Tunability of the PS2 NMC LatticeHannes Bartosik, Yannis PapaphilippouJuly 30th, 2009

Design Parameters Optics constraints

Nominal Working Point (13.25, 8.20)

Parameter Value Units

Injection kinetic energy 4 [GeV]

Extraction kinetic energy ~ 50 [GeV]

Circumference 1346.4 [m]

B 169.8 [Tm]

Transition energy imaginary, adjustable [GeV]

Maximum bending field < 1.7 [T]

Maximum quadrupole gradient < 17 [T/m]

Maximum beta functions < 60 [m]

Maximum dispersion function < 6 [m]

Parameter Value Units

Maximum beta functions 60 [m]

Maximum dispersion function 3.28 [m]

t 36 i [1]

Maximum quadrupole gradient ~ 17 [T/m]

Tunability Studies 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 …

Drift: 0.6m Drift: 0.6mDrift: 0.55m

Magnets lengthened

Gamma transition (t)

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

Ring: NMC cell:

Maximal Beta functions

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!

y below 60m for almost all working points tuned

significantly above 70m only for vertical tunes close to 8 and 9

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

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

Recall: B= 169.8TmLimit: Max. Quad. gradient < 17T/m K1 = 1/(B) (By/ x) < 0.1/m2

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

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

Ring: NMC cell:

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 analysis ongoing (Resonance driving terms, dynamic aperture,…)