\chapter{Operating beam intensity}\label{chapter_rates}

Table~\ref{operates} brings together the diverse set of parameters
that must be considered in evaluating the optimum beam intensity at
which an experiment using the coherent bremsstrahlung beam should operate.
All four columns of numbers were obtained for the same beam conditions,
except that the crystal orientation was adjusted to align the coherent
intensity peak at the energy listed in row one.  The second row, labeled
$N_{\gamma}$, gives the integrated rate of beam photons in the coherent
peak downstream of the collimator.  Note the sharp decrease in the intensity
of the coherent peak as the energy approaches the end point.  By contrast,
the incoherent bremsstrahlung flux is approximately constant over this
range of energies.  The third and fourth row show the height and width of
the peak in the polarization spectrum of the beam.  Rows  five and six
report the height and width of the peak in the tagging efficiency spectrum.
The tagging efficiency is defined as the number of beam photons of a
particular energy reaching the target divided by the corresponding rate
in the tagging focal plane.  Large tagging efficiencies are required in
order to make effective use of tagging.  The width of the peak in the
tagging efficiency spectrum determines the width of the focal plane that
would be active when running with collimation.  The peak integral reported
in row two is summed within the f.w.h.m.\ tagging efficiency window.  Rows
seven and eight give the photon beam power that is incident on the
experimental target (and photon beam dump) and the photon collimator,
respectively.  

The last two rows in Table~\ref{operates} give the inclusive and tagged rates 
for hadronic triggers from a $30$\cmlunit\ liquid hydrogen target placed in
the beam following the collimator.  Note that the total hadronic rate is
dominated by background (\emph{i.e.} non-tagged) events associated with
the low-energy component of the beam.  This is why the total trigger rate
is essentially constant while the flux in the coherent peak varies with peak
energy over an order of magnitude.  This table illustrates the value of
having an electron beam energy well above the photon energy needed for
the experiment.


\begin{table}
\begin{center}
\begin{tabular}{lcccc}
\hline\hline
$E$ of peak & 8 \eunit\ & 9 \eunit\ & 10 \eunit\ & 11 \eunit\ \\
$N_{\gamma}$ in peak & 185 M/s & 100 M/s & 45 M/s & 15 M/s \\
peak polarization & 0.54 & 0.41 & 0.27 & 0.11 \\
\multicolumn{1}{c}{(f.w.h.m.)} & (1140 \Meunit) & (900 \Meunit) & (600 \Meunit) & (240 \Meunit) \\
peak tagging efficiency & 0.55 & 0.50 & 0.45 & 0.29 \\
\multicolumn{1}{c}{(f.w.h.m.)} & (720 \Meunit) & (600 \Meunit) & (420 \Meunit) & (300 \Meunit) \\
power on collimator & 5.3 W & 4.7 W & 4.2 W & 3.8 W \\
power on target & 810 mW & 690 mW & 600 mW & 540 mW \\
total hadronic rate & 385 K/s & 365 K/s & 350 K/s & 345 K/s \\
tagged hadronic rate & 26 K/s & 14 K/s & 6.3 K/s & 2.1 K/s \\
\hline\hline
\end{tabular}
\end{center}
\caption[Operating parameters for an experiment]{\label{operates}
Operating parameters for an experiment using the coherent bremsstrahlung beam.
The calculation assumes a $12$\eunit{} electron beam energy and a 
$3.4$\mmlunit{} collimator $80$\mlunit{} downstream from a radiator of 
thickness $10^{-4}$ radiation lengths.  The electron beam current is taken to 
be $3$\miamps. The rates in the detector (last two rows) are calculated for 
a $30$\cmlunit{} liquid hydrogen target and an open hadronic trigger.}
\end{table}

