1. LOW EMITTANCE CELL WITH LARGE DYNAMIC APERTURE
4th Low Emittance Rings Workshop
September 17, 2014, Frascati, Italy
LOW EMITTANCE CELL WITH LARGE DYNAMIC APERTURE
P.Piminov, A.Bogomyagkov, E.Levichev, S.Sinyatkin, K.Zolotarev
Budker Institute of Nuclear Physics
Novosibirsk, Russia

2. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
GOAL
Design of a basic lattice cell for the next generation Synchrotron Light Sources (or Damping Rings) with emittances εx ~ εz~ 10 pm·rad and large Dynamic Aperture.
The emittances provide diffraction limited SR at λ ~ 1 Å.
“Basic” cell means that it can be used as an universal block for lattices with different energies and emittances.
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

3. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
LIMITATIONS
Emittance reduction gives
Very strong focusing lattice with large chromaticity
Low dispersion in straight sections and reduction of the chromatic sextupoles effectiveness
Strong IBS requires large (dynamical) momentum acceptance and additional decrease of the zero-current emittance…
… See item 1.
Finally, the sextupoles are extremely strong and DA is extremely low.
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

4. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
SOLUTION
Usual approach: many sextupole and octupole families optimizing resonance driving terms, tune-amplitude dependence coefficients, etc. Sometimes it works, sometimes not.
Our approach: low emittance cell with –I transformation in both planes. Pairs of sextupoles in proper positions provide large (ideally for kick sextupoles – infinite) dynamic aperture.
Finite length sextupole pair cancels the second order aberrations, higher orders still exist, but the DA is large (although not infinite). For details see A. Bogomyagkov et al “Effect of the Sextupole Finite Length on Dynamic Aperture in the Collider Final Focus”, arXiv:
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

5. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
CELL PARAMETERS
Our cell example aims the ring with ~10 pm emittance at 3 GeV and large DA (2 cm in horizontal direction)
Energy, E 3
GeV
Length, L
54.04 m
Angle, Θ 8˚
Phase advance, νx/νz
3.43/3.49
Natural chromaticity, ξx/ξz
-7.05/-9.76
Compaction factor, α
2.43·10-5
Horizontal emittance, εx 10
pm·rad
Energy spread, σΔE/E
2.5·10-4
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

6. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
RING PARAMETERS
The ring based on the cell using the horizontal-field damping wigglers
(Anton Bogomyagkov’s talk 9:30 (UTC+2) Thursday, 18 September, 2014)
Energy, E 3
GeV
Length, L
1.379 km
Phase advance, νx/νz
84.52/91.78
Natural chromaticity, ξx/ξz
-184/-251
Compaction factor, α
7.84·10-5
w/o IBS
with IBS
Bunch current, I0 70 μA
Beam current, I 50 mA
Emittances, εx/εz
3.0/8.5
15.6/8.6
pm·rad
Energy spread, σΔE/E
1.2·10-3
1.3·10-3
Bunch length, σs
7.7
8.0 mm
Another ring example using the same approach: A.Papash’s (previous) talk “Low Emittance Model for the Anka Synchrotron Radiation Source Including Nonlinear Effects”
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

7. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
DESIGN PRINCIPLES
Low emittance – TME-like cell. But exact TME is not suitable. We suggest a Split Magnet TME (SM-TME).
TME: compact, low emittance,
No –Ix,z with large DA is found
TME
SM-TME: still compact, still low emittance, –Ix,z with large DA is found
SM-TME
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

8. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
UNIT CELL ηx βz -I βx
μx= π
μz= π
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

9. P.Piminov, Low Emittance Cell with Large Dynamic ApertureX Y Y X M
Dispersion free SS – 5-Bend-Achromat (5BA) – Dispersion free SS
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

10. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
BETATRON TUNE SCAN
Horizontal DA, βx=2.1 m Vertical DA, βz=2.9 m
Note that there are no sextupole resonances (cancelled by the –I transformer)
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

11. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
Observation βx=2.1 m & βz=2.9 m
ΔE/E=0
ΔE/E=+1%
σx = 4.5 μm
~3000 σx
ΔE/E=-1%
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

12. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
ENERGY ACCEPTANCE
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

13. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
DETAILS
IPAC-14
P.Piminov, Low Emittance Cell with Large Dynamic Aperture

14. P.Piminov, Low Emittance Cell with Large Dynamic Aperture
CONCLUSION
Low emittance SM-TME cell with –Ix,z transformer and large DA is proposed
Only 2 sextupole pairs correct the natural chromaticity (second order aberrations are cancelled exactly)
Addition sextupole compensators were introduced to reduce the third order aberrations
Optimal phase advances
The cell can be used to design the ring with any emittance and energy (the cell is quite universal)
P.Piminov, Low Emittance Cell with Large Dynamic Aperture