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

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.

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:

Optics of DANE Siddharta

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.

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

Luminosity tune scan D.Shatilov M.Zobov

DA tune scan

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

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

Off energy DA

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.

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