Download Spin-Flipper Efficiency and Beam Polarization

Beam Polarimetry
Matthew Musgrave
NPDGamma Collaboration Meeting
Oak Ridge National Laboratory
Oct. 15, 2010
Introduction
The neutron beam polarization and the spin flip efficiency of the RFSF
need to be determined to obtain the parity violating physics ϒ-ray
asymmetry from the measured ϒ-ray asymmetry.
A 
Ameasured
Pn   rf  C
Pn is the neutron beam polarization, εrf is the efficiency of the RFSF, and C
is a constant representing the rest of the corrections to the measured
asymmetry.
The goal of the polarimetry measurement is to obtain the polarization of
the neutron beam to within 5% to help achieve a statistical precision of
~10-8 for Aϒ.
Polarimetry
The neutron beam polarization will be determined from relative neutron flux
measurements through a polarized 3He analyzer cell. The neutron spin will be
flipped by a RFSF and the 3He spin will be flipped by adiabatic fast passage to provide
redundant methods of measuring the signal of opposing spin states of the neutrons.
RFSF
3He
analyzer cells
RF Spin Flipper
In the RFSF there is a static field B0=9.7G from the guide field and a RF field
Brf produced by the RFSF oscillating in the direction of the neutron beam.

Beff  B0 yˆ  Brf cos(t ) zˆ
The RF field can be approximated as two counter rotating fields, rotating
normal to the guide field B0.

Brf
Brf
Brf 
(cos(t ) zˆ  sin( t ) xˆ ) 
(cos(t ) zˆ  sin( t ) xˆ )
2
2
If the RF field oscillates at the Larmor frequency of the neutron magnetic
moment in the guide field ωL=ϒB0=29kHz then the frequency of Brf is on
resonance and one rotating component of Brf follows the precession of the
neutron magnetic moment. The other component is off resonance by
twice the Larmor frequency and has a negligible effect on the precession
of the neutron magnetic moment. In the rotating frame of reference of
the neutron magnetic moment there is only a field in the ẑ direction.

Brf
Brf

 
Brot   B0  L  yˆ 
zˆ 
zˆ

2
2


RF Spin Flipper
In the rotating reference frame on resonance, the neutron magnetic moment
precesses about the effective magnetic field at the Larmor frequency for Brot.
rot  Brot
To achieve a spin flip of the neutron beam, the neutrons need to remain in
the RFSF for the time required to rotate the neutron spins by π radians.
t
2n
Brf
Where n=1, 3, 5… The time spent in the RFSF is dependent on the neutron’s
velocity, which for the NPDGamma experiment is characterized by the
neutron’s time of flight.
t
L L
 ttof
v l
Where L is the length of the RFSF and l is the distance to the neutron
moderator. To rotate the neutron spins by π radians, the rf field of the RFSF
must be varied with the time of flight.
Brf 
2n l 1
 L ttof
Efficiency of RFSF at LANL
The efficiency of the RFSF at LANL was measured to be 98.8±0.5%.
Differences in the design of the beam line and the method of polarizing the
neutrons will affect the efficiency of the RFSF and how it is calculated.
LANSCE
SNS
20Hz
9.5cm × 9.5cm
3He spin filter
60Hz
10cm × 12cm
Supermirror polarizer
Field Uniformity
The rf field Brf in the RFSF is not uniform because Brf is produced by a finite
solenoid. If the RFSF is tuned to maximize efficiency in the center of the beam,
the RFSF efficiency will be less than unity off axis.
S. Balascuta
The efficiency of the RFSF off axis is determined by the integral of the
amplitude of Brf experienced by the neutron over the length of the RFSF.
 ( x, y)  
L/2
L / 2
Brf ( x, y, z )dz
Neutron Polarization by Capture on
Polarized 3He
The cross-section for neutrons with spin anti-parallel to the 3He nuclear spin is
very large. Twice the cross-section for unpolarized neutrons.
n
np
p
n np
p
The cross-section for neutron capture on 3He with nuclear spin parallel to the
neutron spin is nearly zero.
n
np
p
n np
p
The strong spin dependence of the neutron capture cross-section of polarized
3He makes it an effective neutron polarizer and analyzer.
How do we polarize 3He?
3He
is polarized through spin exchange with
optically pumped alkali metal such as Rb or K.
•Only electrons in the S1/2 state with ms=-1/2 can absorb the laser light because the
light is circularly polarized with magnetic projection of +1.
•The valence electron in the alkali metal absorbs a photon with angular momentum
of +1 and magnetic projection of +1 and is excited to the P1/2 ms=+1/2 state .
•The excited electron will decay back to the S1/2 ground state with either value for
the spin state.
•Since only the ground state electron in the ms=-1/2 spin state can absorb a photon
but the excited electron can decay to either spin state, the ms=+1/2 spin state will
eventually become populated.
•The 3He is then polarized through spin exchange hyperfine interactions with the
electrons of the alkali atoms.
Spin Exchange Optical Pumping
Collision Mixing
Optical Pumping Station
The 3He cell is polarized in a static magnetic field of 12-14 Gauss, and its
polarization and spin-lattice relaxation time are determined in the lab by NMR.
During optical
pumping the Rb’s
polarization
becomes saturated
in under a second,
but the 3He
polarization takes
several hours to
saturate and is
usually pumped
over night.
The spin-lattice relaxation time of a 3He cell will often be over 100 hours,
which will provide a stable 3He polarization for polarimetry measurements.
3He
Analyzer Cells
Five 3He analyzer cells have been produced for the polarimetry measurement
and named Maxwell, Nambu, Oppenheimer, Ramsey, and Szilard. The 3He cells
are 1in diameter cylindrical cells made of GE180 glass. They are filled with 3He,
N2, and trace amounts of Rb for polarization of the 3He. So far three of the 3He
cells have been characterized.
Length
3He Thickness
3He Pressure
T1 Lifetime
Max. Polarization
Maxwell
Nambu
Oppenheimer
2.5”
0.97 Å-1
2.1 bar
18.1hr
19%
4”
1.24 Å-1
1.7 bar
10.8hr
32%
3”
1.14 Å-1
2.0 bar
11.6hr
37%
3
He _ Thickness 
nl 0
0
3He Analyzer in the Beamline
Neutron Transmission through a 3He Cell
Neglecting normalization, the measured neutron flux of an unpolarized
neutron beam through an unpolarized and polarized 3He cell are given by:
N 0 ( )  e 
N pol ( )  e  cosh( PHe )
Where κ is the 3He cell thickness, which is a function of the 3He density n,
the length of the cell l, and a normalizing reference cross-section σ0 and
neutron wavelength λ0.

