\section{Tagging Spectrometer}
\label{tagger}
\subsection{Specifications}

To satisfy the needs of the \GX{} physics program, the tagged photon
spectrometer should meet the following specifications:

\begin{enumerate}
\item Photon energy detection from 
$70$\% to $75$\% of $E_{0}$ with energy resolution of about $0.1$\% r.m.s.
Percentages refer to the primary beam energy $E_{0}$, i.e.
``$0.1$\%'' means $12$~\Meunit\ energy resolution for a $12$~\eunit\ beam.
%
\item A detector system which allows a counting rate of
at least
$5\times 10^{6}$ electrons per second per $0.1$\% over this range of
photon energies.     
%
\item
An additional capability for photon energy detection from $25$\%
to $90$\% of $E_{0}$, with less stringent resolution and count rate
requirements .
%
\item A quadrupole magnet between the radiator and dipole spectrometer
which images the beam spot on the radiator onto a line on the focal
plane.  This feature makes it possible to envision the use of focal
plane counters with two-dimensional readout, with which one could enhance
the tagging efficiency of the source.  Focal
plane detectors with two-dimensional readout are considered as a
possible upgrade beyond  the baseline design presented in this chapter.
Any improvements obtained using this technique would be over and above
the performance figures presented in this report.
%
\end{enumerate}
%\end{list}

The system described below, based on a room-temperature design, meets
all of these criteria.  The option of a superconducting design was
also studied.  With a superconducting magnet, the spectrometer could
operate at much higher fields, offering the possibility of some
space savings in the size of the tagger focal plane array and larger
head-room for future possible energy upgrades beyond $12$~\eunit .
An iron yoke design was found which would clamp the $5$~\tbunit{} field 
sufficiently to make it possible to operate normal phototubes on the
nearby tagger focal plane.  However, as shown below, rate considerations
require a degree of segmentation in the tagging counters such that it is
impractical to increase the dispersion along the focal plane above
what is provided by a $1.5$~\tbunit{} room temperature magnet.  That being
the case, it was decided that considerations of upgrade margin and
electrical power alone do not justify the additional cost and
complexity of a superconducting magnet.
%---------------------------------------------------------------


\subsection{Magnet}
%New Material 21-September-2004
The original design of the tagger spectrometer, which incorporated a single, 
long  dipole magnet $\sim$ 6.1~m in length weighing about 100~tons, has been 
changed to replace the single dipole with a configuration consisting of two 
identical dipoles in series with each other.\newline

The main reasons for this change are:
\begin{enumerate}
\item It will be difficult to find a supplier of $\sim$ 6.5 m lengths of high 
quality magnetic iron at a reasonable cost.
\item Since the weight of the top and bottom yoke pieces for a single dipole 
tagger will weigh more that 20 tons, either a crane with a capacity of more 
than 20 tons or heavy duty lifting equipment will be necessary to install 
the magnet or undertake any future repairs or modifications.
\item The long  structure of a single dipole tagger will be difficult to install.
\item  Since the energy degraded bremsstrahlung electrons  exit a tagger along 
the whole of its length, it is necessary to have the exit completely open. 
Due to the attractive magnetic force between the poles, the aperture along 
the exit will distort when the field is present. The effect of this 
distortion will probably be less for two smaller dipoles than for a single long dipole.
\item The smaller magnets can be made by more manufacturers and will 
probably be cheaper.
\item Building costs will be less for the two dipole option - cheaper 
crane, smaller access doors etc.
\end{enumerate}


\begin{figure}[h!]\centering
\includegraphics[width=0.9\textwidth]{ch4_taggerplan.eps}
\caption[Plan view of tagging spectrometer]{\label{fig:tagger_plan}
  A plan view of the tagging spectrometer from above, showing the
  path of the primary beam and the trajectory of post-bremsstrahlung
  electrons of various recoil momenta.}
\end{figure}

