Beam Measurements
T. IeiriThankful contributions by:
H. Fukuma, H. Ikeda, Y. Ohnishi, K. Oide and M. Tobiyama!Topics I : Beam Measurement near aHalf-Integer (page 2 to16)
Topics II : Measurement of Wake Effects
using Tune Shift (page 17 to 29)
KEKB Review 2006

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Beam!Measurement
near!a!Half-Integer!!!!

Outline• Backgrounds• Beam Dynamics near a Half-Integer- Dynamic Beam-Beam Effects- Half-Integer Stopband• Measurement 1: tune spectrum• Short Summary• Measurement 2: beam size
• Short Summary
KEKB Review 2006

2Backgrounds• The beam-beam parameter reaches a high level of ξx=0.1.
• The operation point of the horizontal tune is set very near a halfinteger.
• Dynamic beam-beam effects result in heavy distortion in optics,emittance growth and beta beat.
• On the other hand, approaching a half-integer, we would
encounter the stopband, beta beat, and synchro-beta resonance.
No machine exists without errors.

• These are attractive issues from viewpoint of beam dynamics.

KEKB Review 20063

Tune Diagram in Operations• The operating points are crucial for tuning the luminosity.
• Severe wall in the horizontal tune.
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Dynamic Beam-Beam Effects• Beta and emittance change as a function of the tune.
• Dynamic BetaEmittance

Beta*Beta (m)• Dynamic Emittance1+ 2 πξ x cot 2 πνεx ≈ε2 2 x01+ 4 πξ x cot2 πν − 4 π ξ x10080

L_size_cal

ξx=0.11

120
100
80

60

60

40

40

20

20000.5 0.51 0.52 0.53 0.54 0.55

Tune

KEKB Review 2006

at LER SRM
βx0=24.15 m
εx0=17.8 nmrad

5Emittance (nmrad)

β0 (s) βΔβ (s) =Δk * cos(2 πν − 2 Δϕ s )2sin(2 πν )120

Beam-Beam Tune Shift• Beam-beam interaction produces a new set of two tunes.
• We call two modes the H-mode and the L-mode.
Δν bb = ν H + ν L − ν 0+ − ν 0−
• Coherent beam-beam tune shift:• Coherent beam-beam parameter:
A measurement€κ (ν 0+ , ν 0− )
Ξ + Ξ = ξq =Δν bb
Y+q−q+0.55

L-mode0.54

Tune

H-mode€−ν 0=0.506, ν 0 =0.512

B-B H TuneH Mode

0.53
0.52

L Mode0.510.500.02 0.04 0.06 0.08 0.1 0.12

Coherent Beam-Beam Parameter, Ξ++Ξ−KEKB Review 2006

6Half-integer Stopband• Gradient errors cause the half-integer stopband and beta beat.
• The beta beat might be estimated from variations of the beamsize.
Δβ ge
J p eiνφν=− ∑ 2β04 π p ν − ( p /2)2ν≈p2

p : integer

Size (micron)850

1 Δν sb
Δβ ge ≈ −cos( pφ + δ )⋅ β02 (ν − p /2)
Δν sb ≈ J p /2 π : Stopband Width
KEKB Review 2006

€Stopband_cal

Size̲0.002
Size̲0.003
Size̲0.004
Size̲0.006

800
750
700
650
0.504

0.506

0.508

0.51

Tune

φ=∫dsνβ7

Measurement 1 : Distortions by KEK-PS
Current of QF2P (A)• Power supplies of KEKB wasaffected by KEK-PS operation.
• Tune varied, synchronizedwith KEK-PS cycle.
• Tune spectrum was distorted.

Power Supply for Q-Magnets
offon219.76219.755
219.75-15 -10

L/04.10.14

0.508

-505

1015

Time (minutes)

measured0.506

Tune

219.765

Tune Spectrum

0.504
0.502

2.2 s

0.500.5

11.5

2

2.5

Time after P1 (sec)
KEKB Review 2006

8Tune Spectrum (1/2)
The influence of KEK-PS was almost fixed.
We made the tune closer to a half-integer, ---(b)• A sharp spectrum was observed juston a half-integer.
• As the tune approached a halfinteger, the amplitude grew
exponentially and the betatron
amplitude reduced.

(c)

11

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

000.5 0.502 0.504 0.506 0.508 0.51

KEKB Review 2006

Fractional tune

Half-integer amplitude

ξx=0.94

Amplitude at tune(a)9Tune Spectrum (2/2)• The half-integer spectrum depended on chromaticity.

