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Helicity-Correlated Effects For SAMPLE
Experiment
M.Farkhondeh, W.Franklin, E. Tsentalovich, T.Zwart
MIT-Bates Linear Accelerator Center, Middleton, MA, USA
Abstract. In 1998-2001 three series of SAMPLE experiment [1-3] were conducted at the MITBates Linear Accelerator Center. SAMPLE measures parity-violating effects in electron
scattering from protons and deuterons. The measured asymmetry associated with electron
helicity is very small (about 1 ppm). In order to reduce systematic errors, the properties of the
beam (intensity, position, size and energy) must remain unchanged when the helicity of
polarized electrons is reversed. In this paper we analyze the sources of the helicity-correlated
effects in the electron beam and our approach to minimize them.
INTRODUCTION
The electron gun at MIT-Bates [4] is mounted on the top of an accelerator column
and surrounded by a Faraday cage maintained at 300 keV relative to ground. A Ti:Sa
tunable cw laser provides the light source for photoemission. The laser beam travels
over 20 m between the optical table and the GaAs crystal in the gun. Although the
output power of Ti:Sa laser (about 7 W) is sufficient to run the experiments with bulk
GaAs photocathodes, the Quantum Efficiency (QE) of high-polarization (strained or
superlattice) crystals is too low to be used with this laser system. Recently, we
installed a multimode diode array laser on the injector. This laser produces up to 200
W of laser power at fixed wavelength A=810 nm, has excellent stability and is very
convenient to operate. The drawback of the laser is the high emittance of the beam
s=200rmrrmrad, in comparison with 8 « Imnrmrad of the diffraction-limited beam
from the Ti:Sa laser. The existing laser beam transport system was inadequate for the
new laser, and a new wide-aperture 4-m long transport system was designed and
installed (Fig.l). With the new system, the laser beam strikes the photocathode with an
angle of -37°.
POLARIZATION REVERSAL
Circularly polarized light is required to produce polarized electrons. There are two
different ways to transform the linear polarization of light into circular polarization
and reverse the helicity as needed. The first way is to pass the laser beam through a
A/4 wave plate, producing circular polarization. The helicity can be reversed by
inserting a A/2 wave plate. This method is very simple and provides excellent results
even if the beam divergence is high, but the rate of helicity reversal is limited by the
CP675, Spin 2002:15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
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necessity to insert/retrieve the X/2 wave plate and it is very difficult to exceed 1 Hz.
The SAMPLE experiment requires helicity reversal with a rate of 600 Hz; therefore
this approach is inadequate for this experiment.
The second approach involves a Helicity Pockels Cell (HPC). The positive
(negative) helicity is achieved by applying positive (negative) A/4 voltage to HPC.
Slow helicity reversal by inserting a A/2 wave plate changes the sense of helicity,
providing a powerful tool to suppress systematic errors. The performance of Pockels
cells crucially depends on the quality of the alignment, and this performance
deteriorates with large beam divergence. A correlation between angle and position
within a laser beam leads to a gradient of the polarization within a beam profile.
To Liiiac
e beam
MIT-Bates Polarized Injector
FIGURE 1. A schematic view of the MIT-Bates polarized injector with the laser beam paths.
ORIGINATION OF HELICITY-CORRELATED EFFECTS
The main source of all helicity-correlated effects in the beam is Polarized Induced
Transport Asymmetry (PITA), produced by different reflectivity for S and P waves.
Since some fraction of residual linear polarization always exists in the circularly
polarized beam, and the direction and amplitude of this linear polarization might be
different for positive and negative helicity states, the helicity-correlated asymmetries
appear. Let us define the analyzing power 8 of the transport system as an asymmetry in
the transition of light linearly polarized in orthogonal directions. For an air-glass
interface (^=1.0, n 2 =1.5) & varies from 0 to 5 % at incident angles between 0° and
45°. For GaAs crystal (n 2 =4.5) s «25 % at 45°. The analyzing power of strained GaAs
crystals is governed by different mechanism, but it is high (s «5-15 %) even at normal
incidence.
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Modern mirrors with antireflective coating have relatively low analyzing power
(0.2 - 0.5 %). Still, a transport line containing several mirrors might produce
significant helicity-correlated effects. It is important to pair the mirrors in such a way
that the plane of reflection rotates by 90° in the pair in order to balance P- and Sreflections. That allows canceling in the first order PITA effect.
When the HPC for the Ti:Sa laser beam line was located at the beginning of the
transport line, and circularly polarized beam traveled through 4 mirrors, the
imperfections in the mirrors balancing dominated and the resulting analyzing power of
the transport system was of the order of 10"3 -10~ 4 . When we moved the HPC to the
end of the transport line, between the last mirror and the input vacuum window, the
only analyzing elements left after the HPC were the vacuum window and the
photocathode itself, with almost normal incident beam. With a bulk GaAs crystal the
total analyzing power dropped greatly, but with a strained crystal the anisotropy of the
cathode becomes dominant and the analyzing power grows to 5-15%.
The beam from the diode array laser strikes the crystal at an angle of 37°. The
analyzing power is very large (about 20 %) for both bulk and strained crystals.
Since the direction and amplitude of the linear component of polarization is nonuniform across the laser beam, traveling through the transport system with some
analyzing power results in a positional asymmetry. Another important source of
positional asymmetry for strained crystals is the non-uniformity of the analyzing
power across the surface of the crystal. Pockels cells produce very small steering
effect on the beam (angles of the order of 10~7 - 10~8), and this effect may result in the
positional asymmetry as well if the transport line is sufficiently long. This effect can
be suppressed by imaging Pockels cell location onto the crystal.