The parameters of the two dipole tagger are shown in Table~\ref{tab:magnetpars}. 
The object distance is listed explicitly since it has been increased from 
$1.5$~\mlunit{} to $3.0$~\mlunit . This improves the resolution by around 
30\% and gives more room for the goniometer vacuum chamber, the quadrupole 
and monitoring devices. A plan view of the layout of the spectrometer is 
shown in Figure~\ref{fig:tagger_plan}.


\begin{table}[h!]\centering
\begin{tabular}{lc}
\hline\hline
    Radius of curvature	    & 26.7 m \\
    Full-energy deflection  & 13.4$^{\mbox{\rm o}}$ \\
    Object distance           &  3 m \\
    Field at 12~\eunit	    & 1.5 Tesla \\
    Gap width		    & 3.0 cm \\
    Length of each pole	    & 3.1 m \\
    Weight	of each dipole	    & 38 tons \\
    Length of focal plane (25\% to 90\% of $E_0$) & $ \sim $ 9.0 m \\
    Coil power	    	    & 30 kW \\
\hline\hline
\end{tabular}
\caption[Tagging spectrometer parameters]{\label{tab:magnetpars}
  Design parameters for the two dipole tagging spectrometer.}
\end{table}

\begin{figure}[h!]\centering
\includegraphics[width=0.85\textwidth]{ch4_taggeroptics.eps}
\caption[Two magnet tagger optics ]{\label{fig:tagger_optics}
  Comparison of optics properties between the one dipole and the two dipole tagger.}
\end{figure}
The coils for the two dipole tagger will be run in series from a single power supply.

The first dipole magnet analyzes electrons from $1$ to $4.3$~\eunit
corresponding to photon energies of  $7.7$ to $11$~\eunit, and 
the second magnet analysis electrons from $4.3$ $9$~\eunit, corresponding 
to photon energies of $3$ to $7.7$~\eunit. This is ideally matched to  
GlueX which requires photons in the energy range covered by the first dipole. 
It is also clear that a two dipole magnet system is optimum, since with 
more magnets, the energy range required by GlueX would probably have to 
be shared between different dipoles.  


The pole gap has been increased from $2.0$ to $3.0$~\cmlunit. 
The larger gap is more accessible, and is less susceptible to any changes 
to the pole gap caused by the magnetic field. Furthermore since only 
$\sim\, 30\, kW$ are required for the $3.0$~\cmlunit{} gap -compared to 
$\sim\, 17.6\, kW$ for the  $2.0$~\cmlunit{} gap - the coil power consumption 
remains modest. 


The two dipole magnet configuration was only adopted after extensive 
investigations into the magnetic optics confirmed it is possible to 
design such a system with a continuous focal plane. First order TRANSPORT 
calculations of the dispersion, resolution and vertical height along the 
focal plane, as well as beta, the angle at which the analyzed electrons 
cross the focal plane, are compared for the single and two dipole magnet 
systems in Figure~\ref{fig:tagger_optics}.\newline
\vspace{1cm}


\begin{figure}[h!]\centering
\includegraphics[width=0.65\textwidth]{ch4_taggerbeta.eps}
\caption[comparison of beta]{\label{fig:tagger_beta}
  Comparison between the beta for the focal plane calculated using 
  TRANSPORT and the beta for the straight focal plane determined according 
  to the TOSCA results.}
\end{figure}


The resolution and vertical height are essentially unaltered. Although 
the dispersion shows a small discontinuity at an electron energy 
$\sim\, 4.3$~\eunit, which is where the focal planes from the dipoles 
join, along the whole extent of the focal plane the dispersion from 
the two dipole tagger is slightly larger. However, beta shows a 
significant discontinuity at the join of the focal planes.  This 
apparent effect was examined in more detail by ray tracing electron 
trajectories through a 3-D magnetic field obtained from TOSCA. The 
ray tracing calculations were also used to find an acceptable location 
for a straight focal plane which is displaced slightly from the 
curved TRANSPORT focal plane. Figure~\ref{fig:tagger_beta} compares 
the variation of beta along the straight focal plane obtained using 
TOSCA, and along the first order TRANSPORT focal plane. It shows 
that the realistic field computed by  TOSCA leads to a smooth 
variation for beta and also shows that beta is larger  for the 
higher energy section of the focal plane. The magnetic optics parameters, 
calculated by TRANSPORT along the straight focal plane,  are shown 
in section~\ref{sec:4.4.3}.

