Magnetic axis tolerances for the SSS magnets Field Quality Working Group Magnetic axis tolerances for the SSS magnets S. Fartoukh, B. Jeanneret, A. Lombardi and Y. Papaphilippou January 10th, 2006

FQWG, Y. Papaphilippou et al. Misalignment and feed-down (see S.Fartoukh, O.Bruning, LHC Project Report 501) Due to positioning errors i.e. difference of the beam axis with respect to magnetic axis a multi-pole of order n create harmonics of order k with Rref = 17mm and (x0,y0) the transverse displacements Taking k=n-1 and neglecting all higher orders, the leading order multi-pole feed down is The beam axis is taken to be the center of the BPM, after alignment and data post-processing (O. Bruning, Mini-workshop on LHC alignment, 2000) 10/01/2006 FQWG, Y. Papaphilippou et al.

Alignment requirements for SSS (see O Alignment requirements for SSS (see O.Bruning, Mini-workshop on LHC alignment, 2000) Element Alignment Feed down Error Limit MQ (MQT,MQS*) ΔΧ, ΔΥ b1,a1 orbit aperture Roll a2 coupling a2 in MB MS (MSS*) ΔΧ b2 tune, β-beat tune, aperture ΔY a3 chromatic coupling a3 in MB MO b3 Chromaticity, DA Q’=1, b3 in MB a4 (2,-2) resonance a4 in MB MCB coupling to other plane BPM resolution 10/01/2006 FQWG, Y. Papaphilippou et al.

S. Fartoukh and O.Bruning in LHC Project report 501 Alignment specifications for SSS (Mini-workshop on LHC alignment, 2000) Following the previous beam physics arguments, alignment requirements were computed The expected misalignments for SSS are purely random (and within the required ones) All misalignment specifications for the machine budget were estimated and added up (quadratic sum) with respect to the machine axis S. Fartoukh and O.Bruning in LHC Project report 501 10/01/2006 FQWG, Y. Papaphilippou et al.

Misalignments for the MQ The main quad misalignments with respect to the reference closed orbit are expected to be 0.36mm in both planes This corresponds to 40% of the closed orbit machine budget (LHC Project report 501) The rms value of the tunnel motion is 0.28mm The rms tolerance for the MQ magnetic axis with respect to the geometrical axis is This is more than two times bigger than the expected specification (T. Tortschanoff, Mini-workshop on LHC alignment) 10/01/2006 FQWG, Y. Papaphilippou et al.

Misalignments for the MS or MSS The expected misalignments of the lattice sextupoles MS or MSS with respect to the geometrical axis are 0.17mm in both planes Taking into account the rms tolerance of the MQ w.r.t. the GA (0.23mm), the rms positioning error w.r.t. to the MQ before installation is Considering the level arm effect due to the distance between the MQ and sextupoles and the two targets (alignment tolerance of 0.1mm), the rms tolerance after installation is (M. Karppinen, Mini-workshop on LHC alignment) 10/01/2006 FQWG, Y. Papaphilippou et al.

Misalignments for the MO and MQT The misalignments for the lattice octupoles MO are computed for creating a chromaticity < 1 due to feed-down (sextupole) The rms value is estimated at 0.3mm with respect to the MQ (0.2mm w.r.t. to the GA) The random misalignments’ tolerance for the skew quadrupole correctors MQT may be computed for creating an orbit distortion < 0.1mm due to feed-down (dipole) when all families are powered for providing a tune-shift of 0.1 There rms value is estimated at 0.3mm with respect to the MQ (0.2mm w.r.t. to the GA) Note that for both correctors the effect of the level arm is negligible due to the proximity of the BPM to both of them. 10/01/2006 FQWG, Y. Papaphilippou et al.

Summary of magnetic axis tolerances Corrector Reference frame RMS standard deviation [mm ] MQ SSS GA 0.2 (0.1 expected) MO 0.2 (0.2 expected) MQT MS, MSS The tolerance is taken as 2.5 standard deviations 10/01/2006 FQWG, Y. Papaphilippou et al.

Tolerances on roll angle Magnet Reference frame RMS Tolerance [mrad] MQ SSS Mean plane 0.5 MO Not yet rigorously estimated (between 2 and 5 mrad) MQT MS MCB 10/01/2006 FQWG, Y. Papaphilippou et al.

FQWG, Y. Papaphilippou et al. Remarks The SSS magnetic axis tolerances are comfortable with respect to the expectations by the magnet experts Considering the partial drop of the AC mole, the performance may not be compromised if the already existing measurements confirm the expectations A clear disadvantage would be the inability to estimate the SSS field direction This will prevent the use of SSS rotations to put the magnet in tolerance for both apertures, but also correct a magnet tilt, as shown by the great majority of the already treated cases 10/01/2006 FQWG, Y. Papaphilippou et al.