Polarization

Beam polarization information in GeN experiment comes from three different sources: Mott, Moller and Compton
polarimeters measurements.

Mott Polarimeter

A Mott polarimeter has been developed to measure the spin polarization of the electron beams produced at CEBAF, the nuclear physics accelerator at Jefferson Lab. The polarimeter measures the counting rate asymmetry in the elastic Mott scattering process, which is non-zero for spin states perpendicular to the electron scattering plane. The Sherman function determines the relation between measured experimental asymmetry and the degree of polarization of the electron beam.
Mott measurements during GeN experiment

Moller polarimeter

The Hall A beam line is equipped with a Moller polarimeter, whose purpose is to measure the polarization of the electron beam delivered to the hall. The Moller polarimeter consists of

• a magnetized ferromagnetic foil used as a polarized electron target, placed 17.5 m upstream of the central pivot point of the Hall A High Resolution Spectrometers;
• a spectrometer consisting of three quadrupole magnets and a dipole magnet, used to deflect the electrons scattered in a certain kinematic range towards the Møller detector;
• a detector and its associated shielding house;
• a stand alone data acquisition system;
• off-line analysis software which helps to extract the beam polarization from the data immediately after the data are taken.

Moller measurements during GeN experiment

Compton polarimeter

In order to measure the longitudinal polarization of the 3-6 GeV high intensity TJNAF electron beam, a Compton Polarimeter was built by Saclay, Clermont, and Jlab. In contrast to Moller polarization measurement which can not be performed at the same time of data taking process because of the beam, after the interaction with the target, is misdefined in terms of polarization, momentum and position, Compton measurements can be performed simultaneously with data taking. The Jefferson Lab electron beam, which polarization is flipped 30 times per second, is interacting with a laser beam of measured circular polarization. This physical process is described by the Quantum Electro Dynamics (the so-called QED) which allows to calculate the cross sections of the polarized electrons scattering off polarized photons as a function of their energies and scattering angle. The counting rates asymmetry is directly proportional to the laser and electrons beam polarizations and cross sections asymmetry.
Compton runs taken during GeN experiment:

kin1	13012-13020
kin2	13025-13144, 13432-13509
kin3	13147-13429, 13510-13585
kin4	13586-13698

Compton measurements description

A list of the polarization results for all Compton measurements can be found here: Compton Measurements

Precession

As the beam travels around the accellerator, the spin of the polarized electrons will precess in a plane parallel to the ground. The longitudinal polarization of the electrons are dependent on the total precession, which can be calculated. The final angle of the electrons can be found using:

angle = E_l/m *(g-2)/2 * (2n^2-n*(1-2a+b)-a*(1+b/2))*180 + wein_angle

Where E_l is the (single) linac energy (2E_l is energy/pass), n is the number of passes, m is the electron mass. a is the ratio of injector energy to 2E_l (=0.1125). b is is a constant dependent on the extractor arc. For Hall A a_A = -1/2.4, for Hall B a_B = 0, and for Hall C a_C = 1/2.4.

Calculating for our four kinematics:

	Linac E (GeV)	Wien Angle (deg)	Beam Angle (deg)	Polarization
Kin1	0.738	-5.29	179.117	-1.000
Kin2a	0.650	76.43	-17.405	0.954
Kin3a	0.650	92.25	-179.506	-1.000
Kin2b	0.650	92.25	-1.589	1.000
Kin3b	0.650	92.49	-179.260	-1.000
Kin4	0.512	57.21	-175.654	-0.997

It's notable to point out that for any kin2 measurement, there is an additional minus sign relative to the other kinematics.

Also see:
Hall A Moller Spin Dance Page
CEBAF-TN-96-032
JLab-TN-97-021
Phys. Rev. Spec. Top. - Accel. & Beams, Vol 7, 042802 (2004)