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\documentclass{revtex4}
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\begin{document}

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%Title of paper
\title{Monte Carlo study of a mm-scale collimator for use in the GlueX photon beam}

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\author{R.T. Jones}
\affiliation{University of Connecticut}
\homepage[]{http://zeus.phys.uconn.edu}
%\thanks{}
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\date{January 21, 2016}

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\begin{abstract}
Normalization of the absolute flux of the bremsstrahlung photon beam
for the GlueX experiment relies on a direct counting measurement of the
entire beam performed placing a highly efficient calorimeter, the total
absorption counter (TAC), directly in the beam near the position of the
experimental target. This measurement must be done at very low beam
intensity, so as not to overwhelm the TAC with pile-up. The absolute
rate measured with the TAC is used to calibrate a pair spectrometer that
serves as a continuous relative beam rate monitor, so that the flux can
be measured when the TAC is removed. Maintaining stable beam operation 
when the flux is low enough for efficient operation of the TAC is a
challenge because a certain minimum electron beam current is required 
for the beam stabilization system to function properly. It has been 
proposed that reducing the primary photon beam collimator diameter to
around 1~mm would allow the electron beam current to remain at 10~nA
and still achieve sufficiently low photon flux for the happy operation
of the TAC. The photon beam has never been simulated with so small a
collimator, and so it raises the question of whether it would produce
a usable beam, or whether the halo from scraping on the inner walls of
the collimator might overwhelm the flux of the beam that passes through
without interactions. This article reports on results of a detailed
Monte Carlo simulation of the GlueX beamline with a steel collimator
insert inside the standard 5~mm tungsten aperature, with a focus on
the spatial and spectral properties of the beam at the GlueX target.
\end{abstract}

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\section{Introduction}
Commissioning of the GlueX total absorption counter (TAC) is planned to take
place during the winter 2016 run. The purpose of the TAC is to measure the
absolute flux of the collimated beam at or near the location of the GlueX
target. Because it counts every photon in the beam, the TAC can only be
operated at very low photon beam intensity. By running simultaneously with
the pair spectrometer (PS), the TAC runs will set the absolute normalization of
the will be used to which will be used to set the absolute normalization of the
PS, which is capable of running simultaneously with data taking  at the
highest intensities foreseen for GlueX. The remainder of this report is
focused on determining suitable running conditions for the normalization
runs during which both the TAC and the PS converter are in the beam.

The count rates in the PS and the TAC are different by approximately 4
orders of magnitude, 3 of which come from the thickness of the converter
(approx\. 10$^{-3}$ rad.len\.). The fourth comes from the fact that the
TAC sees every photon in the beam, while the PS sees only those above
50\% of the end-point energy and of those, only the fraction whose pair
energy asymmetry falls within the PS acceptance.
Of course there is some freedom in setting
the threshold energy in the TAC, but even when operating at a relatively
high threshold, the flux of low-energy photons in the beam still contribute
to the TAC rate through pile-up. While there is no way to avoid pile-up
at some level in a bremsstrahlung beam, keeping the total rate of photons
above some low energy cutoff like 100 MeV below a certain level allows
the TAC threshold be be set low enough that it has a high uniform efficiency
over the full spectral range of the PS. This is the goal for the PS/TAC
calibration runs.

For the purposes of this study, I consider that optimum operating conditions
for a TAC normalization run would be around 1 MHz of total rate in the 
collimated beam above a 100 MeV cutoff. This may be ultra-conservative, but
if we can achieve stable operation at this level then we are guaranteed to
be able to achieve our goals for this run, and we can always raise the rate
if it is safe to do so. Under these conditions, the actual count rate in the
PS will be a factor $\approx 2$ lower than this (I assume a TAC threshold in
the range 1.0-2.0 GeV), and a corresponding PS trigger rate below 100 Hz.
At these total rates, it would take a 4-5 hr run to achieve 1\% statistical
precision in the independent normalization of 150 PS energy bins.

Over the course of this run, it is important for the beam conditions
to remain stable,
especially the beam intensity and position on the collimator. This is 
achieved by making sure the electron beam intensity and position remain
stable, which in turn relies on beam line locks and monitors that require
a certain minimum current for reliable operation. Over time we expect that
low-current operations will improve, but for the winter 2016 run I assume
that stable operations over a period of several hours requires a minimum
electron beam current of 10 nA. The thinnest photon radiator we have
available is $2\cdot 10^{-5}$ rad.len\. thick, which produces a total
photon flux of $53\cdot 10^{6}$ /s above 100 MeV at the radiator. Reducing
this by a factor 50 requires a collimator with a diameter of order 1~mm.

