1. Some notes on the SuperB Dynamic Aperture
E.Levichev, P.Piminov
Budker INP, Novosibirsk
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

2. Introduction
- All calculations have been made with the 6D tracking code Acceleraticum developed at BINP by E.Levichev and P.Piminov - The results were compared with those by Y.Onishi (04/12/2007)
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

3. Lattice from Pantaleo sb70_newff.mad
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

4. IR sextupoles SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

5. Sextupole families vs. DA
Blue: crab(-), IR(-), SD/SF(+) Green: crab(+), IR(-), SD/SD(+) Red: crab(-), IR(+), SD/SF(+) Black: crab(+), IR(+), SD/SF(+) IR sextupoles dominate in the on-energy DA limitation.
Crab – crabbing sextupoles IR – chromatic sextupoles in the IR SD/SF – chromatic sextupoles in the arcs
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

6. Thin and thick IR sextupoles
Phase advance along the sextupole length destroy the exact –I condition and causes the dynamic aperture reduction
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

7. Sensitivity to the -I Real and ideal –I between the SX4 and SX0.
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

8. Dynamic aperture
Sigma_x = 75 um Sigma_z = 13 um Beta_x = 8.3 m Beta_z = 24.8 m
50 S_z
12 S_x
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

9. Sensitivity to multipole errors
Main effect is due to the errors in the IR quads. Special care for its error should be taken.
Multipole errors in quadrupoles (CDR, p.173 Table 3-10) were considered as 1 rms. 5 random seeds, the distribution is truncated at 2 rms.
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

10. Nonlinear detuning
Strong vertical nonlinearity cause reduction of both vertical and horizontal (through nonlinear coupling) DA.
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

11. Nonlinear chromaticity
Levichev/Piminov Acceleraticum Y.Onishi SAD
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

12. On-energy DA tune scan Hor Ver Luminosity scan by D.Shatilov
DA scan, colors indicate DA size.
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

13. DA optimization - chromaticity vector - sextupole pair
- N small steps for chromaticity correction by every sextupole pair along the
chromaticity vector
- The pair providing the largest DA at the step is fixed
- The procedure is repeated until the chromaticity is corrected
- Off energy aperture optimization is available
- Achromatic sextupole (zero dispersion) is included by the gradient search
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

14. Optimization algorithm
IP beta chromaticity correction step-by-step by the IR sextupoles under condition of maximum DA.
Tunes chromaticity correction by arc sextupoles under condition of max DA.
Dispersion free sextupoles can be used for additional harmonics correction by the gradient search method.
DA betatron tune scan and searching for the best tune point together with luminosity scan.
Re-optimization (usually small) of the DA in this point.
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

15. DANE with crab waist DA optimization
Black – nonoptimized. Red and blue –
optimized for two working points.
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory

16. Conclusions
Main limitation of the SuperB DA is due to the IR chromatic sextupoles in spite of –I condition
–I compensation is sensitive to the small phase detuning or non-zero sextupole length
Additional study of the IR sextupole arrangement is needed
It seems the optimization by the best sextupole pair method can be applied separately for the IR and the rest ring.
SuperB, Paris, May 9-11
E.Levichev, P.Piminov: Dynamic Aperture of the SuperB Factory