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\title{FDC Progress Report (September 2006)}
\author{Simon Taylor \\ Ohio University \\ \\
 Daniel S. Carman \\ Jefferson Lab and Ohio University\\ \\
David Lawrence \\
Jefferson Lab \\ \\
Brian Kross \\ Jefferson Lab }
\begin{document}
\maketitle
\begin{abstract}
This report details progress toward the design of a full-scale prototype
cathode chamber for the FDC system of the GlueX experiment in Hall D at
Jefferson Lab.  This work is based on studies of a small-scale prototype 
that has been under test and an ongoing R\&D program in conjunction with 
the Jefferson Lab Detector Group.  The design of the full-scale prototype 
is based on lessons learned from the small-scale detector and the R\&D 
program with an aim to identify and to mitigate all risk areas.
\end{abstract}

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\section{Forward Drift Chamber System}
\label{fdc_intro}

The Forward Drift Chamber (FDC) system in the GlueX detector in Hall D
at Jefferson Lab (JLab) consists of a set of 24 planar drift chambers
with cathode readout that is grouped into four identical disk-shaped 
packages of six chambers.  This system is designed to track forward-going 
particles from the target ($2^\circ < \theta < 20^\circ$) in the 2~T
magnetic field of the GlueX solenoid.  A schematic picture of a single FDC 
package is shown in Fig.~\ref{fdc_view}.  Details on the FDC prototype 
studies and design work is contained on the FDC web page~\cite{fdc_web}.
Fig.~\ref{gluex} shows the position of the FDC packages within the full 
GlueX detector. 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{6.7cm}
\special{psfile=fdc_cath.eps hscale=85 vscale=85 hoffset=50 voffset=-5}
\special{psfile=fdc_side.eps hscale=80 vscale=80 hoffset=260 voffset=-5}
\caption{A front (a) and side (b) sketch of an FDC package. In (a) the 
wires are schematically indicated as the vertical lines. The $U$ cathode 
strips are in front of the wires and the $V$ cathode strips are behind 
the wires.  In (b) is shown a side view of the upper half of a six-chamber 
package.  The wire planes are shown as the dashed lines, while the cathode 
planes are shown as the solid lines. Ground planes between adjacent chambers 
are not shown.}
\label{fdc_view}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{7.5cm}
\special{psfile=gluex_detector.eps hscale=70 vscale=70 hoffset=40 voffset=0}
\caption{A schematic picture of the GlueX detector showing the location of 
the four FDC packages within the solenoid magnet.}
\label{gluex}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Each chamber is 1.2~m in diameter and consists of a wire plane flanked on 
either side by cathode planes divided into thin strips as illustrated in 
Fig.~\ref{fdc_schem1}.  The strips are oriented at $\pm$45$^\circ$ with 
respect to the wires and 90$^\circ$ with respect to each other.  Neighboring 
chamber layers will be rotated by 60$^\circ$ with respect to each other in 
order to improve track reconstruction decisions on the corresponding 
left/right ambiguities in the wire planes, hence improving the overall 
resolution.  By charge interpolation of the electron avalanche image charge 
in the cathode strip readout, spatial resolutions at the cathode planes are 
expected of better than 200~$\mu$m.  The purpose of crossing the strips is 
to provide redundant coordinate information, as well as to aid in pattern 
recognition in the background environment expected in the GlueX detector
(see Section~\ref{generic_csc}).  The individual hits from each of the 
packages will then be linked via the analysis software to reconstruct the 
spiraling tracks in the GlueX solenoidal magnetic field.  The nominal design 
parameters for the FDC detector system are given in Appendix I.
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{7.5cm}
\special{psfile=geom2.eps hscale=100 vscale=100 hoffset=100 voffset=10}
\caption{Schematic drawing of the orientation of the cathode strips
flanking a given wire plane.  The strip pitch $w$=5~mm and the 
strip-to-strip gap $g$=1~mm.  The sense wire separation $s$=10~mm.  The
two cathode readout views are referred to as $U$ and $V$.}
\label{fdc_schem1}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The primary development issues associated with the FDCs that must be 
addressed are factors affecting the intrinsic resolution of the chambers, 
along with the mechanical and electronics layout.  The goal is to construct 
a tracking detector that meets the required design specifications and has a 
long life time, a uniform and predictable response, a high efficiency, and 
is serviceable in case of component failure. 

