\section{Polarimetry instrumentation}

The majority of bremsstrahlung photons produced in the radiator are
absorbed in the collimator system.  If the radiator and collimator
system are well aligned, the photon spectrum behind the collimators
is dominated by the coherent peak.  The beam parameters can be
determined by using the intensity spectra from the tagger.

Nevertheless, in order to monitor the polarization parameters -- 
degree ($P_{\gamma}$) and direction ($\epsilon_{\gamma}$) -- 
of the collimated photon beam it is crucial to have an independent method, 
either a photon polarimeter detecting the asymmetry of a process 
that is well understood within theory (QED) or a well known hadronic 
process so that the measured beam asymmetry can be compared with theoretical 
(or experimental) expectations. At photon energies above $5$~\eunit, the 
forward production of vector mesons is described by vector meson dominance 
(VMD), resulting in a $sin^{2}\theta_{hel}cos(2\psi)$ dependence of the vector
meson's decay distribution where $\theta_{hel},\phi_{hel}$ are the polar and 
azimuthal decay angles  in the helicity frame and 
$\psi=\phi_{hel}-\epsilon_{\gamma}$.  With $\rho^{0}$ production accounting 
for about $10$\% of all hadronic triggers in the detector, this method 
suffers no lack of statistics. It is limited only by the accuracy of the VMD 
approximation, roughly $5-10$\% at these energies.


The other method, measuring the photon polarization by means of a
polarimeter, can be realized by a pair polarimeter or a triplet
polarimeter.  It involves additional hardware components on the
beamline between the collimator system and the spectrometer magnet. 
Both types of polarimeter require a thin radiator and a detector in a field
free area followed by a dipole magnet and counters for the trigger.
Space is available upstream of the spectrometer in \hd\ for the
insertion of a polarimeter.

QED based calculations for the latter process show 
that the angle and energy of the soft (triplet) electron is 
almost independent of the energy of the incident photon 
($\bar{E}_{triplet} \approx 0.7-0.9$\Meunit).
The low rate of this process and the technical challenge for a
counter device measuring accurately the angular distribution of low energy
electrons do not favor this type of polarimeter. 

For pair production, on the other hand, the opening angle between the
produced electron and positron decreases with increasing energy 
making the measurement more complicated at higher energies.
A magnetic separation is not desirable because the deflection cannot be
determined very accurately.  The proposed polarimeter consists of a
thin scintillator ($d=50$\micron{}) as an active target, $1.5$~\mlunit{} 
in front of a silicon microstrip detector arrangement, followed by a dipole
magnet and two scintillators $10$~\cmlunit{} apart from the beamline for
triggering on symmetric $e^{+}e^{-}$ pairs.  The microstrip detector
consists of four layers having $512$ channels each of silicon wafers
with a spatial width for a single channel of $25$~\micron .  The second
and third layer are oriented at $\pm 60^{\circ}$ with respect to the
first layer, the fourth perpendicular to one of the previous layers, thus
allowing to measure the full angular range of produced $e^{+}e^{-}$-pairs
without any gap in the acceptance.  A Monte Carlo simulation of this
device including multiple scattering in the target, the microstrip
detector, and foils in the vacuum system (using GEANT) shows that an
analyzing power of $25$\% is achievable (cf. fig~\ref{fig:pairprod}).
QED calculations predict an angular distribution for pair production 
proportional to $(1+P_{\gamma}\alpha\cos 2(\phi-\epsilon_{\gamma}))$ 
with an analyzing power of $\alpha=0.28$ for incident photons in the range
of $6$-$10$~\eunit.  Because of the thickness of the microstrip layers 
($300$~\micron{}) it is convenient to measure the beam polarization for 
fifteen minutes every time the orientation of the crystal radiator or the 
electron beam parameters have changed.  The scintillator target as well as the
detector device have to be mounted on motor driven stages so that
they can be removed from the beamline.

\begin{figure}[h!]\centering
\includegraphics[width=0.8\textwidth]{ch4_pairprod.eps}
\caption[Angular distribution for pair production by polarized photons]
{\label{fig:pairprod} Angular distribution for pair production by linearly 
polarized photons as measured by a polarimeter in comparison with theoretical 
prediction (\emph{dashed line}). The count rate corresponds to $15$ minutes 
of data taking.}
\end{figure}

A research and development program is underway at the Yerevan Physics
Institute to test these ideas using the $2$~\eunit\ coherent bremsstrahlung
beam line at YerPhi (Yerevan, Armenia).  This $2$-year program is funded 
by the U.S. Civilian Research and Development Fund, and supports a
collaboration of Armenian and U.S. collaborators from the University
of Connecticut.  One of the primary goals of this project is to show
the accuracy with which the polarization of a coherent bremsstrahlung
beam can be calculated based upon QED and the measured shape of the
intensity spectrum.