(b)

Half-integer amplitude

(a)

10.8

0.505

0.6

0.506

0.4
0.2
00.2 0.4 0.6 0.81

1.2 1.4 1.6

Chromaticity, ξ x

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Simulating the spectrum• The betatron tune spectrum well simulates the real one.
• But, no distortion can be seen at half-integer.

- Conditions • Phase relation is the same
• Assuming a single particle• No machine error

KEKB Review 2006

11Short Summary on Tune Spectra• Even though KEK-PS was off, the tune spectrum was distorted.
• The amplitude of the half-integer spectrum depended on the tuneand chromaticity.
• However, a simple simulation did not indicate such a spectrum
on a half-integer.
• The distortion in the spectrum is caused by off-momentum
particles jumped into an unstable region of a half-integer
resonance.
• Need to consider dynamics of off-momentum particles.

KEKB Review 200612

Size Measurement (1/2)

Non-colliding BunchSize̲gate

Horizontal size of a pilot bunch wasmeasured using a gated CCD camera.

Size_gate (a.u.)y = 119 + -198.46x R= 0.60719
25L̲tune̲051129

2015100.504

0.506

0.508

0.51

Tune

• Linearly fitting line shows horizontal size slightly
increases by 6.4% with large error bars, when the tunechanged from 0.510 to 0.504.
• Change in the size may suggest an effective stoband ofΔν sb cos( pφ + δ ) = 0.002 to 0.003.
KEKB Review 2006

€13Size Measurement (2/2)
Size̲int
y = 7715 + -13148x R= 0.94274
1150Size (micron)

Horizontal size of colliding bunches
were measured using the interferometer.

• Horizontal size increased by 7.6%
when tune changed from 0.510 to 0.504.

L_tune_051129

1100
1050
1000
950
0.502 0.504 0.506 0.508

Tune
Non-colliding bunch• The measurement might be affected byboth dynamic beam-beam andstopband effects
KEKB Review 2006

Note:
Tune of colliding bunches isdifferent from that of pilot bunch.
140.51

Consideration for Size Measurement in Collision
Dynamic Size at SRM
3000

Horizontal Size (µm)• Colliding bunches have twomodes of tune; L-mode and Hmode.
• Assuming ξx=0.11 or 0.10,
two tunes can be estimatedfrom unperturbed tunes.
• By using the H-mode tune,
measured size agrees withcalculated one.
• Effect of stopband would besmall.

L_size_cal

2500

Size̲0.11
Size̲0.10
Size̲L
Size̲H

2000
1500
1000
500
0.5 0.51 0.52 0.53 0.54 0.55 0.56

Tune

σx0=656 µm
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Short Summary on Beam Size
• Horizontal size of non-colliding bunch slightly increased
when the tune approached to a half-integer.
• The increase of the size might affect the distortion in thetune spectrum at a half-integer.
• However, quantitative evaluation is difficult due to large
error bars in size measurement, needs more precise
measurement.
• Colliding bunches is mainly caused by dynamic beambeam effects.
• The tune in the H-mode should be used to evaluate thedynamic beam-beam effects, not that in the L-mode.
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Measurement of Wake Effects
using Tune ShiftOutline••••••

Motivation
Tune Shift
Gated Tune Monitor
Measurement MethodResults
Summary
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Motivation• The LER suffers from an increase of the vertical beam size.
• Caused by a strong head-tail instability due to electron clouds.
• A resonatorlike wake is proposed to explain the sideband.
• Can the tune shift catch the wake?
• The detection is an integrated value
over a whole bunch.

From J. Flanagan et al., PRL 94 054801(2005)
KEKB Review 200618

Tune Shift• Dipole fields acting a bunch change the tune.
dFy1Δν y =∫βds
4 πEdyFy: Forces acting a bunchΔν>0 : focusing, Δν<0 : defocusing• Head-tail wake makes a negative tune shift.
Δν = −

T0 I b∑ βi ki
4 πE / e iki : kick factor V/(Qm)• Space charge due to electron cloud causes a positive tune shift.
reΔν y = ∫ ρβ y ds
2γ

ρ: cloud density /m3
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Gated Tune Monitor
Some improvements were carried out in last year.
• New Spectrum Analyzer- Sweep Time, 8 to 1.5 sec- Data Points, 250 to 1000
• Shorten Deflection Pulse- Width: 50 ns + long tail to 10 ns-> bunch-by-bunch deflection• Stabilizing the oscillation detector• Adding 2nd Monitor- Simultaneous measurement for two bunches
KEKB Review 2006

Deflection Pulse

100 ns/div.

5 ns/div.

