IR Coupling Correction with Detector Solenoid Off

1. IR Coupling Correction with Detector Solenoid Off Yuri Nosochkov XV SuperB General Meeting California Institute of Technology Pasadena, USA, Dec 14 – 17, 2010

2. Summary of the detector solenoid correction scheme • (Detailed report presented at the XIV SuperB General Meeting, September 2010, http://agenda.infn.it/conferenceDisplay.py?confId=2303) • The IR correction system is designed to compensate the solenoid effects independently in each half-IR. The corrector elements per half-IR: • To cancel detector solenoid field outside of ±55 cm region: • Bucking solenoids (designed by K. Bertsche and M. Sullivan). • For coupling correction: • Rotation angle in the QD0P permanent quads. • Skew quad winding coil in the QD0 and QF1 SC quads. • SC anti-solenoid on beam axis with strength of 1.5T x 0.55 m. • 4 skew quads at non-dispersive locations. • For correction of vertical dispersion: • 2 skew quads at dispersive locations. • For orbit correction: • 2 vertical and 2 horizontal dipole correctors. • For correction of Twiss functions and horizontal dispersion: • The nominal IR quads. • (based on v.12 lattice with SC QD0, QF1)

3. IP region Detector Solenoid Bucking QD0P (M. Sullivan)

4. Solenoid corrector locations Correctors within ±7.5 m of IP (symmetric relative to IP) Anti- solen LER H2 V1 Detector solenoid H1 QS1 V2 IP H2 QD0P QS1 H1 QF1 V1 Anti- solen QD0 V2 HER QS1 QSDY QSDPY QS2 QS3 QS4 IP CCY CCX ROT Skew quads in one half-IR QS1,QS2,QS3,QS4 – at zero dispersion QSDY,QSDPY – at non-zero dispersion [bxby]1/2

5. Solenoid OFF assumptions • Ideally, when the detector solenoid is turned off, all the solenoid correctors should be turned off for uncoupled ideal lattice. • However, the assumption is that the skew quad coil strength in the SC quads cannot be changed since it is assumed to be part of the main coil design. • It is also assumed that the rotation angle in QD0P permanent quads is either unchanged or can be adjusted. • With these assumptions, the remaining effect is the betatron coupling from the skew coil in the SC quads and QD0P rotation angle.

6. Coupling correction considerations Skew quad locations QD0P rotation SC skew coil QS1 QS2 QS3 QS4 IP CCY CCX ROT [bxby]1/2 • In the solenoid ON case, the solenoid coupling is mainly canceled by the anti-solenoid, while the QD0P rotation angle and SC skew coil produce minimal coupling because they are effectively aligned with the solenoid rotation angle. As a result, the QS1,QS2,QS3,QS4 skew quads are rather weak. • In the solenoid OFF case, the QD0P rotation angle and the SC skew quad coil produce large coupling . Therefore, the correcting QS1,QS2,QS3,QS4 skew quads will be stronger. • Since the QD0P and SC skew quad coupling is created at about the same phase (≈p/2 from IP), it may be possible to localize its correction using mostly the QS1 skew quad (located at similar phase) and adjustment of the QD0P angle, leaving the QS2,QS3,QS4 relatively weak. • Two options were studied: • QD0P rotation angle is kept the same as in the case of solenoid ON. • QD0P angle is adjusted for most local correction (where QS2,QS3,QS4 are weak).

7. Quad phase locations near IP QD0P, SC quads QD0, QF1, and QS1 skew quad are about at the same phase, therefore it should be possible to localize the coupling correction by adjustment of QS1 strength and QD0P angle. QD0P QD0 QF1 QS1 IP

8. LER corrector strengths weak • Solenoid OFF, option 1 • QS1,QS2,QS3,QS4 strengths are increased compared to solenoid ON. • Solenoid OFF, option 2 • QD0P angle is adjusted by a factor of -3.87 for more local correction. • Most of the correction is done by stronger QS1 quad. • Strengths of QS3, QS4 are very low.

9. HER corrector strengths weak • Solenoid OFF, option 1 • QS1,QS2,QS3,QS4 strengths are increased compared to solenoid ON. • Solenoid OFF, option 2 • QD0P angle is adjusted by a factor of -0.94 for more local correction. • Most of the correction is done by stronger QS1 quad. • Strengths of QS3, QS4 are almost canceled.

10. LER coupling angle (TILT1) • Comparison of coupling angle after correction for solenoid ON and OFF cases using MAD command EIGEN which calculates tilt angles for two normal mode ellipses projected onto XY plane: TILT1 and TILT2 (in degrees). IP is at center. • Solenoid OFF option 2 significantly reduces the residual coupling perturbation. Solenoid ON Solenoid OFF Option 1 Solenoid OFF Option 2

11. LER coupling angle (TILT2) Solenoid ON Solenoid OFF option 2 leaves a smaller residual coupling perturbation. Solenoid OFF Option 1 Solenoid OFF Option 2

12. HER coupling angle (TILT1) Solenoid ON Similarly to the LER, the HER solenoid OFF option 2 leaves a smaller residual coupling perturbation. Solenoid OFF Option 1 Solenoid OFF Option 2

13. HER coupling angle (TILT2) Solenoid ON Solenoid OFF option 2 leaves a smaller residual coupling perturbation. Solenoid OFF Option 1 Solenoid OFF Option 2

14. Summary • The IR lattice v.12 with SC QD0, QF1 quads was used. • It was assumed that the skew quad coil strength in the SC QD0, QF1 quads cannot be turned off or changed when the solenoid is OFF. • It was assumed that the rotation angle in the permanent quad QD0P can be adjusted. • It is shown that when the detector solenoid is OFF and the bucking solenoids and anti-solenoid are OFF, the correction of QD0P and QD0, QF1 coupling can be done using the included QS1,QS2,QS3,QS4 skew quads. • The solenoid OFF coupling correction is most efficient and localized when the rotation angle in the QD0P permanent quad is optimized.