Several designs have been considered for the vacuum system. The most 
promising approach is to use the magnet poles as part of the vacuum 
chamber. Either the poles could be welded to a stainless steel vacuum 
chamber, or the seals between the vacuum chamber and the poles could 
be made by compressing a viton O-ring between the top and bottom lids 
of the vacuum chamber and a lip machined round the pole shoes.


A reasonably detailed design for a two dipole magnet tagger, which 
incorporates a vacuum chamber using O-ring seals, has been completed. 
The design has been sent to Russian groups within the GlueX collaboration 
who will examine the technical feasibility of the design and investigate 
if ISTC funding can be obtained to construct the tagging spectrometer. 
It should be possible to assemble and test the complete spectrometer in 
Russia since a feature of the design which uses O-ring seals is that 
the spectrometer can be fully assembled and tested in the factory 
where it is built, and  then be taken apart and subsequently re-assembled 
in Jefferson Lab.    

%end of new material
%---------------------------------------------------------------

The detector package is divided into two parts: a set of $141$ fixed
scintillation counters spanning the full energy range from $25$\% to
$95$\%, and a movable ``microscope'' of more finely-segmented counters
designed to span the region of the coherent peak.

The fixed array provides access to the full tagged photon spectrum,
albeit at a modest energy resolution of $0.5$\% and reduced photon
spectral intensity.  These detectors are well suited for running with
a broadband incoherent bremsstrahlung source.  They enable experiments
to be performed with the highest photon energies possible with the
source.  When running with a coherent source they play an essential
role in the crystal alignment procedure, and provide a continuous
monitor of the performance of the source.  The microscope is needed
in order to run the source in coherent mode at the highest polarization
and intensities, and whenever energy resolution better than $0.5$\% is
required.  Using the microscope, the source is capable of producing
photon spectral intensities in excess of $2\times 10^{8}$ photons/\eunit,
although accidental tagging rates will limit normal operation to
somewhat less than this.


\subsection{Spectrometer Optics}\label{sec:4.4.3}

Table~\ref{tmagprops} and Table~\ref{taggerres} give some of the tagger
optics parameters as functions of the photon energy.  They were calculated
for the one-magnet spectrometer option, but the differences between the
optics of the two-magnet and one-magnet designs are not very significant,
as shown in Figs.~\ref{fig:tagger_optics}-\ref{fig:tagger_beta}. The energy
resolution and transverse position resolution were calculated assuming
the beam properties listed in Table~\ref{elecprop}.
%\begin{center}
%\begin{tabular}{c}
%     $\Delta E/E_0$ = 0.080\% r.m.s. \\
%     $\Delta x$  =   1.7\mmlunit\ r.m.s. \\
%     $\Delta y$  =   0.5\mmlunit\ r.m.s. \\
%     $\Delta x'$ =  .020 mr r.m.s. \\
%     $\Delta y'$ =  .005 mr r.m.s. \\
%\end{tabular}
%\end{center}
The intrinsic energy resolution (i.e. the energy resolution
independent of detector size) is limited in most cases by the $0.08$\% 
energy spread of the primary electron beam.


