John J. LeRoseTechnical Review of the Super BigBite Project

January 22, 2010

SBS Magnet, Optics, and Spin Transport

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

48D48 Basic Geometry

The magnet is “available”.

To guarantee that it’s ours we need to formally

transfer ownership.

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

Shielded Beam pipe

Field Clamp

Layout of system with part of yoke removed

Modified Coils

B at target < 2 Gauss

With magnetically shielded pipe with 1kA/cm current density solenoid

Calculations by Stepan MikhailovUsing “Mermaid” (units are kG, cm)

Nice clean magnetic field

5105.369.360013.0

69.3611

B

Bdl

mTBcGeVP

mTdlBy3

' 103.1

yy’

x

x’

θ

1 mm @ 30mEffect on beamline by transverse field is effectively eliminated

Various Views of the Modified Magnet

Optics

It’s really very simple!

This is what it looks like to me!

x

y

0

Reference Trajectory

Arbitrary Trajectory

Magnetic Midplane

y

x

z

TRANSPORT formalism

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)

…...

All trajectories are characterized by their difference from a reference trajectory*

l

y

x

Xx

zx

z

y

zy

z

*”The Central Trajectory”

zx

xx

l = length difference between trajectory and the reference trajectory

TRANSPORT formalism cont’d

yxz

0

0

ppp

Relative change in momentum

General Solution of the equation of motion:

000000

),,,,(),,,,(),,,,(),,,,(),,,,(

),,,,(

0,000

0,000

0,000

0,000

0,000

0,000raycentral

yxzlyxzyxzyyxzyxzx

yxzF

Each component can be expressed as a Taylor series around the Central Ray:

......

......),,,,(

......),,,,(

......),,,,(

......),,,,(

)(0

)(00

)(00

)(00

)(00

)(00,000

)(0

)(00

)(00

)(00

)(00

)(00,000

)(0

)(00

)(00

)(00

)(00

)(00,000

)(0

)(00

)(00

)(00

)(00

)(00,000

zzzzzz

zzzzzz

zzzzzz

zzzzzz

ll

yy

xx

yxz

yllyyy

yyyx

xyyxzy

ll

yy

xx

yxz

xllxxy

yxxx

xxyxzx

TRANSPORT formalism cont’d

The first order transfer matrix:

f

f

f

f

f

f

XXMor

l

y

x

l

y

x

lyxllllyllxl

lyxylyyyyyxy

lyxxlxxyxxxx

0

0

0

0

0

0

00000

00000

00000

00000

00000

00000

||||||||||||||||||||||||||||||||||||

For static magnetic systems with midplane symmetry:

f

f

f

f

f

l

y

x

l

y

x

llxllylyyyylx

xlxxxx

0

0

0

0

0

00

000

000

000

000

100000|100||0|||000|||00||00||||00||

1|| M

0

0

00

00

||||

yyyyy

y

f

f

01 XXM f

eg.0

0 xxxx

TRANSPORT formalism cont’d

If you know how well you can measure x, θ, y, and φ, you know how well you can determine the target parameters.

Projected Errorsbased on projected detector performance and general setup

mradP(GeV/c)

mrad

mm36.114.0

07.0

yx

1st orderResolution

1st OrderP = 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-φmeasy0-ymeas

δ0-δmeas θ0-θmeas

φ0-φmeasy0-ymeas

1st Orderresolution

1st OrderP = 8 GeV/c

SNAKE P = 7-9 GeV/c

δ (%) (Momentum) 0.03P+0.29 0.53 0.48

θtar (mrad) 0.09 + 0.59/P 0.16 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

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

Super BigBite Relative Acceptance

P (GeV/c)

8 GeV/c

1 GeV/c

Spin Transport )1(Non-dispersive precessionDispersive precession )1(

to Reaction Plane Reaction Plane

2tan

2)( e

p

ebeam

l

t

Mp

Ep

MEE

PP

GG

PP

PP

t

l

tfp

nfp s in

)1(sin

2tan

2)(

fpl

fpte

p

ebeam

Mp

Ep

PP

MEE

GG

TargetTarget

outin

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).

-0.0025 -0.002 -0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015 0.002 0.00250

20

40

60

80

100

120

140

160

SBS Δφ σ = 0.00046

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

Conclusion

• Magnet exists and is available• Magnet will work nicely

–with proposed modifications• Optics are very simple