E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 DYNAMIC APERTURE OF THE STRONG RF FOCUSING STORAGE RING E.Levichev, P.Piminov (Budker Institute of Nuclear Physics, Novosibirsk)

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Main goal Simulation of the dynamic aperture and non-linear effects in the SRFF regime for the DAFNE storage ring with strong coupling of the transverse and longitudinal particle motion. It was expected that powerful synchro-betatron resonances can reduce the area of the beam stable area.

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Tool 6D tracking code Acceleraticum which used G.Ripken (DESY) formalism with realistic path elongation in magnetic elements. Canonical variables are: Transformation of the longitudinal coordinate was solved explicitly for various magnetic elements.

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Model DAFNE “structure A” (C.Biscari) with high compaction factor and high synchrotron tune. Main parameters: Q x /Q z 4.824/5.212 Q s at U RF = 5 MV  at IP  x0 /  z0 –6.27/–13.53  x /  z sext OFF 3.58/–17.43  x /  z sext ON 0.36/–10.79 xx 6.37×10 -7 m-rad  E /E 3.82×10 -4

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Bunch length modulation

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 On-energy dynamic aperture ► Wigglers only. ► Wigglers+sexts mm m m

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Main transverse resonances Maximum DA (mm) as a function of the tune point.

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Main resonance harmonics CosSin  C nm Horizontal harmonics A 15 (m -1/2 )–0.08–0.17–1.11 A 314 (m -1/2 )0.28– Coupled harmonics B 15 (m -1/2 )0.27–0.37–2.60 B +15 (m -1/2 ) B - -6 (m -1/2 )0.65–

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Transverse space trajectories

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Off-energy dynamic aperture Sigma_E = 0.04%

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Transverse DA vs. synchrotron tune

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Energy dynamic aperture

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Longitudinal phase space 0 MV1 MV 5 MV 10 MV

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Off-energy tune scan - 1 Initial amplitude of energy oscillation = 0 Black – betatron resonances Red – satellites

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Off-energy tune scan - 2 Initial amplitude of energy oscillation = 0.25 % Black – betatron resonances Red – satellites

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Off-energy tune scan - 3 Initial amplitude of energy oscillation = 0.5 % Black – betatron resonances Red – satellites

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Synchrobetatron resonances (a) Resonances excited by the dispersion in the chromatic sextupoles ResonanceWidth (b) Resonances excited by momentum oscillation + chromaticity (vert.!) Satellite strength

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Alternative tune point Old tunes: (4.825, 5.212) New tunes: (4.939, 5.212)

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Example of the SBR study at VEPP-4M (single beam)

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Example of the SBR study at VEPP-4M (colliding beams)

E Levichev -- Dynamic Aperture of the SRFF Storage Ring Frontiers of Short Bunches in Storage Rings INFN-LNF, Frascati, 7-8 Nov 2005 Conclusions (1) Due to the strong coupling, synchrobetatron resonances decrease the dynamic aperture in the chosen tune point. (2) It is possible to find alternative working point by fine tune adjustment to obtain the dynamic aperture which seems large enough. (3) Improvement in the vertical chromaticity compensation seems reasonable to reduce strength of the modulation synchrobetatron resonances. (4) New sextupole arrangement may provide both chromaticity correction and reduction of the synchrobetatron lattice factors.