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

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

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 4 + 4 coefficients) 06/12/2005 LOC meeting, AL and YP

Sector 3-4 features 45 SSS quads, following the pattern 1+2*2+3+3*4+6+9+10=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

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

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 4 + 4 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

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

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

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

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