Emittance Preservation in Linac
2011.02.07 Super KEKB Review

Emittance Measurement @2009.07.01
AB

J-ARC

C

Wire scanner

DC-Gun213Emittance Measurement
HorizontalEmittance

Emittance Measurement
VerticalEmittance

800

350

600
500
400

1nC

300

1nC

3nC

250

3nC

5nC

200

5nC

γεy

700

γεx

54300

150
100

200
100

5000

B

C
Sector

5B

C

5SectorInitial emittance looks low considering φ16 big cathode.
Problem is emittance growth.
Machine study from 2010/10

Overview of emittance source and growthLonger bunch can reduce
space charge effect inside RF-Gunand also CSR at J-ARC.
GunBJCSRC

Current charge & emittance:e- :1 nC, 300 mm mrade+ :1 nC, 2100 mm mrad

1.1GeV@DRRequirement:

APFTarget @1‐4
3.5 GeV 10nC x 2

12BCSECS

345ECS

for LER
4.0 GeV 4nC x 2
εy < 6 mm mrad

C‐bandDue to mis-alignment:- Dispersion- Short range wakefieldfor HEROne feed coupler (x480)
7.0 GeV 5nC x 2
causes of RF emittance.
ε < 20 mm mrad(Δγε ~ 1.2 mm mrad is estimated) yApparent emittance growth due toDispersion and Short Range Wakefield- Mis-alignment : σx=0.5 mm- Initial emittance = 10 mm mrad
− δp : 0.1 %, σz : 1mmDispersion(only from ηx)γε(mm mrad)

605040enx
eny

30

20

1000100

200300400500enx (m.rad)600z (m)enx (m.rad)1009080[Short Range Wakefield]- Charge : 5 nC

enx (mrad)

70
60
5040
30201000100

200300s (m)400500Emittance Compensation

Alignment

Alignment tolerance:
becomes severe without compensation=> Compensation is required.
should be determined by second order effect andcompensation error.
→ Machine & simulation study of emittance source.

– Dispersion : compensated in BT line.
– Short range wakefield : Initial offset→ Monitoring using RF-Deflector is required.
– RF Emittance : RF-Deflector can compensate– CSR : longer bunch length.
RF-Deflector => bunch slice emittance
TM110 Cavity Chainz

Machine study
from 2010.10

Machine study• Emittance growth measurement– Charge dependence– Optics dependence• R16, R36 measurement• Response orbit measurement→ Beam based alignment→ Dispersion calculationBA

PF Injection

J-ARCC12345

Emittance measurement

γεx [mm mrad]

1200
1000
800

800

0.5nC
1nC
3nC
5nC
1.0nC
3.0nC
5.0nC
7.0nC

700
600

γεy [mm mrad]

1400

600
400

500
400

0.5nC
1nC
3nC
5nC
1.0nC
3.0nC
5.0nC
7.0nC

300
200

200

100

00
B

C

Sector

5B

C

Sector5

Emittance measurement
Improvement of emittance measurement will be required:- Optimize phase advance during PF injection.
=> Use injection intervals to change Q-magnets.
- RF-gun installation to obtain lower emittance.
Wire scanner should install more:BAPF Injection

J-ARC
C12345

Dispersion (R16, R36)
• Emittance growth was observed at 1 nC.
• Large dispersion was measured at sector 5.
• Dispersion leak from J-ARC is small by comparing
energy change before and after ARC section• 3～5 sector has small dispersion→ Determine the dispersion source

BA

J-ARC
C

12345

Horizontal Dispersion(One by one unit standby)• 1-7 to 2-2 has horizontal dispersion source
2-2 Standby

Δp = 140 MeV (p=4 GeV)

1-7 Standby→ R16 = 50 mm

Kink at 2-1 was observed before.

