1. IR Lattice with Detector Solenoid
Yuri Nosochkov
XIV SuperB General Meeting
INFN-LNF, Frascati, Italy, Sep 27 – Oct 1, 2010

2. Outline New configuration of IR final doublet quadrupoles
(from M. Sullivan) for v.12 lattice
Implementation and IR optics rematch
Detector solenoid model
(based on scheme by K. Bertsche and M. Sullivan)
Solenoid model implementation
Orbit correction
Coupling correction
Vertical dispersion correction
Twiss and horizontal dispersion correction

3. IR quadrupole modifications
L* = 32 cm
QDP
QD0A
QD0B
QF1
QD0P
QD0
QF1A
L* = 30 cm
v.12 IR
New IR
HER
LER
QD0P: permanent; QD0, QF1: SC with the same gradient in LER & HER; QD0A, QF1A: adjustable SC quads in HER. HER and LER quads are better separated. Suggested crossing angle: 60 mrad, energies: 4.18 and 6.69 GeV.

4. Beta functions at the doublet
LER v.12
HER v.12
LER new
HER new
After optics rematch: No large change in IR beta functions.

5. Simplified detector solenoid model in the IR
Assumptions and simplifications based on proposed scheme by K. Bertsche and M. Sullivan:
Detector solenoid field is 1.5 T in the ±55 cm region near IP (between left and right SC cryostats) and cancelled outside of this region by means of compensating solenoids.
MAD model:
Hard edge solenoid is tilted with respect to beams by ±33 mrad (for v.12 crossing angle).
Overlap of permanent quads and the solenoid is modeled using thin lens quads with thick solenoid slices between them.
Note: Constant solenoid field profile can be easily replaced by a more realistic Z-dependent profile using many slices with gradually changing field.
HER
LER

6. Solenoid effects
Detector solenoid creates the following linear effects on the beam:
Coupling of X & Y betatron motion (rotation around S-axis).
Vertical orbit due to the solenoid horizontal angle with respect to the beam.
Horizontal orbit induced by vertical orbit and coupling.
Vertical and horizontal dispersion due to the Y and X orbit bending.
Perturbation of Twiss functions due to weak focusing in X & Y planes.
Note:
MAD solenoid element assumes hard edge field profile. The end effects are included in approximation of a linear radial field (Br ~ r) integrated over the edges.
A soft edge profile can be simulated by using a sequence of solenoid slices with gradually changing field.
Higher order terms may not be completely included (such as sextupole fringe terms).

7. Solenoid orbit and rotationBz Bs Bx
Bx(edge)
Horizontal field projection due to crossing angle creates vertical orbit. Horizontal field at the solenoid edge provides some compensation.
Solenoid rotation angle:
For one side of solenoid:
q = 29.6 mrad at 4.18 GeV
q = 18.5 mrad at 6.69 GeV

8. Correction of solenoid rotation
Ideally, one wants to compensate solenoid as local as possible without interference with FF chromatic sections.
In case of no magnets inside the solenoid and enough free space, the simplest correction consists of anti-solenoids at each end. This works for all particle energies.
BzL
-BzL/2
In our case, the solenoid overlaps permanent quads, and the free space exists only after the SC quads. An overlapped quad causes additional coupling because the beam sees it as a skew quad. This can be corrected by rotating the quad frame by the angle of the beam rotation. The SC quads should be also rotated by the solenoid angle in order to use anti-solenoid after them to compensate the rotation. Alternatively, skew winding on SC quads can be used to simulate the rotation. Some residual coupling will remain because the quads cannot be rotated continuously with the solenoid angle. This can be corrected with additional weak skew quads. Q

9. Correction system Other correctors are outside of this region
The designed correction system compensates each half-IR independently and contains on each side of IP:
Rotated permanent quads.
Skew winding on SC quads to simulate rotation.
SC anti-solenoid of strength 1.5T x 0.55 m aligned with the beam axis.
2 vertical and 2 horizontal dipole correctors for orbit correction.
4 skew quads at non-dispersive locations for coupling correction.
2 skew quads at dispersive locations for correction of vertical dispersion and slope.
The nominal FF quads are used to rematch the Twiss functions and horizontal dispersion.
Solen
QS1 V1 H1 H2 V2
Anti-
solen
Other correctors are outside of this region

10. Skew quad locations based on sensitivity
QS1
QS3
QS2
QSDY
QS4
QSDPY
Coupling
sensitivity
[bxby]1/2
CCX
CCY
ROT
Dxby1/2sinmy
Dxby1/2cosmy
Vert. dispersion
slope sensitivity

11. FF orbit after correction
LER
Orbit is cancelled within ±7 m of IP
HER

12. FF dispersion after correction
LER
Vertical dispersion is localized
within the FF
HER

13. FF beta functions after correction
A few constraints were slightly adjusted to make a good match.
LER
HER

14. Coupling angle-1 for complete ring
LER
For graphic representation of coupling MAD command EIGEN can calculate tilt angles for two normal mode ellipses projected onto XY plane: TILT1 and TILT2 (in degrees).
HER
Coupling is localized within the FF

15. Coupling angle-2 for complete ring
LER
HER

16. Skew quad K-values (m-2) and dipole corrector angles (mrad)
LER (L/R)
HER (L/R)
QS1 / /
QSDY / /
QSDPY / /
QS2 / /
QS3 / /
QS4 / / V1 /
0.155 / 0.155 V2
0.113 / 0.113 / H1 / / H2 / /
Mostly weak correctors.
Asymmetry is due to FF optics asymmetry (mostly dispersion).

17. Conclusion
An example of detector solenoid correction is designed based on hard edge solenoid field and updated configuration of FF doublet quadrupoles.
The solenoid model can be updated to include solenoid field variation.
The system uses rotated permanent FF quads, skew winding on SC quads, an anti-solenoid and a full set of skew quads and orbit correctors for complete compensation on each side of IP. Most of the correctors are rather weak.
Other options were tried (without anti-solenoid and/or without quad rotations) which require stronger correctors.
If Panofsky quads are used instead of SC quads, the skew windings may not be possible, but the whole quad assembly may be rotated. In this case, there will be vertical quad offsets (correctable by dipole correctors) and the rotation will not be optimal for one or both beams. Therefore, the residual effects and corrector strengths should be higher.
The solenoid effects on FF bandwidth and dynamic aperture require evaluation.
Missing non-linear solenoid field effects need to be studied and modeled.