1. A. Lombardi and Y. Papaphilippou
LOC meeting
Preliminary Sorting for the Short Straight Section quadrupoles of Sector 3-4
A. Lombardi and Y. Papaphilippou
December 6th, 2005

2. Sorting purpose and strategy
Minimize the effect of quadrupole error (b2) with respect to beta-beating
Quality factor – integrated 2nd order resonance driving term
Four coefficients, one for each plane and aperture:
Compare with random distribution of N=47 quads
06/12/2005
LOC meeting, AL and YP

3. Local compensation and HP magnets
Best match of b2 between pairs of quads with phase advance of ~π/2
Control evolution of 4 coefficients along the sector
Treat high-permeability (HP) magnets with high b2 individually
Check that when HP effect disappears (smaller b2), quality factor still smaller than for random distribution (minimise globally coefficients)
06/12/2005
LOC meeting, AL and YP

4. Sector 3-4 features
45 SSS quads, following the pattern 1+2*2+3+3* =45 (as in all sectors)
All 10 types of SSS only available in this sector
4 SSS with high permeability magnets already allocated, but not frozen (move them around within a type)
4 SSS of one type are not yet assembled, giving flexibility to choose from a large pool of individual MQs (around 30)
06/12/2005
LOC meeting, AL and YP

5. Typical b2 distribution (Sector 3-4)
HP magnets
Taking the raw b2 the rms values for aperture 1 and 2 are 17 and 20 respectively (10 and 13 for b2 without the HP effect)
06/12/2005
LOC meeting, AL and YP

6. Algorithm and results Pair magnets within a type having similar raw b2
Match pairs across neighboring SSS types
Reiterate until coefficients are minimum
Check robustness of sequence when effect of HP magnets when disappears
Try to balance the coefficients to a minimum (least square sense)
Final result:
Coefficients for raw b2 : 5, 7 and 22, 2 (compared with 60 and 70)
Coefficients for “corrected” b2 : 9, 31 and 3, 1 (compared with 43 and 49)
For both cases, sorting achieves coefficients below 1 rms
06/12/2005
LOC meeting, AL and YP

7. Sequence and driving term evolution
06/12/2005
LOC meeting, AL and YP

8. Driving term evolution with corrected HP effect
06/12/2005
LOC meeting, AL and YP

9. Comparison with other sectors
4-5 and 3-4 are better, as it was possible to choose magnets at the quadrupole level (less constraints)
06/12/2005
LOC meeting, AL and YP

10. Overview Perspectives discussion S.Fartoukh and M.Giovannozzi
Robust sorting for sector 3-4 using driving term minimization
Sequence to be verified by magnet experts (M.Modena and T. Tortschanoff)
More efficient when choosing individual MQ’s (as for 45)
Perspectives discussion S.Fartoukh and M.Giovannozzi
Control local beta beating by using
Correct effect of permeability on b2
Function by P.Hagen and E.Todesco
Apply it to all the magnets or only HP ones
Minimize globally both cases (for raw and corrected b2 )
Check evolution of dispersion beating
Check effect of sorting on linear tune-shift
06/12/2005
LOC meeting, AL and YP