\begin{table}
\begin{center}
\begin{tabular}{cccccc}
\hline\hline
   k   & Bend & Drift &  Angle & cm/\%$E_0$ & cm/\%$E_0$ \\
 (\eunit) & (deg) & (m)  &  (deg) &  perp.to ray
& along FP \\
\hline
   6  &  17.270 & 3.7790 &    6.035 &  1.467 & 13.956 \\
   7  &  17.664 & 3.2039 &    6.428 &  1.568 & 14.008 \\
   8  &  18.28 & 2.6276 &    6.992 &  1.716 & 14.096 \\
   9  &  19.108 & 2.0485 &    7.872 &  1.954 & 14.264 \\
  10  &  20.695 & 1.4626 &    9.459 &  2.407 & 14.644 \\
  11  &  24.608 & 0.8560 &   13.372 &  3.668 & 15.860 \\
\hline\hline
\end{tabular}
\end{center}
\caption[Geometry of the tagger]{\label{tmagprops}
Geometrical parameters of the tagging spectrometer for $E_0 = 12$~\eunit : 
Bend = deflection angle; Drift = distance from exit edge to focal plane;
Angle = angle between electron path and focal plane; 
\cmlunit /\%$E_{0}$ = dispersion in units of cm per percent of the incident 
energy}
\end{table}

\begin{table}
\begin{center}
{\small
\begin{tabular}{ccccccccc}
\hline\hline
   k  &  (x x) & (y y) & (y y') & $\Delta k_{beam}$ & $\Delta k_{spot}$ &
 $\Delta k_{tot}$ & $\Delta y_{tot}$ & $y_{char}$ \\
{\scriptsize (\eunit)} &
{\scriptsize  (mm/mm)} &
{\scriptsize  (mm/mm)} &
{\scriptsize  (mm/mr)} &
{\scriptsize  (\%$E_0$)} & 
{\scriptsize  (\%$E_0$)} &
{\scriptsize  (\%$E_0$)} &
{\scriptsize  (mm)} &
{\scriptsize  (mm)} \\
\hline
\multicolumn{9}{l}{Without quadrupole:} \\
\hline
   6 & -0.701 & 2.737 & 18.882 & 0.080 &  0.081 &  0.114 &  1.372 &  0.804 \\
   7 & -0.667 & 2.708 & 16.538 & 0.080 &  0.072 &  0.108 &  1.357 &  0.986 \\
   8 & -0.625 & 2.670 & 14.178 & 0.080 &  0.062 &  0.101 &  1.337 &  1.207 \\
   9 & -0.569 & 2.617 & 11.788 & 0.080 &  0.050 &  0.094 &  1.310 &  1.506 \\
  10 & -0.494 & 2.539 & 9.341 & 0.080 &  0.035 &  0.087 &  1.270 &  1.989 \\
  11 & -0.389 & 2.402 &  6.745 & 0.080 &  0.018 &  0.082 &  1.201 &  3.159 \\
\hline
\multicolumn{9}{l}{With quadrupole:  (length = 50 cm, gradient = -0.4 kGauss/cm)}\\
\hline
   6 & -0.628 &  0.451 & 17.622 & 0.080 &  0.073 &  0.108 &  0.242 & 0.750 \\
   7 & -0.583 &  0.348 & 15.121 & 0.080 &  0.063 &  0.102 &  0.190 & 0.901 \\
   8 & -0.526 &  0.202 & 12.535 & 0.080 &  0.052 &  0.095 &  0.119 & 1.068 \\
   9 & -0.449 &  -0.024 & 9.792 & 0.080 &  0.039 &  0.089 &  0.050 & 1.251 \\
  10 & -0.338 & -0.427 &  6.699 & 0.080 &  0.024 &  0.083 &  0.216 & 1.426 \\
  11 & -0.162 & -0.416 &  2.474 & 0.080 &  0.008 &  0.080 &  0.708 & 1.159 \\
\hline\hline
\end{tabular}
}
\end{center}
\caption[Optical properties of the tagger]{\label{taggerres}
Optical properties and resolutions of the tagging spectrometer
at the focal plane, for $E_0 = 12$~\eunit :
(x x),(y y),(y y') = first-order transport matrix elements where x and y
are radial and transverse coordinates respectively; the focal plane is 
defined by (x x')=0.; 
$\Delta k_{beam}$ = r.m.s.\ energy resolution due to beam energy uncertainty;
$\Delta k_{spot}$ = r.m.s.\ energy resolution due to spot size on radiator;
$\Delta k_{tot}$ = total r.m.s.\ energy resolution excluding detector size;
$\Delta y_{tot}$ = transverse r.m.s.\ position resolution due to spot size
on radiator;
$y_{char}$ = transverse size corresponding to one characteristic electron 
angle $\theta_{Ce} = (m/E_0)(k/(E_0 - k))$.}
\end{table}