Kink of 2-1
Wall- 0.26mrad

PathwayVertical Dispersion（One by one standby）

C-4 Standby

C-3 Standby→ Building connection between C3 and C4 unit
causes 1 mm mis-alignment.
Dispersion source is almost found, but so large dispersion (200mm)

Response measurement• All magnets : Q, Steering, Sextupole
QD_C3_4±10%Δy=1mmcalculation

Gunxymeasurement
5 mm

5 sector

Calculated dispersion
from response measurement
1.2
Dispersion
(m)
10.8
0.6
0.4
Line-R16
Line-R36

0.2
0-1000-0.2-0.4-0.6-0.8100200300

400500600700Z(m)Emittance preservationand compensation

Alignment• Conventional alignment– Wire positioning for horizontal– Hydraulic leveling for vertical• Beam based alignment

2011.04 => Alignment– Response from all magnets• Laser alignment– R&D for continuous measurement.

Beam based alignment
10.8
0.6

misallignment(mm)0.40.2

X
Y_4_4_4_4

F_C4

F_C5

F_C6Q

Q

D_C8_QQ

4

D_C7_Q_4

4

D_C6_Q

F_C3

4

D_C5_QQ

4

D_C4_Q_4

4

D_C3_QF_C24

D_C2_Q

Q4D_C1_F_C14-0.2
QQ

0-0.4
-0.6
-0.8

0.02
X0

Absolute Displacement (m)

0150

200

250300

350

400

500

550

600

0.28mrad

-0.02

-0.04

-0.06

450

From C-sector-0.08-0.1z(m)C-sector

Dispersion reduction (Weak lens)
J-ARC

Emittance measurement at 5-sector
PF Injector

AB

Weak lens
1C3254γε y (mmimrad )γε x (mmimrad )
800

600

700
500

600
400

500
400

300

300
200200100

100

00-100020406080100120020406080

100

C to ２ sector Q-magnet [ % ]C to ２ sector Q-magnet[ % ]Kink at 2-1 is dominant ?

Quadrupole mis-alignment
may be dominant.

120

Dispersion compensation by beam orbit

kickkick back

Reference (green line)
C-1 Standby (blue line)

Short range wakefield(simulated using ELEGANT)
Charge : 5 nC
Mis-alignment : σx=0.5mm
Initial emittance = 10 mm mrad
δp : 0.1 %, σz : 1mm
enx (mm.mrad)

enx @sector 5 (mm.mrad)
100

2.00E+0290

1.80E+0280

1.60E+02

enx (mm.mrad)

70

1.40E+0260
1.20E+02

41.8501.00E+02

40
8.00E+0130

6.00E+0120
100-0.2

-0.15

-0.1

-0.05

4.00E+01

12.2
2.00E+01

00.05

0.1

0.15

DX0 (mm)

Initial offset (mm)

0.2
-0.5

-0.4

-0.3

-0.2

0.00E+00
-0.1
00.1

0.2

Initial offset (mm)

0.3

0.4

0.5

Beam diagnostic station

RF-Deflector => Longitudinal slice observation.
- Compensation of RF-Emittance- Measurement of short range wakefield => Initial offset
ω Δt ⎞ ⎛⎛ eVX-band TM110 Cavity ChainβΔx= β⎜⎟ sin ⎜ φE⎝⎠ ⎝zdeflector

screendeflector

RFdeflector → screen

screen=π⎞beamσ x = β screenε screen

yΔxscreen / σ x =xσ y (t ) = β yε y (t )tβ deflector ⎛ eVdeflectorωRF Δt ⎞⎜⎟ε screen ⎝Ebeam⎠

Vdeflector = 20 MV , f RF = 2.856GHz , Δt = 1 ps, β deflector = 10m→ Δxscreen / σ x = 4
Vdeflector = 50 MV , f RF = 11.424GHz , Δt = 1 ps, β deflector = 10m→ Δxscreen / σ x = 40

Placed at 3rd switch yard⎟2⎠

Summary and plan for machine studyFY2010:• Improvement for machine study:– Agreement of measured and simulated optics.
– Emittance measurement.
– Continuous machine study during PF injection.

•Dispersion:– Both of measurement and simulation are proceeding.
– Determine cancellation method as soon as possible.