\section{photon beam simulation}
The smallest collimator we currently have available in Hall D has an
aperture diameter of 3.4~mm. The geometry of the clean-up collimator and
shielding downstream of the primary collimator has been optimized using
Monte Carlo simulation and shown to produce a clean photon beam with
negligible halo. As one reduces the collimator diameter, at some point
this should cease to be the case as the ratio of surface to area of the
acceptance region shrinks. The purpose of this study is to answer the
following questions.
\begin{itemize}
\item What halo would be expected for a collimator with a mm-size diameter
hole?
\item If it were constructed as a steel insert that fits inside the
existing tungsten collimator, would it work?
\item What would be the effect if it were shorter than the full 18 cm length
of the tungsten bore?
\item Is the halo described above sufficiently small that its effect on
the systematics of the absolute beam normalization using the TAC will be
negligible.
\end{itemize}

In this study I used a steel insert with an outer diameter of 5 mm and an
inner diameter of 1.1~mm. It was just 15 cm long (8.5 rad.len\.) inserted
until the front end is flush with the front of the tungsten collimator. A
cut-away view of the collimator is shown in Fig.~\ref{colgeom}.

\begin{figure}
\includegraphics[width=8cm]{colgeom.eps}
\caption{\label{colgeom}Cut-away view of the collimator with the steel
insert, as defined in the Monte Carlo geometry used for this study.
The beam enters from the left in this figure, and passes through the
5-mm hole in the active collimator (the left half of the figure) before
reaching the front face of the primary tungsten collimator located at the
vertical midplane in the figure. The
inner steel insert is inside a 5-mm hole through a tungsten block, which
in turn is placed inside the larger lead collimator that surrounds it.
The figure shows a beam photon that interacts in the steel collimator and
generates a shower that gets absorbed in the collimator material.}
\end{figure}

\begin{figure}
\includegraphics[width=8cm]{tagspectrum.eps}
\includegraphics[width=8cm]{targspectrum.eps}
\caption{\label{beamspectra}
Simulated photon beam spectrum for all photons exiting the diamond radiator
(left) and for all photons that reach the GlueX liquid hydrogen target 
(right) with the steel insert installed in the 5-mm tungsten primary
collimator.
}
\end{figure}

\begin{figure}
\includegraphics[width=8cm]{halospectrum.eps}
\caption{\label{halospectrum}
Spectrum of the 3\% of all particles in the photon beam that reach the
GlueX liquid hydrogen target, having been generated through interactions
somewhere between the radiator and the GlueX target.
Of these, 95\% are photons, with the remainder being mostly electrons
and positrons. The energy spectrum of the charged 5\% component is
similar in shape to the one shown above for the aggregate.
}
\end{figure}

One million beam photons were generate in the simulation, starting from
a 12~GeV electron beam with nominal CEBAF emittance and beam properties
for GlueX incident on a 20 micron diamond radiator. The crystal radiator
is oriented to place the coherent edge at 9~GeV. This is not the same
radiator as the thinner $2\cdot 10^-5$ rad.len\. radiator to be used
for TAC runs, but for the purposes of answering the above questions it
is completely adequate, and it gives additional information through the
structure of the spectrum about how much scattering in the collimator
walls is contaminating the beam. The photon spectrum in the tagger and
at the GlueX liquid hydrogen target are shown in Fig.~\ref{beamspectra}.
From the right-hand plot in the figure, it is clear that the collimator
is doing its job of selecting the central core of the photon beam, and
is not significantly contaminated by secondary photons from showers in
the collimator. To check if those photons might be present in the beam at
lower energies in the spectrum, I measured the total fraction of all
photons reaching the liquid hydrogen target that had seen {\em any}
interactions since leaving the diamond radiator. The result is 3\%,
and their spectrum is shown in Fig.~\ref{halospectrum}.

\begin{figure}
\includegraphics[width=8cm]{beamspot.eps}
\includegraphics[width=8cm]{beamspot2.eps}
\caption{\label{beamspot}
Transverse impact distribution of all particles in the photon beam
reaching the GlueX liquid hydrogen target (left) and only those
over 500 MeV (right). Photons are shown by blue points, and charged
particles with red points. In the left plot, 84\% of all impacts are
within the innermost intense dot. In the right plot, the corresponding
fraction is 97\%, increasing to 98\% if the low-energy cutoff is
raised to 2~GeV.
}
\end{figure}

The impact distribution of all particles in the photon beam are shown in
Fig.~\ref{beamspot}. The left plot shows all particles, and the right
shows only those over 500 MeV at the point where they passed through the
target entrance plane. The innermost circle within which the maximum
intensity occurs is the shadow of the 1.1~mm steel insert in the
primary collimator. The next circle outside that is the shadow of the
5~mm tungsten collimator inside which the steel insert is embedded. 
Even though the steel stops most of the photon flux, the tungsten around
it is still needed to absorb the debris that the insert creates. The
larger circle outside that is the shadow of the secondary clean-up
collimator. The right plot shows that most of the beam halo is very
low energy electromagnetic radiation at the few hundred MeV scale or below.
Considering only particles in the beam area with energies above 500~MeV,
the halo fraction is 3\%, dropping to 2\% if the low-energy cutoff is
raised to 2~GeV.

\section{Conclusions}
Given that the beam spot does show tails around the central disk, the
last question to be answered is how this halo translates into a systematic
error in the absolute beam flux normalization measured using the TAC.
For this, one must define an effective acceptance radius for the beam.
This clearly must be smaller than the radius of the liquid hydrogen target
and also the entrance aperture of the TAC. The target tapers from a radius of
12.37~mm at the upstream end down to 0.78~mm at the downstream end. The
entrance aperture to the TAC is larger than this, so I take 0.75~mm as
the effective acceptance diameter of the photon beam at the GlueX target.
According to the simulation described above, the fraction of the total
photon flux within this radius at the GlueX target is 99.3\% for photons
of all energy above 1~MeV, rising to 99.98\% for all photons reaching
the GlueX target with more than 500~MeV energy. By almost any standards,
the systematic normalization error coming from the photon beam halo in
this simulation is negligible.

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