1. DANE Upgrade DA Optimization
December 12, 2006
E.Levichev, P.Piminov, P.Raimondi, M.Zobov

2. Optimization algorithm
- 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
6D aperture optimization is available
Harmonic sextupole (zero dispersion) is included by the gradient search.

3. Starting point: DANE Siddharta
Lattice from Manuela Boscolo
Betatron tunes
Qx/Qy
5.103/5.179
Compaction factor α
0.0193
Damping times (ms)
τx/ τy/ τs
39.8/34.5/16.1
Horiz emittance (nm-rad) x
390
Energy spread
E/E
3.910-4
Natural chromaticity
ξx/ ξy
-3.2/-25.9*)
IP1 betas (m)
β*x/ β*y
0.2/0.006
Beam size at IP1 (m)
*x/*y
284/3.4
*) With sextupole term in the wiggler end pole
Corrected chromaticity:

4. Optics of DANE Siddharta

5. Optimization scenario
Original DA
Optimization of the original DA
DA tune scan and tune point choosing together with the luminosity scan
Checking of other nonlinear elements: octupole magnets, wiggler end poles, etc.

6. DA at the original tune point
Original sextupoles
Sextupoles optimized by the best pair method

7. Luminosity tune scan
D.Shatilov
M.Zobov

8. DA tune scan

9. Optimized tune and DA Original {5.103, 5.179]/non optimized
Point from region 1 {5.105, 5.160}/optimized
Point from region 2 {5.131, 5.116}/optimized

10. Summary table Tune Point Nx Ny Comments 5.103, 5.179 +13/-16 180
Original
+16/-23
250
Original, optimized
5.105, 5.160
+20/-26
300
5.131, 5.116
+20/-23
270
Coupling resonance

11. Off energy DA

12. Other nonlinearities adjustment
Influence of octupoles to the optimized sextupole set is negligible
Wiggler end pole sextupole including in the optimization process gives practically the same value (10-15% less) as it is now. It seems there is no necessity to modify it.

13. Summary
Best sextupole pair optimization provides increasing of the DANE Upgrade DA
Tune point with high luminosity and large DA is chosen
No necessity to modify mechanically the wiggler pole