ELIC Low Beta Optics with Chromatic Corrections Hisham Kamal Sayed 1,2 Alex Bogacz 1 1 Jefferson Lab...

ELIC Low Beta Optics with Chromatic Corrections

Hisham Kamal Sayed1,2

Alex Bogacz1

1 Jefferson Lab2 Old Dominion University

Hisham K. Sayed EIC Meeting Hampton University 2008

2

Chromaticity effects

•Chromaticity is the derivative of the betatron tunes versus fractional momentum offset

•If chromaticity & momentum spread become large enough that the betatron tunes overlap a nonlinear resonance particle loss

d

dC xx

)(

Δp/p>0

Δp/p=0

Δp/p<0

quadrupole

Δp/p>0

Δp/p=0

Δp/p<0

quadrupole

Sextupoles


3

•ELIC have very large values of βmax (~ 3/32 km for electron ring) at the ultra strong final focus quadrupoles high sensitivity to the misalignments and field errors.•Low β* (~ 5/5 mm for electron ring) & small momentum compaction huge chromatic aberrations and large momentum acceptance.

Why chromaticity correction is important for ELIC?

0001.00003.0/ pp

Effect of chromaticity and momentum offset on beta functions around IR’d

Bet

a x,y


4

The final focus chromatic correction system

• Pairs of sextupoles. • Sextupoles in each pair are placed at –I (minus identity

transformation in transverse phase space) from each other the resulting adverse spherical aberrations induced by the sextupoles are cancelled.

• There must be dispersion at the sextupoles the sextupole strengths are at a minimum.

• Dispersion needs to be generated around the IR and terminated at the matching section

QdQ

fS`

d

S``

d

S`f S``f


5

1800

Wed May 14 12:15:03 2008 OptiM - MAIN: - D:\Hisham Work\Accelerator Physics\Alex\IR\ELIC\IR_Arc\IR_elect_mirror

30

00

0

10

-10

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]

BETA_X BETA_Y DISP_X DISP_Y

IPIP

Matching Two IR’s for ELIC Electron Ring

1800

Fri May 16 10:05:15 2008 OptiM - MAIN: - D:\Hisham Work\Accelerator Physics\Alex\IR\ELIC\IR_Arc\IR_elect_mirror

10

00

50

BE

TA_

X&

Y[m

]

DIS

P_

X&

Y[m

]


IPIP

64.1237115.876


10

00

10

-10

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]


Matching Quadrupoles


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IR Dispersion wave and 1.2o degrees chicane with vertical crossing

1800


30

00

0

10

-10

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]


•Dispersion wave generated and confined with 4 vertical dipoles

•Dispersion is zero at IP

•Dipole parameters L[cm]=110 B[kG]=4.5

IPIP

Dipoles


7

Vertical layout of the electron IR

IP IP

Longitudinal direction (m)

Ver

tical

dire

ctio

n (c

m)

20 m 50 m50 m


8

β Chromaticity correction with sextupoles

β- functions around the interaction region, the green arrows represent the sextupoles pairs.

The phase advance, showing the –I transformation between the sextupoles pairs

1800

Thu May 15 15:29:20 2008 OptiM - MAIN: - D:\Hisham Work\Accelerator Physics\Alex\IR\ELIC\IR_Arc\IR_elect_mirror

90

00

5-5

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]


1800

Thu May 15 15:30:10 2008 OptiM - MAIN: - D:\Hisham Work\Accelerator Physics\Alex\IR\ELIC\IR_Arc\IR_elect_mirror

0.5

10

PH

AS

E_

X&

Y

Q_X Q_Y

Vertical dispersion

Horizontal dispersion


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Phase space in vertical plane before and after applying the correction scheme

Initial phase spacephase space after two pass through 2 IR’s No correction

phase space after two pass through 2 IR’s after correction

Vertical plane Δp/p~0.0006

0.003-0.003 Y [cm] View at the lattice beginning

1.2

-1.2

Y`[

mra

d]

Y

Y`

0.006-0.003 Y [cm] View at the lattice end

1.2

-1.2

Y`[

mra

d]

0.0006-0.003 Y [cm] View at the lattice end

1.2

-1.2

Y`[

mra

d]


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The tunes versus the momentum offset

Tune Vs Momentum offset

-3.00E-05

-2.50E-05

-2.00E-05

-1.50E-05

-1.00E-05

-5.00E-06

0.00E+00

5.00E-06

1.00E-05

1.50E-05

-0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006

Dp/p

Tu

nes Qx

Qy

Tune variation due to passing through two IR’s for horizontal and vertical directions

•Target The tunes should show a reduced nonlinear behavior with the change in momentum offset


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Momentum compaction versus momentum offset

Momentum compaction Vs Momentum offset

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

0.0004

-0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006

Dp/p

Mo

men

tum

co

mp

acti

on

alpha

Momentum compaction variation due to passing through two IR’s for horizontal and vertical directions

Target smaller change in compaction factor with the change in the momentum offset


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The chromaticity versus the momentum offset

chromaticity versus the momentum offset Horizontal direction

-509

-508

-507

-506

-505

-504

-503

-502

-501

-0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006

Dp/p

chro

mat

icity

chromaticity versus the momentum offset vertical direction

-4500

-4450

-4400

-4350

-4300

-4250

-4200

-0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006

Dp/p

Ch

rom

atic

ity

nuxy

Chromaticity variation due to passing through two IR’s for horizontal and vertical directions

Target fixed chromaticity for different Dp/p


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Conclusion & Future Work

A novel design for the interaction region and matching section for EIC electron

ring presented (A. Bogacz).

A scheme for correcting inherent lattice chromaticity was implemented into the

design

The scheme was verified via multi-particle tracking simulation through the lattice

using a matrix based optics code OptiM.

Presented results show a proof-of-principle for an effective chromaticity

correction scheme.

Further simulations and optimization will be carried out with more robust tracking

package ELEGANT.

Dynamic aperture studies will be carried out.

Considering adding octupoles to correct higher order effects and spherical

aberrations from sextupoles (S. Derbenev)

ELIC Low Beta Optics with Chromatic Corrections Hisham Kamal Sayed 1,2 Alex Bogacz 1 1 Jefferson Lab...

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