Moeller Polarimeter: Spin-Dance Measurement

Spin-Dance Measurement

Last updated: Fri, 19 June 1998 moller@jlab.org

General

Let the particle's momentum to rotate by an angle theta. Then its spin would turn with respect to the momentum by an angle: angl=(g-2)/2*gamma*theta, where gamma=E/m and (g-2)/2=0.00115965 for electrons. So, spin turns to the same direction as the momentum and by a larger angle.

Spin Precession at CEBAF

In a note TJNAF-TN-97-021 C.Sinclair derived the expected spin turns for the halls A,B,C at CEBAF. The value of theta depends on the number of passes and on the angle in the hall's extraction arcs, taking into account the beam acceleration:
theta=(2n-1)*180^o;
angl=E_L/m*(g-2)/2*(2n²-n*(1-2a+b)-a*(1+b/2))*180^o
where:

E_L is the linac's energy
n is the number of passes
m is the electron mass
a=0.1125 is the ratio of the injector energy to the linac's energy
b=-1/2.4 for Hall A, =0 for Hall B and 1/2.4 for Hall C; this factor comes from the extraction arc.

Let us assume Hall A is running 5 passes at E_L=0.812 GeV, so theta=4.5*360 degrees. Then spin makes an angle of about 22.167*360^o to the momentum. Measuring the spin precession with an accuracy of 5^o one can potentially measure the electron energy with an accuracy on about 0.06%. However the initial spin angle is not defined with a precision comparable to that and a better way of measuring the spin precession is to compare the syncronously measured beam polarizations from 2 halls running at different energies. This procedure is nicknamed "spin-dance". The direction of spin is changed on the injector and by convention the positive direction is clock-wise, as the direction of accelerated electrons is. It is convenient to run at a so-called "magic" energy when both halls should have a zero longitudinal polarization at the same angle at the injector. Since at the zero point the accuracy of the phase measurement is the highest, both halls should be able to measure this point at the same angle at the injector.

April, 26 1998

"Spin-dance" measurement was performed on April,26 1998 by Moeller polarimeters in halls A and B, at a "magic" energy of about 0.8395 GeV per pass. Hall A ran at 4 passes while Hall B ran at 1(?) pass. The initial angle at the injector was 70.6 degrees.

The angle at the injector was decreased which means turning the spin anti-clockwise looking from the top, accordingly to Charles Sinclair. In our notation it is the positive direction - from Z to X. In the Hall A polarimeter the transverse polarization in the horizontal plane changes the measurements while in Hall B it does not. The supermendur "bottom" target was used (which is in fact the upper target). The target plate is positioned at about -20^o to the beam. At beam spin orientation of, say 80^o the longitudinal and transverse components of asymmetry have different signs. Therefore at a spin angle of 90^o the observed asymmetry should be non-zero and negative, if at 0^o it is positive. The observed asymmetry curve is shifted by the transverse polarization by +3.0+/-0.4^o with respect to a curve one would obtain if there were no transverse polarization influence.

The observed spin-dance curve crosses zero at about -13+/-0.3^o. Therefore the beam helicity should be zero at about -16+/-0.6^o.

May, 23 1998

The assumed energy per pass was 0.812 GeV. The initial angle at the injector was -61.6^o.

Spin-dance results
hall # passes plot angle at max (^o) precession/360. ang.shift(^o) energy shift %

A 5 plot -53.3+/-0.2 22.168 -7.1+/-0.2 -0.089+/- 0.003

B 3 . -59.0+/-2.6 7.169 -2.0+/-2.6 -0.077+/- 0.010

A-B . . . . . -0.095+/- 0.048

Spin-dance results
hall	# passes	plot	angle at max (^o)	precession/360.	ang.shift(^o)	energy shift %
A	5	plot	-53.3+/-0.2	22.168	-7.1+/-0.2	-0.089+/- 0.003
B	3	.	-59.0+/-2.6	7.169	-2.0+/-2.6	-0.077+/- 0.010
A-B	.	.	.	.	.	-0.095+/- 0.048

Two ponts at the lowest injector angle fall out of the COS curve. Their errors are increased by hand. The reason has not been found. It may happen that at these angles the wien filter does not provide the spin turn expected.

July, 13 1999

Assumed linac was 0.5437 GeV, 3 passes in hall A. The initial angle at the injector was 45.6^o.

Spin-dance results
Wien angle Polarization

-74.8 29.4+/-0.2

-47.6 -4.3+/-0.2

-20.3 -36.2+/-0.2

45.6 -75.9+/-0.2

Spin-dance results
Wien angle	Polarization
-74.8	29.4+/-0.2
-47.6	-4.3+/-0.2
-20.3	-36.2+/-0.2
45.6	-75.9+/-0.2

The results presented on a plot show the zero crossing at about -50.8+/-0.5^o. That would mean that the optimal settings should be 39.2^o (not 45.6^o as it had been set by the accelerator). The angle predicted by my program (E.Ch) for the linac energy of 0.5437GeV is about 40.7^o. We rounded the number to 40.^o and asked the MCC to tune to this angle for the future.