1. Compensation of Detector Solenoid with Large Crossing Angle
Y. Nosochkov, A. Seryi
ILC-Americas Workshop, SLAC, October 14-16, 2004

2. Detector solenoid model
Large horizontal crossing angle (~35 mrad) in the IR-2 for g-g collisions.
Beams travel at an half-crossing angle to the solenoid field.
Solenoid field overlaps one or both the Final Focus quadrupoles.
Example of solenoid field model for Silicon Detector (SiD) and Large Detector (LD) in the NLC FFS (IP is at z = 0). The plotted field is on a beam path at 10 mrad angle with respect to the solenoid axis (for 20 mrad crossing angle).
SiD 16.7 Tm
LD 14.4 Tm

3. Solenoid perturbation of beam optics
Coupling of x-y betatron motion.
Vertical orbit due to beam passing at horizontal angle and offset.
Vertical dispersion due to the horizontal angle and FF horizontal dispersion.
Focusing in x-y planes.
If FF quadrupoles are outside of detector solenoid
Solenoid coupling is just an x g y beam rotation causing a modest vertical beam size growth at IP (less than a factor of 2).
Vertical orbit and dispersion from solenoid cancel at IP due to opposite effects of the longitudinal and radial solenoid fields (but the IP angle is not zero).
If FF quadrupoles are inside the solenoid
Solenoid and quad overlap generates the new dominant coupling term <yx’> (x’ g y) causing a large growth of vertical beam size at IP (a factor of 100).
Overlap creates residual vertical orbit and dispersion at IP.
Solenoid analysis below is based on the NLC study for 20 mrad crossing angle and the design IP parameters: L*=3.51 m, bx=8 mm, by=0.11 mm, h’x=0.0094, sx=243 nm, sy=3 nm, sxp=30.4 mrad, syp=27.3 mrad, sE=0.25%, and beam energy E=250 GeV (details in SLAC-PUB-10592).

4. Strong coupling due to solenoid and quad overlap
Example of the test “Tiny” solenoid model without quad overlap (red) and with additional small field D1=0.1 Tm (blue) and D2=0.5 Tm (black) added on top of the first FF quad. IP phase space is normalized to the ideal beam sigma (green – no solenoid, red – with “Tiny” solenoid). Even a small part of the solenoid field inside the FF quad significantly increases the IP vertical beam size.
Tiny 18 Tm
0 Tm
0.1 Tm
0.5 Tm
The left figure presents a test, where the detector solenoid is replaced by a short and weak test solenoid (0.5 Tm), and its effect on the IP beam size, coupling (<yx’>), vertical dispersion (<yE>), normalized, and IP orbit is shown versus the solenoid position z. Clearly, the largest effect is created when the solenoid overlaps the FF quads, at z= m.

5. Comparison of solenoid effects at IP for 250 GeV beam with 20 mrad crossing angle for different detector models without solenoid compensation. Here, BL is the total solenoid field on one side of IP, and BLFD is its fraction over the FF quads. The normalized coupling terms are in units of beam size growth. Note the strong dependence of vertical beam size growth on the amount of BLFD field.

6. Phase space at IP (normalized to ideal sigma) for different detector models without solenoid compensation. Green – no solenoid, red – with solenoid. Note that the beam size growth is of similar magnitude for zero and 20 mrad crossing angles.
“Tiny” model, q = 20 mrad
LD model, q = 20 mrad
SiD model, q = 20 mrad
LD model, q = 0
A compensation system for detector solenoid is required to achieve the design beam size and position at IP.