At the focal plane, the characteristic bremsstrahlung angle corresponds to
a few millimeters of transverse displacement.  The vertical beam spot
size at the radiator ($0.5$~\mmlunit\ r.m.s.) contributes a
comparable amount because of the large transverse magnification in the
dipole transport matrix.  However, placing a quadrupole magnet between
the radiator and the tagger dipole magnet reduces this magnification
nearly to zero over a substantial range of photon energies without
substantially changing the other optical properties.  Including the
quadrupole in the design makes possible a future upgrade of the photon
source to employ tagging detectors with two-dimensional readout.


\subsection{Tagger Detectors}
\subsubsection{Fixed Focal Plane Array}

Tagging of photons over the full range from $25$\% to $95$\% of $E_{0}$
is not required as part of the physics program here proposed for \GX,
but is desirable for two separate reasons.  First, it will increase the
flexibility of the source by providing a broad-band incoherent bremsstrahlung
tagging mode, enabling access to photons of the highest energy
possible at Jefferson Lab.  Second, the process of aligning the crystal
radiator for coherent bremsstrahlung requires rotation about several axes and
rapid observation of the resulting energy spectra, as described in 
section~\ref{alignment}. The low-energy portion of the spectrum, between 
about $25$\% and $50$\% of $E_{0}$, is most sensitive to these rotations, and 
experience with the coherent bremsstrahlung beam at 
Mainz~\cite{MainzTS,MainzFP} indicates that the alignment process would be 
severely compromised if photon energies below $0.5\  E_{0}$ were not 
measurable.

%A high resolution in the tagger is not deemed necessary for 
%these purposes.  A counter width spanning $0.5$\% of $E_{0}$ is considered
%sufficient in most cases.  For operations with an amorphous radiator,
%these counters would be capable of running a broad-band photon beam
%with the highest intensities compatible with tagging.  Crystal alignment
%procedures are not normally carried out at full source intensity, so
%rate capacity is not a limitation in that application.  If a need
%arose to operate the source in collimated-coherent mode at lower
%photon energies, for example to obtain increased polarization, then
%full-intensity operation would always be possible by repositioning the
%microscope on the focal plane.  In this case, the fixed array would
%be useful in the energy calibration of the movable segment.
%When used as the primary tagging detectors, the fixed array
%would be capable of pre-collimated intensities up to $80$~\mhz /\eunit.

\begin{figure}[ht]\centering
\includegraphics[angle=-90, width=\textwidth]{ch4_fixedarray.eps}
\caption[Fixed array of tagging counters]{\label{fig:fixedarray}
  Layout of the tagging counters on the high-energy end
  of the tagger focal plane, corresponding to the lowest-energy
  electrons from the spectrometer.  The view is from above.}
\end{figure}
\begin{figure}[ht]\centering
\includegraphics[width=\textwidth]{ch4_microscope.eps}
\caption[Conceptual design of tagging microscope]{\label{fig:microscope}
  Conceptual design of a segment of the tagger microscope, showing
  the two-dimensional array of scintillating fibers and the clear
  fiber light guides that couple the light to the silicon photomultipliers.}
\end{figure}

The design for the fixed tagger focal plane array consists of 141
non-overlapping scintillation counters.  The scintillators are 0.5~$cm$
thick and 4~$cm$ high and are read out by 1-inch phototubes located
below the mid-plane of the spectrometer.  The scintillator paddles
are oriented perpendicular to the scattered electron rays and are
distributed along the focal plane to give essentially 100\% coverage
of the range from 25\% to 95\% of $E_0$.  The size and spacing of
the counters varies along the focal plane, according to the dispersion
and crossing angle listed in Table~\ref{tmagprops}.  The high-energy
end of the array is shown in Fig.~\ref{fig:fixedarray}, which
corresponds to the lowest-energy electrons from the spectrometer.

