\chapter{Tagging spectrometer}
\label{chapter_tagger}

\begin{center}
Sections left out here...
\end{center}

\section{Tagger detectors}
\subsection{Focal plane microscope detector}

\begin{table}
\begin{center}
\caption{
\label{tab:specs of microscope}
Specifications for the tagging microscope counters.
}
\vspace{2mm}
\begin{tabular}{ll}
\hline\hline
Parameter & Requirement \\
\hline
photon energy resolution & $<60$ MeV rms \\
tagger timing resolution & $<200$ ns rms \\
tagging efficiency in coherent peak & $>70$\% \\
maximum integrated counting rate & 250 MHz (0.5 randoms/2 ns) \\
maximum single-channel occupation & 10\% \\
maximum tagger background fraction & 1\% \\
dynamic range in rate & $>10^4$ \\
gain match between channels & 10\% \\
detection efficiency for good tags & $>90$\% \\
\hline\hline
\end{tabular}
\end{center}
\end{table}

The microscope is designed to cover the region in photon energy
within the primary coherent peak 8.4-9.0~GeV, with segmentation
sufficient to allow running with polarized beam at the highest
intensities compatible with tagging.  
The primary specifications for the microscope are listed in
Table~\ref{tab:specs of microscope}.

The detector consists of a
packed two-dimensional array of square $2\times 2$~mm$^2$ fast-green
scintillating fibers arranged along the focal plane with the fiber
axis aligned with the tagged electron trajectories.  A single energy
channel consists of a vertical stack of 5 fibers, and there are 100 such
energy channels for a total of 500 fibers.  The columns are bundled in
rectangular blocks of $5\times 5$ parallel fibers.  The bundles are
mounted individually on a rail system that allows each one to be
aligned with the local electron trajectory at its position.  In its
nominal position on the focal plane, the 100 energy channels map onto
the range 8.3 - 9.1~GeV, which fully contains the desired region 
8.4 - 9.0~GeV of the polarized peak, with some room on either side.
The way the fibers are mounted allows the microscope to be reconfigured
for running at other photon energies, from about 6~GeV to above 11~GeV.

\begin{figure}
\begin{center}
\epsfig{file=microreadout.eps,width=3.8in}
\caption{
\label{fig:layout of microscope readout}
Diagram of the readout scheme of the tagger microscope.  The SiPMs
are connected to the scintillating fibers through clear fibers so
that they can be mounted out of the radiation zone near the mid-plane
of the spectrometer.
}
\end{center}
\end{figure}

The scintillators are 2~cm long, and are glued at the back
to clear acrylic fibers of the same cross section.  The clear fibers
guide the scintillation light to photosensors located out of the
plane of the spectrometer, as illustrated in
Fig.~\ref{fig:layout of microscope readout}.
The design employs silicon photomultiplier
(SiPM) devices for photosensors.  These relatively
new devices have a unique combination of characteristics that are
well suited to this application
\cite{silicon_photomultiplier_overview_article},
\cite{silicon_photomultiplier_assessment_study}:
gains of order $10^6$, sub-ns rise time, and rate capability in excess
of $10$~MHz.  Compared with photomultiplier tubes, they are much more
compact, which makes them ideally suited for reading out scintillating
fibers.  In addition, they require no high voltage and no shielding
from magnetic fields, and their cost is substantially less than
phototubes.  The microscope requires 500 photosensors
to instrument the entire array.

Extensive bench tests have been carried out on SiPM devices to
confirm their suitability for use in the tagging microscope.
Three different devices produced by the vendors Photonique and
Hamamatsu were studied, measuring their photon detection efficiency,
gain, dark rate, and inter-pixel cross talk as a function of operating
temperature and bias voltage
\cite{silicon_photomultiplier_assessment_study}.  The results of
this study ruled out the Hamamatsu device as unsuitable for high-rate
applications\footnote{Three of the Hamamatsu 400-pixel 1~mm$^2$ devices
were tested, and all three showed anomalously frequent after-pulses with
a probability distribution extending beyond 150~ns after the primary pulse.}
but the Photonique $2\times 2$~mm$^2$ device what shown to meet all
requirements \cite{milestone_6/2008_report_on_prototyping}.

The gain of a SiPM is quite sensitive to the applied bias voltage.
The $2\times 2$~mm$^2$ Photonique SiPM has a gain coefficient of
1.8/V at room temperature, which means that raising the bias voltage
by 1~V increases the gain by nearly a factor 2.  In addition, individual
devices vary in their threshold bias voltage by as much as 2~V.  Meeting
the 10\% gain match specification in Table~\ref{tab:specs of microscope}
requires that the bias voltages on each SiPM be adjustable with a
precision of 0.1~V.  The microscope readout electronics incorporates
a low-voltage supply with individual programming of the bias voltage
on each SiPM in steps of 10~mV.  The temperature coefficient for these
SiPMs is 3\%/degree, which is quite small, given the range of
temperature variations that are expected in the tagger hall.
Nevertheless, provision has been made to monitor local temperatures
on the digital and analog readout boards.

\begin{figure}
\begin{center}
\epsfig{file=microvdist.eps,width=5in}
\caption{
\label{fig:microscope vertical segmentation results}
The distribution in vertical coordinate of the post-bremsstrahlung
electrons at the tagger focal plane in the region of the coherent peak,
for all tags (upper curve) and those that pass the photon collimator
(lower curve).  When all fibers except the central row in the microscope
are inhibited, only electrons with $|y|<1$~mm contribute to the tagging
rate.
}
\end{center}
\end{figure}

For reasons of cost, there is only one data acquisition channel per
energy channel.  Each data acquisition channel consists of a flash
ADC (250 MHz, 8 bit) and a constant-fraction discriminator coupled
to a high-resolution TDC (50~ps least-count).  Each of these sees
the summed output from the 5 fibers in an energy channel.  In addition,
4 columns equally-spaced along the fiber array are instrumented with
separate data acquisition channels on each fiber, for a total of 
120 data acquisition channels.  For the column sums, each of the 5
fibers can be inhibited in the column sum simply by lowering its bias
voltage below the SiPM avalanche threshold.  The advantage of inhibiting
some fibers in each column can be seen by the two curves in 
Fig.~\ref{fig:microscope vertical segmentation results}.  Eliminating
out-of-plane electrons reduces the rate in the tagging counters by
about 30\%, while keeping essentially all of the tags for photons that
pass the collimator.
