1. SBS Magnet, Optics, and Spin Transport
John J. LeRose
Technical Review of the Super BigBite Project
January 22, 2010

2. SBS: a “large” acceptance, small angle, moderate resolution device

3. 48D48 Basic Geometry

4. To guarantee that it’s ours we need to formally transfer ownership.
The magnet is “available”.

5. Needed Modifications to the Magnet
For small angles at short distance
Cut opening in Yoke
Modify coils
For Polarized Target & background control
Add field clamp to reduce field at target
For beam transport to the dump
Field clamp (again)
Add magnetically shielded beam pipe
Add solenoid

6. Layout of system with part of yoke removed
Field Clamp
Shielded Beam pipe
Modified Coils

7. With magnetically shielded pipe with 1kA/cm current density solenoid
B at target < 2 Gauss
Calculations by Stepan Mikhailov
Using “Mermaid” (units are kG, cm)
Nice clean magnetic field

8. Effect on beamline by transverse field is effectively eliminatedx x’ θ
1 30m
Effect on beamline by transverse field is effectively eliminated

9. Various Views of the Modified Magnet

10. It’s really very simple!
Optics
It’s really very simple!

11. This is what it looks like to me!

12. TRANSPORT formalism Arbitrary Trajectory Reference Trajectory y x r0
Magnetic Midplane
References:
K.L. Brown, D.C. Carey, C. Iselin and F. Rothacker, Designing Charged Particle Beam Transport Systems, CERN (1980)
K.L. Brown, SLAC Report-75 (
…...

13. Relative change in momentum
TRANSPORT formalism cont’d
All trajectories are characterized by their difference from a reference trajectory*
*”The Central Trajectory” x z y z x
Trajectories are represented by column vectors.
l = length difference between trajectory and the reference trajectory
Relative change in momentum

14. TRANSPORT formalism cont’d
General Solution of the equation of motion:
Each component can be expressed as a Taylor series around the Central Ray:
Use the central ray as a basic solution and do a Taylor series expansion around it.

15. TRANSPORT formalism cont’d
The first order transfer matrix:
For static magnetic systems with midplane symmetry:
Same as on previous page, just introducing a new notation.
If you know how well you can measure x, θ, y, and φ, you know how well you can determine the target parameters.

16. Projected Errors based on projected detector performance and general setup
1st order
Resolution
1st Order
P = 8 GeV/c
δ (%) (Momentum)
0.03P+0.29
0.53
θtar (mrad) /P
0.16
ytar (mm) /P
1.09
φtar (mrad) /P
0.31

17. Higher Order Effects? Strategy:
Use SNAKE to create a database of trajectories and then fit the reconstruction tensor. (higher order terms)
Use the reconstruction tensor in a Monte-Carlo fashion to evaluate the errors.
δ0-δmeas
θ0-θmeas
φ0-φmeas
y0-ymeas
δ0-δmeas
θ0-θmeas
φ0-φmeas
y0-ymeas

18. 1st Order resolution P = 8 GeV/c SNAKE P = 7-9 GeV/c δ (%) (Momentum)
0.53
0.48
θtar (mrad) /P
0.16
ytar (mm) /P
1.09
0.9
φtar (mrad) /P
0.31
0.30
Higher order terms, while necessary to accurately reconstruct the target variables, don’t contribute to the uncertainties in the measurements.
i.e. They’re small corrections!

19. Momentum Dependence of ΔΩ
8 GeV/c
1 GeV/c

20. Spin Transport Dispersive precession Non-dispersive precession Target
to Reaction Plane
Reaction Plane

21. Systematic error is 10% of projected statistical error
Spin Transport
Because of Pl - Pt mixing, the non-dispersive bend angle contributes by a factor of ~100 to the FF ratio systematic error.
However, it is very small: ±1.1 mrad (FWHM) and can be reconstructed with high precision (~0.1mrad).
Systematic error is 10% of projected statistical error

22. Calibration Scheme Will need to: Calibrate Momentum (P0 and δ)
Calibrate Angle reconstruction (θ0 & φ0)
Calibrate Vertex reconstruction (y0)

23. Calibration scheme cont’d
Do a series of elastic scattering runs (H2(e,e’p))
δ scans (P0 and δ)
with and without sieve slit (θ0 & φ0)
Requires a proton arm in coincidence
Segmented extended target (y0)
i.e. a series of thin targets along the beamline
Has been very successfully done with BigBite
Compare to Magnet off
straight throughs

24. Magnet exists and is available Magnet will work nicely
Conclusion
Magnet exists and is available
Magnet will work nicely
with proposed modifications
Optics are very simple