\subsubsection{Focal Plane Microscope Detectors}

The design energy resolution of $0.1$\% r.m.s.\ (see Table~\ref{taggerres})
is met by non-overlapping detectors which span an energy range
of $0.1$\% each. The principal limitation on detector size is imposed
by the design goal of tagging collimated photons at rates
up to 100 MHz over the coherent peak.  The nominal collimated coherent peak 
has its highest intensity between about $8.5$ and $9$~\eunit\ (see 
Fig.~\ref{collimcuts}). However, the the tagger sees both collimated and 
uncollimated photons, and the total tagging rate in this region is more than
twice the collimated rate (see Fig.~\ref{collimcuts}), about $250$~\mhz.
The nominal position of the microscope on the focal plane is spanning the
region 70\% - 75\% of $E_0$.  Dividing this range into 80 bins of equal
size limits all channels to less than 5~\mhz, which is well within the
operating range of the silicon photomultiplier (SiPM) devices foreseen
to be used for this detector.

The detector is composed of a two-dimensional array of square scintillating
fibers of cross section 1~$mm^2$, as shown in Fig.~\ref{fig:microscope}.
Electrons from the spectrometer follow a path approximately parallel to
the axis of the fibers, creating a large light yield which effectively
suppresses omnidirectional background in the hall and permits the
operation of the SiPM detectors with a high discriminator threshold
where their dark rate is low.  Multiple scattering of electrons in the
fiber material effectively produces some degree of overlap between the
channels, but does not appreciably degrade the energy resolution of the
device.  Clear fibers attached to the back end of the scintillating fibers
transport the light out of the spectrometer mid-plane to a region with
low radiation where the SiPM detectors are located, each with an active
area of 1~$mm^2$.  The microscope will be located immediately in front of
the fixed array.

In the baseline operating mode, all five fibers in a column shown in 
Fig.~\ref{fig:microscope} will be summed into one electronics channel.
The vertical segmentation of the device also permits its operation in
an enhanced mode, where only one fiber in each column is active.  In
the enhanced mode with the tagger quadrupole switched on, the detector
counts only a narrow band of scattered electrons that lies close to the
spectrometer mid-plane.  This has the advantage that the tagger is blind
to those electrons which scatter at large vertical angles in the radiator,
whose corresponding photon will be lost on the photon collimator. This
can be accomplished efficiently by delivering the power to the SiPM
devices independently by row.  Simply by selectively powering the
individual rows of the array, the readout can be switched from tagging
the full vertical range of the beam to counting only a central stripe
which corresponds to the size of the photon collimator.

\subsection{Beam Dump Optics} 

Although the full-energy beam leaving the tagger magnet is diverging in 
both directions, the range of angles is small enough that the 
beam does not blow up rapidly. For a dump distance of $30$~\mlunit{} the 
r.m.s.\ beam size is $6.3$~\mmlunit\ horizontal (dominated by the $0.08$\% 
beam energy spread) and $0.7$~\mmlunit\ vertical (combination of vertical 
spot size and multiple scattering in a $10^{-4}$ radiation length radiator.)

These values scale approximately linearly with distance from the magnet to 
the dump, and are not very sensitive either to the quadrupole or to small 
rotations of  the exit edge of the tagger magnet.  Thus the beam dump design 
is quite insensitive to the beam optics, and depends only on the lateral and 
longitudinal spread of the shower in the absorber.

