Q sols. off

Q sols. on
Q sols. off

Peak Height

Integral around peak

2-Bucket Spacing
450 mA total
1.1 mA/bunch

2-Bucket Spacing
450 mA total
1.1 mA/bunch

There is no clear difference in the data with or without the solenoid field in thequadrupoles.

Sideband peak size (3 bucket spacing)
3-Bucket Spacing, 450 mA total, 1.4 mA/bunch
Q sols. on
Q sols. off

Q sols. on
Q sols. off

Integral around peak

Peak Height

DifficultpeakfindingDifficultpeakfinding

Sideband-betatron peak separation (2 bucket spacing)
Q sols. on
Q sols. off

Difficultpeakfinding

2-Bucket Spacing
450 mA total
1.1 mA/bunch

peak separation

Peak location (3 bucket spacing)
Q sols. on
Q sols. off

3-Bucket Spacing
450 mA total
1.4 mA/bunch

sidebandbetatron

There is no clear difference in the data with or without the solenoid field in thequadrupoles.

3) Vertical beam size measured by the interferometer
The size at the synchrotron radiation source point is translated
into that at I.P.
Comparison of beam size w/wo Q solenoid

Comparison of beam size w/wo Q solenoid

3.0

3.0
Fill pattern 4/80/3(train /bunch in a train /bunch spacing)Fill pattern 8/50/2(train /bunch in a train /bunch spacing)
2.5

solenoid offsolenoid on

Vertical beam size at I.P.(micron)Vertical beam size at I.P.(micron)

2.5

2.0

1.5

1.00.500.0200

250

300

350

400

Total beam current(mA)

450

500

solenoid offsolenoid on
2.0

1.5

1.00.50

0.0
200

250

300

350

400

Total beam current(mA)

Behavior of the beam size is almost same with or without thesolenoid field in the quadrupoles.

4505004. Effect on luminosity
The effect of the solenoids in the quadrupoles on the luminosity wasinvestigated during physics run.

solenoid offsolenoid on

KEKB was operated with turn-on the solenoids in the quadrupoles from thisJanuary.

2005.12.01 - 12.26

2006.02.01 - 02.28

solenoid offsolenoid on

No improvement of the specific luminosity was found with turnon the solenoids in the quadrupoles.

5. Simulations
The results of the experiment were compared with simulation
by ECLOUD and CLOUDLAND.

a) Simulation by ECLOUD (F. Zimmermann)

1.3mA/bunchElectron cloud in quadrupole field of 5 T/m(Three different integration routines were tried for the electron motions.)
m-1

2 spacing

4 spacingElectron line
densitym-3
Electroncentraldensitysec
The electron central density is less than 1012 m-3.
The density will not be enough to cause the ECI according to
the rough estimation of the threshold cloud density of the ECI.

Electron cloud in quadrupole field of 5 T/mwith weak solenoid
Solenoid field : 0, 20, 60, 600G

2 spacing

4 spacing

m-1
Electron line
densitym-3
Electroncentraldensitysec
There is no effect of the weak solenoid on the electron density.

Weaker quadrupole field of 0.1T/m with solenoid field
Solenoid field : 0, 20, 60, 600G

2 spacing

4 spacing

m-1
Electron linedensitym-3Electroncentraldensitysec

A solenoid of 60 or 600G is effective in reducing the electron density.

b) Simulation by CLOUDLAND (T. Morimoto)
Effect of the solenoid on the electron density(4 bucket spacing, 2mA/bunch, photoelectron yield 0.1)
Quadrupole field 5 T/m-3electron central volume density [m ]1.0x1011

Quadrupole field 0.1 T/melectron central volume density [m-3]3.0x1011
2.5x1011

8.0x1010

2.0x1011

10

6.0x101.5x1011

4.0x1010

1.0x1011

2.0x1010
0.0

5.0x1010

010200.00102030

405060

Solenoid field [G]Solenoid field [G]No effect of the solenoid.

The solenoid is effective.

The results are qualitatively consistent with those of theECLOUD.

6. Summary
A flat cable solenoid was developed and installed in quadrupoles toinvestigate the electron clouds in the quadrupole field.
No clear effect of the solenoids in the quadrupole magnets was found on
the sideband, the vertical beam size and the luminosity.
The result of the experiment is consistent with the simulations.
The direct measurement of the electrons by the electron monitor may
give a clearer answer on the information of the electron clouds in thequadrupole field (K. Oide).