•

Determine alignment tolerance by simulation.

FY2011:• Alignment (Beam-based & Conventional method)• Installation of RF-Gun.
=> Emittance measurement using lower emittance beam
• Development of RF-Deflector
to measure short range wakefield and compensate RF emittance=> Install by FY2012• Installation of wire scanner.

Plan to SuperKEKB injection• Final Target:– Multi-line beam optics control software development– Continuous emittance preservation corresponding to emittancemeasurement during operation.

• Emittance preservation– Research for emittance growth• Dispersion (Yoshida, Iida)• RF emittance (Matsumoto, Yoshida)• Short range wakefield ( Zang, Sato, Iida(e+), Yoshida )• CSR (Zang, Yoshida)– Hardware development for beam diagnostics and compensation• X-band RF deflector (Matsumoto, Yoshida)• 3rd switch yard – Beam diagnostic station (Sato, Yoshida)• Q-magnet with active mover• Pulse steering (Kamitani)– Alignment• Beam based alignment(Yoshida), Laser alignment(Suwada)/ Wire + Water pipe (Sugawara)

Appendix:Emittance sourceApparent emittance growth caused by dispersion

K=eg
dp, dx = η xpp

η′( s) = 0
Δε dispersion =px2x 2 − px x

(α = 0, βγ = 1 → γ =η (s) δ (s)≈2 β221β2− ε0 =)δ ( s ) : energy spread(ε 0 β x + (ηδ )2)()′

ε 0γ x + (η ′δ ) − ( ε 0α x + ηη ′δ 2 ) − ε 022x( sB ) = R11 x( s A ) + R12 x ( s A ) + R16δ ( s A )δ ( sB ) = δ ( s A ) for given acceleration phaseδ ( sB ) =p( sA )
δ ( s A ) for a part of energy changep ( s A ) + Δp

⎛ R11 … R16 ⎞⎛ x ⎞⎜⎟⎜ ⎟⎜⎟⎜ ⎟⎜R⎟
R66 ⎟⎜⎝ 61⎠⎝ δ ⎠

δ ∼ 0.1%, β ∼ 50m
γΔε ∼ 0.016 mm ⋅ mrad ( for η ∼10 mm )γΔε ∼ 6.4 mm ⋅ mrad ( for η ∼200m m <=) measured valueRF emittance caused bycoupler of accelerating structure• Dipole, Quadrupole

2～5×10-5Ez = E0 sin(ωt )∑ an r n cos nϕΔε1 =eE0 L
a1σ yσ z
22me c πeE0 L2Δε 2 =2aσ2 y σz
22me c π
E0 = 17 MV / m, L = 35mm ,σ y = 2mm, σ z = 3mm = 10 ps
a1 = 5 ×10−5 , 480cell→ Δε1 = 80 nm → γΔε = 1.2 mmimrad

a1 was determined bysimulation

Short Range Wakefield
2e2 N e ∞d ⎛d⎞ ⎛ 2π ⎞δ′ρzW()( z′ − z, s ) x ( z′, s ) dz′⎟⎟ γ ( s ) x ( z , s ) =t
⎜ γ ( s ) x ( z , s ) ⎟ + ⎜⎜2 ∫zds ⎝dsm0 c⎠ ⎝ λ (s) ⎠Wt ( s ) = ∫ ρ ( s′ ) Wt δ ( s − s′ ) ds′ ∝γΔε x =2σza3L β ⎛ e 2 N eWt ( z ) ⎞⎜⎟ , γ ( s ) = γ ( 0 ) (1 + G f s )22γ ( 0 ) G f⎝ m0 c⎠xalignment

2σ z ∼ 10 ps = 3mm, xalignment = 0.1mm, q = 5 nC , Wt δ ( z ) = z × 3 ×1015 V / C / m 2γ ( 0 ) = 4000, G f = 0.01 (from C sector)
γΔε x = 2.9 mm ⋅ mrad