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How to measure
Use a pilot bunch as a probe.
Pilot Bunch, <1 mA

Bunch Train Nb=200 or 1371
Bunch
Current

time

D
Bucket Distance between train end and pilot bunch

1. A bunch train was stored on ahead.
2. A pilot bunch was injected one by one from behind.
3. The tune was measured as a function of pilot-current
during each injection under constant train-current.
KEKB Review 200621

Machine Conditions

Beam
Bunch Structure
Bunch Current
SolenoidVc, νsξx, ξyMeasurement 1

Measurement 2

Positron
4/200/4
0.5 ~ 0.7 mA
OFF
8 MV, 0.025
1.6, 4.6

Positron
1/1371/3.5
1.0 mAON
8 MV, 0.025
0.9, 3.2

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Measurement 1 : Bucket-Dependent Tune-Shift (BDTS)
Without Solenoids
After Train

Along Train

0.008
0.006
0.004
0.002
00.008
0.006
0.004
0.002
00200

400600H1̲380V1̲380Distance0.01

Tune Shift

Tune Shift

0.01

L/tune/train

H1̲380V1̲380800

Bucket0102030405060Distance in Bucket

Note: The tune of the leading bunch of a train is used as a reference.
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Measurement 1 : Current-Dependent Tune-Shift (CDTS)
Vp̲900Vp̲856
Vp̲826

0.005

L/tune̲400

0.004

Vertical Tune Shift

Vertical Tune Shift

Vertical

0.003
0.002
0.001
0-0.001
0.2

0.4

0.6

0.8

11.2

Bunch Current (mA)

0.012

Vp̲808Vp̲805
Vp̲802
Vp̲799L/tune̲400

0.01
0.008
0.006
0.004
0.002
00.2

0.4

0.60.811.2

Bunch Current (mA)

• The CDTS is not linear.
• Approximated by two lines.

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Measurement 1 : Current-Dependent Tune-Shift (CDTS)- Two values correspond to the CDTS around 0.4 mA and 0.8 mA.
VerticalHorizontal
CDTS of single bunch
0.005

CDTS (/mA)

CDTS (/mA)

0dn/dc̲H̲380
Shift̲Distance-0.001

dn/dc̲V̲380

Shift̲Distance

0-0.005-0.002-0.003-0.004010 20 30

40 50 60

Distance in Bucket-0.01-0.015010 2030

40 5060

Distance in Bucket• The vertical CDTS abruptly changed around D=10.
• Positive CDTS at D<10.
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Measurement 1 : Tune Spectra at short distance• Observed two-peak spectrum
and Flanagan sideband (?)
at a short distance of 3 underhigh train-current.
Train:380 mA
around threshold
D=3

Train:580 mA
above threshold
D=3
KEKB Review 2006

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Measurement 2 : Bucket-Dependent Tune-Shift (BDTS)
H Tune ShiftAlong Train

Horizontal

1/1389/3.5
0.003

With Solenoids

0.002
0.001
0-0.001

01000 2000 3000 4000 5000

After Train

Bucket0.015

1/1389/3.5

dV̲750dV̲1400

Tune̲0.4mA
Tune̲0.8mA

Shift_1400

0.020.015

0.01

Tune

V Tune ShiftdH̲750dH̲14000.0050.005

Vertical

0.01

0001000 2000 3000 4000 5000

BucketKEKB Review 2006

0102030405060

Distance from Train /bucket
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Measurement 2 : Current-Dependent Tune-Shift (CDTS)
CDTS of Single Bunch

VerticalHorizontal
Shift_H_1400

0CDTS (/mA)

Tune Shift (/mA)

0-0.001-0.002-0.00301020304050

shift/mA

Shift̲1400-0.002-0.004-0.006-0.00860

Distance in Bucket-0.01010 203040 50

60

Distance in Bucket• Horizontally, completely damped by solenoids.
• Vertically reduced, but the structure is preserved.
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Summary of Tune Shift• The CDTS (Current-Dependent Tune-Shift) was measured aftera bunch-train in the LER with and without the solenoids.
• As a pilot bunch approached a train, the vertical defocusing
force was stronger, but changed to a focusing force within abucket distance of around 10.
• The change may suggest a direct effect of electron clouds.
• At a short distance of 3 with a high train-current, the tunespectrum was heavily distorted, two peaks with the sideband(?).
• Though the BDTS is almost the same between horizontal andvertical directions without the solenoids, the CDTS is quite
different, which might suggest a strong wake vertically.
• Horizontal CDTS was small and completely damped by thesolenoids.
KEKB Review 200629