s x * Limitations and Improvements Paths

Frank Zimmermann, CLIC “Away Day” 26 March 2006

x* Limitations and Improvements Paths

Damping Rings

Maxim Korostelev, Frank Zimmermann


ATF single-bunch emittances:x~3.5-4.3 m (CLIC: ~0.5 m)y~13-18 nm (CLIC: 3 nm)z~8640 eVm (CLIC: <5400 eVm)

6D phase-space density in CLIC ~70 times higher

how can we go further?

?

ATF

CLICnew CLIC?


2004: CLIC-NLC comparison for ITRP “Wise Men” NLC DR CLIC DR

energy 1.98 GeV 2.42 GeV*

circumference ~299 m 364 m

arc cell length ~6 m 1.8 m

hor. phase advance/arc cell* 108o 210 o

#arc TME cells* ~30-40? 100

total wiggler length* 44 m 152 m

wiggler period* 27 cm 10 cm

bunch population 7.6-15.2x109 4.2x109

longit. emittance , s 10.6 keVm 5.5 keVm

transv. emittances x, y ~3000 nm, 30 nm 660 nm, 3.3 nm

damping times x,y, s 3.63, 4.08 ms, 2.18 ms 2.64 ms,1.32 ms

*smaller emittance due to smaller bend angle / arc cell,less emittance detuning, more damping, smaller Hx in wiggler

*higher energy reduces intrabeam-scattering effect


further progress in 2005Wiggler 1

permanent magnet

Wiggler 3

Nb3Sn superconductor

Bw 1.7 T 2.5 T

w 10 cm 4.5 cm

x 550 nm

(133 nm w/o IBS)

354-375 nm

(79 nm w/o IBS)

y 3.3 nm

(0.8 nm w/o IBS)

2.9-2.3 nm

(0.5 nm w/o IBS)

z 4724 eVm

(2551 eVm w/o IBS)

4817-4997 eVm

(3433 eVm w/o IBS)also: less charge per bunch


possible approachesfor achieving even smaller emittance

1) larger damping-ring circumference

(weaker arcs & longer wigglers)

+ increased beam energy

2) damping in linac

3) laser wiggler?


1) larger circumference + higher energy

not self-consistent,artificially kept longitudinal emittance at

constant value (4500 eVm), opening-angle effect not included

w/o IBS horizontal emittance is 100 nm w/o

IBS at 3.74 GeV

MAD-X calculation


4/3,

4/3,

22/12/1ˆ43232

;

ˆ2

15322/12

4/3,

4/3,

2/7

ˆ43,2

;

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15322/12

4/3,

4/3,

2/7

ˆ43,2

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152

32,1;

ˆ)(ˆ

)1()(2

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)1()(2

ˆ2ˆ2

2

3

2

22

2/1

2

3

2

22

2/1

2

3

2

53

yNxNw

sB

Bdwws

wsN

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syNxN

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wyN

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syNxN

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dr

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w

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analytical equations including IBS (Bane approx.) & opening angle

H. Braun, M. Korostelev, F. Zimmermann, CLIC Note 594, 2004

dispersive terms opening angle

IBS


result of my analytical calculation

includes opening angle

Karl Bane’s IBS approximation

almost self-consistent (z fixed = 1 mm)

for case 2x circumference,I find large discrepancy in z

(w/o IBS) between analyticalformula and MAD-X!?


exact calculation by Maxim“nominal” 2x arc 2x arc

2x straights

2x straights

E 2.42 GeV 3.74 GeV 3.74 GeV 3.74 GeV

C 365 m 529 m 704 m 530 m

x 375 nm

(79 nm)

421 nm

(73 nm)

340 nm

(66 nm)

315 nm

(135 nm)

y 2.3 nm

(0.5 nm)

2.65 nm

(0.5 nm)

2.14 nm

(0.415 nm)

1.98 nm

(0.862 nm)

z 4997 eVm

(3433 eVm)

5030 eVm

(4100eVm)

4975 eVm

(4221 eVm)

5020 eVm

(4480 eVm)

best


exact calculation by Maxim cont’d

“nominal” 2x arc 2x arc

2x straights

2x straights

Q’x -102 -187 -200 -114

Q’y -135 -254 -266 -148

SF

[103 m-3]

7.85 14.1 15.0 8.76

SD

[103 m-3]

-9.99 -18.2 19.3 -11.06

>10% larger sextupole strength implies >10% smaller dynamic aperture


new ring parameters?present option

circumference 357 m 530 m

energy 2.424 GeV 3.746 GeV

rf frequency 1.875 GHz

rf voltage 2.39 MV 20.5 MV

energy loss/ turn 2.19 MeV 18.93 MeV

total wiggler length

152 m 304 m

synchr. radiation power

0.3 MW 1.9 MW


2) damping in linacH. Braun, M. Korostelev, F. Zimmermann, CLIC Note 594, 2004

damping factor 2

beam energy 34 GeV

addt’l linac length 640 m / side (~1/Bw)

addt’l voltage 48 GV (~1/Bw)

wiggler peak field Bw 10 T

wiggler period w 1.5 cm

x,y 1.5 m, 8 m

final x 272 nm (~x w2 Bw

3)

final y 3.5 nm (~y Bw )

wiggler parametersquite challenging


3) laser wigglernaturally small periodassume laser parameters of Snowmass Posipol Proposal (CLIC note 639)

2laser

w

laserw IZ

cB 02

2laser wiggler equivalence:

zyx

laserlaser

cAI

2/32type YAG

Alaser 592mJ

w 0.53 m

x,y 5 m

z 0.9 mm

Ilaser 5x1020 W/m2

Bw 4090 T

Tm 01.0Tm 002.0 wwBundulator regime!

7-min,; 106.9

10

3

laser

cyxN

13.0

ionGeV/collis 4.43

16 22

E

E

ArE e ~6% transverseemittance reductionper laser collision!however →50%!


conclusions

laser wiggler → unacceptable energy spread

superconducting wiggler in linac beyond present state of the art

double wiggler length & increase beam energy to 3.74 GeV→15% reduction in x & y; but expect impact on dynamic aperture ~10% & 6x increased heat load


spare slide


DR equilibrium emittance without IBS & w/o 1/

7.9/1/1 22 arcw

6.1// 33 arcw

HH present design:

11.0 ,15

8/

/1/11

//1

min3

23

22

3333

FC

NH

HH

J

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w

w

arcw

arcw

x

arcqx

arcdiparcww

arcarcdipwwww

x

arcqx LlLB

LlLB

J

FC2222

5525233

const1

const1

above can also be written as

s x * Limitations and Improvements Paths

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