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

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

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

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:0909.4872. P.Piminov, Low Emittance Cell with Large Dynamic Aperture

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

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

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

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

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

P.Piminov, Low Emittance Cell with Large Dynamic Aperture BETATRON TUNE SCAN Horizontal DA, cm @ βx=2.1 m Vertical DA, cm @ 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

P.Piminov, Low Emittance Cell with Large Dynamic Aperture Observation point @ 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

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

P.Piminov, Low Emittance Cell with Large Dynamic Aperture DETAILS http://arxiv.org/abs/1405.7501 MOPRO017 @ IPAC-14 P.Piminov, Low Emittance Cell with Large Dynamic Aperture

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