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Tunability of the PS2 NMC Lattice. Hannes Bartosik, Yannis Papaphilippou. July 30 th , 2009. Design Parameters. Optics constraints Nominal Working Point (13.25, 8.20). Tunability Studies. Drift: 0.6m. Drift: 0.55m. Drift: 0.6m. Magnets lengthened.
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Tunability of the PS2 NMC Lattice Hannes Bartosik, Yannis Papaphilippou • July 30th, 2009
Design Parameters • Optics constraints • Nominal Working Point (13.25, 8.20)
Tunability Studies Drift: 0.6m Drift: 0.55m Drift: 0.6m Magnets lengthened • NMC lattice tuned to about 800 working points • Tuning the phase advance in the NMC cell: x = [255°, 288°] y = [147°, 194°] yields working points in the range of Qx = [12.85, 14.00] Qy = [7.8, 9.2] • Present PS2 lattice with slight modifications in quadrupole lengths and drifts used for the study (module FODO cell quads lengthened from 0.6 to 0.8m, drifts shortened adequately) • Chromaticity is corrected in first order (using 4 family scheme) • The following plots show data for the entire ring …
Gamma transition (t) Ring: NMC cell: t imaginary and bigger than 28i for all working points t in the NMC cell itself between 19i and 39i Missing working points could not be matched due to the vicinity to the integer tunes
Maximal Beta functions • y below 60m for almost all working points tuned • significantly above 70m only forvertical tunes close to 8 and 9 x around 60m below half integers (13.5,8.5) reaches high values (> 100m) for horizontal tunes close to the integers 13 and 14 High peak values in the Suppressor!
Chromaticities before correction • x between -20 and -30 for almost all working points apart from the integers of horizontal tune (13, 14) • values up to 500 for Qx~14 • y between -13 and -15 for almost all working points … • Values up to 23 for certain working points
Quadrupole gradients – NMC Cell K1 = 1/(B) (By/ x) < 0.1/m2 • All quads in the NMC Module below 0.1/m2 for all working points, except first doublet quadrupole (PS2.MQB.MOD.3 with length=2m) • Gradient in tune region of interest only slightly above target value • In present lattice not much space for increasing the length of this magnet (orbit corrector and sextupole in either side) • Required gradient ~ 18T/m
Quadrupole gradients - Suppressor • All quads below the limit value of 0.1/m2 for all working points, except PS2.MQD.SUP.6 (length=2.8m) • This type of magnet appears only in the suppressors of the present lattice • High gradient due to space constraints (short doublet cell) • Potential solution: increase length of Suppressor while shortening long straight section
Maximal Dispersion Dx Ring: NMC cell: Required maximal dispersion Dx below 6m is easily achieved for all realistic working points … Maximal dispersion in the NMC module itself never exceeds 3.25m
Conclusion Present NMC lattice provides good tunability t and Dx under control and within required region For optimal tunability, quadrupole lengths may have to be revised to meet maximal gradient requirement Possible improvement by shortening the straight section and increasing the length of the dispersion suppressor Non-linear analysisongoing (Resonancedrivingterms, dynamicaperture,…)