7. Since the dominant solenoid aberrations are generated in the overlapped FF quadrupoles, it is important that the compensation system is effective against this part of the solenoid field.
In earlier studies, the main approach for solenoid correction was to use a skew quadrupole placed near the FF quad (or a rotation of the FF quad). This compensates the major part of IP coupling, but further correction, including orbit and dispersion, requires the use of additional correctors such as tuning knobs. Note that for the lower energy beam options (to 50 GeV), all these correctors have to be optically stronger.
It is desirable to achieve the most local compensation of the aberrations created by the solenoid overlap with the FF quads. Therefore: why not to physically reduce this part of the solenoid field by an opposite compensating solenoid field? This leads to the idea of using short and weak antisolenoids placed at the FF quad locations as part of the detector. This way, the detector solenoid field in the FF quads is directly reduced by the antisolenoids for the most local correction. And since the overlapped field is typically small, rather weak antisolenoids are needed. The extra advantage is that by removing the most of the overlapped field, the antisolenoids restore the properties of a bare solenoid with self-compensation of the vertical orbit and dispersion. It has been shown that the antisolenoid method provides a better correction than the skew quads, and it is more robust at lower beam energies. However, the technical implications and impact on detector design have not been studied.

8. Example of SiD solenoid compensation using one weak antisolenoid (1
Example of SiD solenoid compensation using one weak antisolenoid (1.74 Tm) placed at the first FF quad.
Total field with and w/o antisolenoid
IP phase space with an antisolenoid, dsy = 29%
With antisolenoid and linear knobs, dsy = 0.3%
Corrected IP orbit. Although y’¹0, e+e- collide head-on in y-plane due to e+e- orbit antisymmetry.
Orbit and coupling at IP versus half-crossing angle without (top) and with antisolenoid (bottom). Correction is optimized at +10 mrad. It can be reoptimized for other angles.

9. Example of LD solenoid compensation using two weak antisolenoids (2
Example of LD solenoid compensation using two weak antisolenoids (2.26 and 0.07 Tm) placed at two FF quads.
Total field with and w/o antisolenoids
IP phase space with antisolenoid correction , dsy = 23%
With antisolenoids and linear knobs, dsy = 0.9%
Corrected vertical IP orbit

10. Energy dependence of antisolenoid compensation for SiD
Solenoid aberrations are significantly increased at lower beam energies, and the vertical focusing <yy’> becomes the 2nd largest linear term after <yx’>.
For the same antisolenoid field, a good correction of the dominant coupling term <yx’>, vertical dispersion and orbit is maintained for a full range of energies ( GeV).
Additional tuning of IP beam size using the linear and second order optics knobs is needed at the lowest energies.
Relative beam size growth at IP versus beam energy ( GeV) for SiD compensation using one antisolenoid and several linear optics knobs. The second order knobs may be used at low beam energies to reduce the enhanced high order terms such as <yx’x’>.

11. Technical issues (not studied)
Antisolenoid at location of the first FF quad (closest to IP) should be an integral part of the detector solenoid and aligned on the detector axis.
It should have two coils for adjustment of its field and longitudinal position.
It should be compact to minimize interference and space taken from the detector.
It should be able to withstand the longitudinal forces from the detector solenoid field. These forces prohibit aligning this antisolenoid on other than the detector axis.
The 2nd antisolenoid (if needed) may be actually wound and aligned on the 2nd FF quad since the forces from the detector field should be already small.
Position of antisolenoid in SiD

12. Conclusions
It is found that the method of weak antisolenoids provides a good compensation of the detector solenoid aberrations at IP in a linear collider.
The antisolenoid method is found to be more efficient than a skew quad correction.
The optimum parameters of the antisolenoid depend on the detector solenoid model and the crossing angle, but not on IP b-functions. With a proper optimization, this method should provide an adequate compensation at the larger crossing angle of ~35 mrad for g-g.
The antisolenoid compensation is found excellent at the nominal beam energy of 250 GeV and should be sufficient at much lower energies when using additional linear and 2nd order tuning knobs.
Antisolenoid has to be placed at the FF quad location and designed as part of the detector. It is desirable to have means for fine tuning of antisolenoid strength and effective position. The technical issues of this design and impact on the detector need to be studied.
As a 2nd choice, the skew quad correction with the aid of tuning knobs should still be able to provide the correction.