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

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

48D48 Basic Geometry

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

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

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

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

Effect on beamline by transverse field is effectively eliminated x x’ θ 1 mm @ 30m Effect on beamline by transverse field is effectively eliminated

Various Views of the Modified Magnet

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

This is what it looks like to me!

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 80-04 (1980) K.L. Brown, SLAC Report-75 (http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-r-075.pdf) …...

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

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.

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.

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) 0.09 + 0.59/P 0.16 ytar (mm) 0.53 + 4.49/P 1.09 φtar (mrad) 0.14+1.34/P 0.31

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

1st Order resolution P = 8 GeV/c SNAKE P = 7-9 GeV/c δ (%) (Momentum) 0.53 0.48 θtar (mrad) 0.09 + 0.59/P 0.16 ytar (mm) 0.53 + 4.49/P 1.09 0.9 φtar (mrad) 0.14+1.34/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!

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

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

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

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

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

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