If the electron beam in the accelerator has an intensity asymmetry, loading effects
in the accelerating structure lead to an energy asymmetry.
All three asymmetries (intensity, position, energy) are mutually dependent. If the
electron beam with an energy asymmetry travels through a section with a large
dispersion, differential scraping (losing electrons on one side of the beam for positive
helicity, and on another side for negative helicity) may occur, resulting in a positional
asymmetry. The beam with a positional asymmetry traveling through a narrow
aperture may develop an intensity asymmetry.
There could be other, more exotic asymmetries, which we considered negligible for
the SAMPLE experiment, but they could be significant for more demanding
experiments ([5] for instance): beam size asymmetry, beam shape asymmetry,
asymmetries with a temporal profile (for instance, an intensity asymmetry can be
positive at the beginning of the pulses, and negative at the end. Averaged over the
pulse, the asymmetry becomes zero, but non-linear effects could affect the systematic
errors.)
SUPPRESSION OF HELICITY-CORRELATED EFFECTS
The most general recipe in dealing with the helicity-correlated effects is to
minimize the asymmetries using miscellaneous alignment techniques, and to control
the residual asymmetries with active feedback loops.
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Since the effects are usually proportional to the degree of linear polarization in the
laser beam, the first step is to maximize the circular polarization. This is a rather
challenging task for the diode laser beam due to the very large emittance. In order to
minimize the angular spread of the beam traveling through the HPC we have to
maximize the size of the beam (we didn't want to lose a significant fraction of laser
power using collimators). In order to achieve an extinction ratio of about 150 we had
to increase the beam size to 50 mm. The Pockels cell used had a clear aperture of 75
mm.
Balancing P- and S-reflection, careful alignment of Pockels cells and polarizers are
the obvious steps to minimize helicity-correlated effects. When strained crystals with a
high anisotropy are used, the direction of the residual linear polarization must be lined
up along the axis of the photocathode. If the A/2 wave plate is placed after the HPC,
the intensity asymmetry depends on the rotation angle 0 of the wave plate as
a = z[A - sin(4<9 - a) + y - sin(2<9 - b) + /?]
where 8 is the analyzing power, A term corresponds to asymmetric retardation errors
for the HPC, y terms corresponds to the imperfection of the A/2 plate itself and P term
corresponds to the birefringent components in the transport line [6]. Since the
positional asymmetries usually have the same origin as intensity asymmetry, they
generally exhibit the same behavior. Fig.2 demonstrates the results of intensity and
positional asymmetry measurements with a strained crystal, and the laser beam
striking the cathode at 37° angle.
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Angle (degrees)
FIGURE 2. The intensity and positional asymmetries as a function of wave plate angle. The solid lines
represent the fit.
The helicity-correlated effects are large: thousands of ppm in intensity, tens of
microns in position. Our feedback systems were designed to control the initial
asymmetries of the order of hundreds ppm and hundreds nanometers. Therefore,
several conditions must be satisfied: the lines on Fig.2 must cross zero, the lines for
intensity and both positional asymmetries must cross zero at about the same rotational
angle of the 7J2 plate, and the asymmetries must be stable with time. Our preliminary
measurements didn't provide a clear answer to this question. It was concluded that
further tests were needed, and due to scheduling constraints, the production runs for
SAMPLE were carried out with a bulk GaAs cathodes and Ti:Sa laser.
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Three feedback systems were used in SAMPLE experiments: two positional (x and
y) and one intensity feedbacks. We found that it is essential to have these three
systems separate and orthogonal.
Our first approach of adjusting the HPC voltage to correct for the intensity
asymmetries failed to adhere to this rule. Adjustment of the HPC voltage essentially
changes the fraction of linear polarization in the beam, and it affects both intensity and
positional asymmetries. In order to separate the intensity and positional feedbacks, we
introduced an additional Correction Pockels cell (CPC), installed between two linear
polarizers before the HPC. CPC is biased to a voltage of VO-500 V, and small (>10V)
helicity-correlated corrections on the bias control the intensity asymmetry without
affecting the positional asymmetries. The sensitivity can be adjusted by altering the
VO voltage, and is usually set to about 50 ppm/V.
Since some Pockels cells deteriorate with a constant bias applied, we developed
another scheme, where CPC bias is set to zero, but a A/10 plate is inserted in front of
CPC. The plate introduces some elliptical polarization in the laser beam and in this
scheme the sensitivity is set by changing the X/10 plate rotational angle.
A piezo-electric system [7] for positional feedback was developed by the SAMPLE
collaboration. A thin optical flat was inserted in a laser beam path. The angle of the
plate could be adjusted with a frequency exceeding 1 kHz, thus altering the beam
position by as much as several hundreds nanometers. The flat was installed in the 3point suspension holder, allowing to control x and y components independently.
RESULTS AND CONCLUSIONS
During the production SAMPLE runs the intensity feedback functioned
automatically, updating the measurements every 3 minutes. The statistical error in
each measurement was of the order of 10 ppm. Averaged over a full day of running,
the error reduced to less than 1 ppm.
Positional asymmetries were very stable, and required only occasional adjustments.
When the piezo-electric system was used for the first time, it allowed reducing
positional asymmetries from several hundreds to about 30 nm. In the last SAMPLE
production run the positional differences averaged over several days were less than 10
nm.
As a result, all three SAMPLE experiments were successfully completed using a
bulk GaAs photocathodes and Ti:Sa laser. More development is required to conduct
parity-violating experiments with strained photocathodes and high power diode laser.
REFERENCES
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G.D.Cates et al, NIM A278, 293 (1989).
SLAC Proposal E-158, 1997.
B.Humensky, Princeton University, to be published.
T.Averett et al, NIM A438, 246 (1999)
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