1. Study and Optimization of Dynamic Aperture for the SuperKEKB LER E.Levichev and P.Piminov, BINP SB RAS, Novosibirsk, Russia

2. LER Main Parameters ParameterValueUnit Circumference, L3.0162km Energy4.0GeV Horizontal emittance, ε x 5.77nm·rad Compaction factor, α2.76·10 -4 Betatron tunes, ν x /ν z 45.53/45.57 Natural chromaticity, ξ x /ξ z -107.4/-807.5 Comp. chromaticity, ξ x /ξ z -0.76/-3.66 Horizontal beta @ IP3cm Vertical beta @ IP270um Horizontal sigma13um Vertical sigma0.08um (the lattice from ItalyIP19B-work3c3.sad)

3. IR Optical Functions

4. Main sources of the DA limitation QC1 fringe field Vertical sextupoles SL2 QC2 fringe field Kinematics term Fringe fields of other quadrupoles Arc sextupoles In order of weakening

5. DA from the main nonlinearities QC2 Kinematic QC1SL2 Other lenses

6. QC1 and QC2 DA optimization QC1 and QC2 fringes can be compensated by octupole corrector distributed in the quad + separate octupoles in the IR vertical chromatic section Magenta – QC1&QC2 fringes corrected, green – QC1&QC2 + other quads corrected, blue – QC1&QC2 + other quads + kinematics corrected, black – uncorrected DA

7. SL2 sextupoles optimization Thick SL2 sextupoles are corrected by additional low strength sextupole correctors placed close to the main ones Blue – corrected SL2 sexts, red – all other sextupoles added, black – uncorrected DA

8. Situation before global sextupole optimization Tune momentum dependence. Black – initial one: horizontal tune for positive and negative momentum deviation goes to 0.5 at ±1.4%; vertical tune for -1% goes to 0.5. This value define the bandwidth. Red is after optimization. On- and off- energy dynamic aperture. Synchrotron oscillations are on

9. Global sextupole optimization Tune momentum dependence after global sextupole optimization (red). The bandwidth increases to –2.4%, +2.2% On- and off- energy dynamic aperture is also increases after global sextupole optimization. Synchrotron oscillations are on

10. Horizontal DA vs momentum deviation Black is initial, red is final

11. DA tune scan (Very preliminary, resolution is poor) Such scans are useful for the DA optimization together with luminosity optimization Horizontal DA to the left and vertical DA to the right. Color indicates the DA size. High order resonances are not identified yet.

12. Recommendations for the Crab Sextupoles Insertion - The best location for the crab sextupoles is seems just after the chromatic correction sections. - The chromatic correction sections could be designed more compact and the vertical beta (as it seems) may be decreased - It is better to arrange linear and the nonlinear dispersion function zero in the crab sextupole - Arcs is not a proper place for the crab sextupoles from our experience - Additional sextupole compensator to correction the length effects of the crab sextupoles can be applied - In principle, our experts can consider the linear optics for the crab sextupoles insertion

13. CRAB = 0, IR Sext = 0 CRAB = 0 CRAB = 1 Y Sections Distorted by CRAB Spin Rotators Distorted by arc sexts Example from SuperB: Distortion of the particle motion due to nonlinear coupling Picture show horizontal envelope of the last stable vertical trajectory vs azimuth of the storage ring. CRAB+ CRAB-

14. Compact Y Chromatic Section Beta functions of the Vertical Chromatic Section of the Super-Tau-Charm Factory Bmax Bmin M(1→2) M(2→3)=-I 1 2 3

15. After several optimization steps, it was managed to improve the dynamic aperture of the SuperKEKB LER for both on-and off-momentum particles. The quadrupole fringe field nonlinearities and kinematical effects were compensated by octupole correctors inserted in the FF quadrupoles (main sources of perturbation of this kind). The strong sextupoles of the IR vertical chromatic section, which deteriorate the dynamic aperture through the third order aberration terms, can be corrected by small additional sextupole correctors placed in the same section. Global optimization of all sextupole families by simplex method allows increasing the dynamic aperture for on- anf off- momentum cases. The same algorithm can be applied to the HER of the SuperKEKB project. As the strong crab sextupoles can reduce the dynamic aperture just like the SL2 sextupoles in the vertical chromatic section, their influence can be corrected by the same low strength sextupoles located in the vicinity of the main sextupoles. Summary