1. sx* Limitations and Improvements Paths
Damping Rings
Maxim Korostelev, Frank Zimmermann
Frank Zimmermann, CLIC “Away Day” 26 March 2006

2. Frank Zimmermann, CLIC “Away Day” 26 March 2006
ATF single-bunch
emittances:
gex~ mm
(CLIC: ~0.5 mm)
gey~13-18 nm
(CLIC: 3 nm)
gez~8640 eVm
(CLIC: <5400 eVm)
6D phase-space density
in CLIC ~70 times higher
how can we go further?
ATF
CLIC ?
new
CLIC?
Frank Zimmermann, CLIC “Away Day” 26 March 2006

3. Frank Zimmermann, CLIC “Away Day” 26 March 2006
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
x109
4.2x109
longit. emittance , ges
10.6 keVm
5.5 keVm
transv. emittances gex, gey
~3000 nm, 30 nm
660 nm, 3.3 nm
damping times tx,y, ts
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
Frank Zimmermann, CLIC “Away Day” 26 March 2006

4. Frank Zimmermann, CLIC “Away Day” 26 March 2006
further progress in 2005
Wiggler 1
permanent magnet
Wiggler 3
Nb3Sn superconductor Bw
1.7 T
2.5 T lw
10 cm
4.5 cm
gex
550 nm
(133 nm w/o IBS) nm
(79 nm w/o IBS)
gey
3.3 nm
(0.8 nm w/o IBS) nm
(0.5 nm w/o IBS)
gez
4724 eVm
(2551 eVm w/o IBS)
eVm
(3433 eVm w/o IBS)
also: less charge per bunch
Frank Zimmermann, CLIC “Away Day” 26 March 2006

5. possible approaches for achieving even smaller emittance
larger damping-ring circumference
(weaker arcs & longer wigglers)
+ increased beam energy
2) damping in linac
3) laser wiggler?
Frank Zimmermann, CLIC “Away Day” 26 March 2006

6. larger circumference + higher energy
MAD-X calculation
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
Frank Zimmermann, CLIC “Away Day” 26 March 2006

7. analytical equations including IBS (Bane approx.) & opening angle
H. Braun, M. Korostelev, F. Zimmermann, CLIC Note 594, 2004
dispersive terms
opening angle
IBS
Frank Zimmermann, CLIC “Away Day” 26 March 2006

8. result of my analytical calculation
includes opening angle
Karl Bane’s IBS approximation
almost self-consistent (sz fixed = 1 mm)
for case 2x circumference,
I find large discrepancy in ez
(w/o IBS) between analytical
formula and MAD-X!?
Frank Zimmermann, CLIC “Away Day” 26 March 2006

9. exact calculation by Maxim
“nominal”
2x arc
2x straights E
2.42 GeV
3.74 GeV C
365 m
529 m
704 m
530 m
gex
375 nm
(79 nm)
421 nm
(73 nm)
340 nm
(66 nm)
315 nm
(135 nm)
gey
2.3 nm
(0.5 nm)
2.65 nm
2.14 nm
(0.415 nm)
1.98 nm
(0.862 nm)
gez
4997 eVm
(3433 eVm)
5030 eVm
(4100eVm)
4975 eVm
(4221 eVm)
5020 eVm
(4480 eVm)
best
Frank Zimmermann, CLIC “Away Day” 26 March 2006

10. exact calculation by Maxim cont’d
“nominal”
2x arc
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
-9.99
-18.2
19.3
-11.06
>10% larger sextupole strength implies >10% smaller dynamic aperture
Frank Zimmermann, CLIC “Away Day” 26 March 2006

11. Frank Zimmermann, CLIC “Away Day” 26 March 2006
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
Frank Zimmermann, CLIC “Away Day” 26 March 2006

12. Frank Zimmermann, CLIC “Away Day” 26 March 2006
2) damping in linac
H. Braun, M. Korostelev, F. Zimmermann, CLIC Note 594, 2004
e 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 lw
1.5 cm
bx,y
1.5 m, 8 m
final gex
272 nm (~bx lw2 Bw3)
final gey
3.5 nm (~by Bw )
wiggler parameters
quite challenging
Frank Zimmermann, CLIC “Away Day” 26 March 2006

13. Frank Zimmermann, CLIC “Away Day” 26 March 2006
3) laser wiggler
naturally small period
assume laser parameters of Snowmass Posipol Proposal (CLIC note 639)
laser wiggler equivalence:
type
YAG
Alaser
592mJ lw
0.53 mm
sx,y
5 mm sz
0.9 mm
Ilaser
5x1020 W/m2 Bw
4090 T
undulator regime!
~6% transverse
emittance reduction
per laser collision!
however sd→50%!
Frank Zimmermann, CLIC “Away Day” 26 March 2006

14. Frank Zimmermann, CLIC “Away Day” 26 March 2006
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 gex & gey;
but expect impact on dynamic aperture
~10% & 6x increased heat load
Frank Zimmermann, CLIC “Away Day” 26 March 2006

15. Frank Zimmermann, CLIC “Away Day” 26 March 2006
spare slide
Frank Zimmermann, CLIC “Away Day” 26 March 2006

16. Frank Zimmermann, CLIC “Away Day” 26 March 2006
DR equilibrium emittance without IBS & w/o 1/g
present design:
above can also be written as
Frank Zimmermann, CLIC “Away Day” 26 March 2006