σz=1mmCSR (ARC section)zdE ( s )12qe− xeσz=−dxds
2π 3 3R 2σ z4 ∫−∞z
32.00E-07

σzx2−2−x

1 3 3σ z
γ R= 0.03 mradθ rad 2 ∼1.00E-07-10-8-6-4

0.00E+00-20246810dE/ds-1.00E-07-2.00E-07-3.00E-07-4.00E-07-5.00E-07-6.00E-07
s/σs

Emittance growth is calculated
similar to Dispersion

222⎛⎛ W ΔErms ⎞ ⎞⎛⎛ W ′ΔErms ⎞ ⎞ ⎛⎛ ΔErms ⎞ ⎞⎟⎜ ε 0γ x + ⎜⎟ − ⎜ ε 0α x + WW ′ ⎜⎟ε = ⎜ ε0βx + ⎜⎟⎟⎟⎜⎝ E0 ⎠ ⎟⎜⎝ E0 ⎠ ⎟⎠ ⎜⎝⎝ E0 ⎠ ⎟⎠⎝⎠⎝= 1.2 nmγε = 0.02 mmimrad

2

Dispersion (change energy by ARC)

r0_kbe 1.6092 → 1.6249 GeV
R16= 53 mm R16 = 210 mm(Δp = 0.0153 GeV)γη ( s ) δ ( s )∼ 30 mm ⋅ mrad
δ = 0.1% (8ps) , η = 210 mm =>2 β22

C-1 Standby での Dispersion

SP_28_4 -2.417 -0.233 2.139↓
SP_28_4 2.463 -2.127 1.220

R16 = 5mm / (160MeV/1.6GeV) = 50 mm @ 2-8
R36 = 2mm / (160MeV/1.6GeV) = 20 mm @ 2-8
Same as r0_kbe → J-ARC dispersion is not large.

Injector control softwarefor SuperKEKB• Multi-line / Multi-bunch : orbit & dispersion
compensation• Continuous measurement using study mode

• Response measurement for all magnets.
→ Paraxial & reference orbit measurement→ Beam based alignment / Dispersion

Paraxial and reference orbit
MultipoleQSteering
Steering

Transfer matrix⎛X⎞⎛ X ⎞ ⎛ O0 ⎞⎜ ′⎟⎜ ′⎟ ⎜ ′ ⎟=XM⎜ ⎟⎜ X ⎟ + ⎜ O0 ⎟ ,⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠Reference matrix⎛ X0 ⎞⎛ X 0 ⎞ ⎛ x0 ⎞⎜ ′⎟⎜ ′⎟ ⎜ ′⎟=XMref0⎜ ⎟⎜ X 0 ⎟ + ⎜ x0 ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠x = X − X 0 , x′ = X ′ − X 0′
⎛x⎞
⎛x⎞
⎜ ′⎟
⎜ ′⎟=xM
paraxial⎜ ⎟⎜x ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠Q

Paraxial↓calculation⎛ X 0 ⎞ ⎛ x0 ⎞⎛X⎞
⎛x⎞⎜ ′⎟ ⎜ ′⎟⎜ ′⎟⎜ ′⎟=+XMxM
paraxialref⎜ X 0 ⎟ + ⎜ x0 ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠⎝ ⎠ ⎝ ⎠⎛ X 0 ⎞ ⎛ x0 ⎞⎛X⎞⎜ ⎟ ⎜ ⎟⎜ ⎟= M paraxial ⎜ X ′ ⎟ + ( M ref − M paraxial ) ⎜ X 0′ ⎟ + ⎜ x0′ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠Emittance measurement
700

Recent modification of fitting program for the wire scanner
700

1nC (FWHM:10.509ps)

3nC (FWHM:9.658ps)
5nC (FWHM:9.776ps)

600

3nC (FWHM:9.658ps)
5nC (FWHM:9.776ps)

500

7nC (FWHM:11.118ps)

500

7nC (FWHM:11.118ps)

γε y [π .mm.mrad]

γε x [π .mm.mrad]

1nC (FWHM:10.509ps)

600

400
300
200
1000

400
300
200100B

Csector50BC
sector5