nl 0
0
The polarization of the neutron beam is given by:
PnHe ( )  tanh( PHe )
If the wavelength of the neutrons is known, the polarization can be
rewritten as a function of neutron flux measurements through the cell.
 N ( ) 

PnHe ( )  1   0
 N ( ) 
 pol

This is the analyzing power of the 3He cell.
2
Transmission of a Polarized Neutron Beam
through a 3He Cell
Assuming the neutron spin can be flipped with unit efficiency, the
transmission of an unpolarized neutron beam can be approximated
from a polarized neutron beam by flipping the neutron spins and
averaging the flux measurements of the two neutron spin states.
N pol ( ) N  ( )  N  ( )

N 0 ( )
2 N 0 ( )
The analyzing power of the 3He cell can then be determined from a
polarized neutron beam.
2
2
(
R

R
)
4


2
N
(

)


0
 
PnHe ( )  1  

R  R
 N  ( )  N  ( ) 
Where R↑=N↑/N0 and R↓=N↓/N0 are ratios of the flux measurements.
Polarization of the Neutron Beam
The effective efficiency of the supermirror polarizer and the polarized 3He cell
is the product of their polarization efficiencies, PnPnHe. The detected neutron
flux through the supermirror and the 3He cell can be determined from the
effective efficiency.
N P P He
n n
R  R
 Nunpol (1  P P )  R 
(1  Pn PnHe )
2
He
n n
The polarization of the neutron beam as a function of neutron wavelength can
then be calculated from relative neutron flux measurements.
2 R 
R  R
1 

Pn ( )  He 1 
Pn  R  R 
( R  R ) 2  4
Neutron Flux Measurements
Four neutron flux measurements through a polarized 3He cell will be measured
corresponding to the RFSF on and off and the two 3He spin states tuned by AFP.
N PHe ( )  N 0 ( ) cosh( PHe )(1  Pn tanh( PHe ))
N Fsf PHe ( )  N 0 ( ) cosh( PHe )(1  (1  2 rf ) Pn tanh( PHe ))
N FafpPHe ( )  N 0 ( ) cosh(  (1  2 afp ) n PHe )(1  Pn tanh(  (1  2 afp ) n PHe ))
N Fsf FafpPHe ( )  N 0 ( ) cosh(  (1  2 afp ) n PHe )(1  (1  2 rf ) Pn tanh(  (1  2 afp ) n PHe ))
Where N0(λ)=e-κλ is the neutron flux through an unpolarized 3He cell. These
measurements will also be done at several 3He polarizations. Since the
polarization of the neutron beam is independent of the polarization of the 3He,
these additional measurements will provide a redundant check on the beam
polarization. The efficiencies of the RFSF and the AFP coils can also be
determined from the neutron flux measurements.
RFSF Efficiency
The 3He polarization can be flipped with nearly 100% efficiency by adiabatic fast
passage. By assuming no loss in polarization of the 3He, the efficiency of the RFSF
can be determined by ratios of sums and differences of neutron flux measurements.
Rsf 
R0 
TFsf FafpPHe  TFsf PHe
TFsf FafpPHe  TFsf PHe
TFafpPHe  TPHe
TFafpPHe  TPHe
 (1  2 sf ) Psmp tanh( PHe )
 Psmp tanh( PHe )
1  Rsf
 sf  1 
2
R0



Statistical Precision
To determine the polarization of the neutron beam to within 5%, the
statistical precision of each neutron flux measurement will be measured to
better than 1.5%. This equates to about 5000 neutrons detected by the
neutron detector. Neutron flux measurements will be taken for about 20 time
bins to determine the polarization at different neutron wavelengths .
Assuming a neutron flux of 108 n/cm2s, an aperture of 1 cm2, 20 time bins,
5×102 n/time bin, a relative neutron transmission of 0.01 through a thick 3He
cell, and a 10% capture efficiency in the neutron detector. A conservative
estimate for the time of a statistically significant neutron flux measurement
can be calculated.
(20t.b.)(5 103 n / t.b.)
 1s
(1cm2 )(108 n / cm2 s)(0.01)(0.1)
The time required to make a neutron flux measurement is small enough that
the polarimetry measurement will not be statically limited.