\subsection{FDC Design Details}

Each wire plane consists of alternating field and sense wires, with a sense 
to field wire separation of 5 mm and a wire plane to cathode plane 
separation of 5~mm.  The nominal design for the cathode planes calls for
a strip pitch of 5~mm and a strip-to-strip separation of 1~mm (see
Fig.~\ref{fdc_schem2}.  The strips will lay on a 2-mil thick Kapton backing.  
The strips themselves will be copper with a thickness of 0.25~oz.  Studies of 
our small-scale prototype with copper layers of two thicknesses (1.0~oz  
and 0.25~oz) have been carried out and the 0.25~oz option is the 
thinnest copper layer that allows for signal integrity above our specifications.  
Minimization of the overall chamber thickness is important to reduce multiple 
scattering and energy loss.  A ground plane is included between neighboring 
cathode planes to ensure minimal signal cross-talk.  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{4.0cm}
\special{psfile=geom1.eps hscale=100 vscale=100 hoffset=20 voffset=10}
\caption{Schematic end view (wires projecting into and out of the
plane of the page) defining the nominal electrode geometry of the
FDC system}
\label{fdc_schem2}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

To limit wire tensions and operating voltages implies that the wire diameter 
has to be minimized.  The anode wire for the chambers will consist of
20-$\mu$m diameter gold-plated tungsten, the smallest practical choice.  
Tungsten is a good choice because of its durability, and the gold-plating of 
the wires ensures chemical inertness as well as a smooth surface finish.  
The expected electronics gain and thresholds dictate that the gas gain be a 
few times 10$^4$.  Under this condition, the electric field at the surface 
of the sense wires is $\approx$280~kV/cm.  The field-wire diameter is 
chosen to ensure that the electric field at their surface remains below 
20~kV/cm to minimize conditions causing cathode deposits
\cite{kadyk,cathode}.  The field wire diameter will be chosen to be
100~$\mu$m.  Gold-plated aluminum is a good choice because it has the
longest radiation length of any practical wire material and thus minimizes 
multiple scattering.  Additionally, the low density of aluminum means that 
the field wires can be strung at lower tension than a more dense wire, with 
minimal gravitational sag.  This minimizes the forces on the support
frames.  Presently we are seeking out vendors to supply the wire for
the chambers that will meet our tolerances and specifications.  We will
rely on our experiences from construction of the drift chambers in Hall B
to make the final vendor selection.

The wires that cross through the beam line require special treatment to
handle the otherwise unmanageable rates.  Several possibilities are
currently being considered.  The first is to deaden the wires out to
a radius of $\sim$3.5~cm by placing a material such as Styrofoam around
them.  Another attractive alternative that has been perfected at
Fermilab~\cite{fnal} is to deposit a layer of metal on that portion of
the wires to be deadened to build up the wire diameter.  This technique
then reduces the surface electric field on this portion of the wire
to the point where the gain is reduced below the level necessary for
the electron avalanche to be formed.

\subsection{Readout}

The readout of the full set of FDC detectors will require on the order of 
2850 anode (sense wire) channels and 11400 cathode channels.  The exact 
numbers are subject to the details of the mechanical design, which is 
presently underway.  The signals will be amplified at the detector using 
an 8-channel ASIC preamplifier/shaper chip based on the ASDBLR ASIC used 
to readout the ATLAS-TRT (see Fig.~\ref{asic_pic}).  The pulse shape will 
be chosen as a compromise between noise and pileup, both of which degrade 
the resolution.  The electronics must also be designed to minimize cross-talk, 
particularly to non-adjacent channels. The design of this component is the 
responsibility of the University of Alberta and the University of Pennsylvania.  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{5.7cm}
\special{psfile=asic_pic.eps hscale=50 vscale=50 hoffset=60 voffset=-5}
\caption{Photographs of two ASDBLR ASICs used in the ATLAS-TRT detector.}
\label{asic_pic}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The nominal data acquisition plan calls for the cathode strips to be read 
out with commercially available 100 MHz flash ADCs and the anode wires to be 
read out with commercially available F1 TDCs. We are also investigating an 
alternative approach in which we would use flash ADCs to read out the anode 
wires as well as the cathode strips.  In our small-scale prototype, we are 
employing the same preamplifiers as used for the CLAS drift chambers, as
the ASIC chips for GlueX are not yet ready for detector testing, but our
readout electronics employ the flash ADCs and TDCs expected to be used
for the final GlueX FDC readout.

The 100~MHz flash ADCs that will be employed for the cathode readout have
a sampling rate that corresponds to a 10.0~ns time bin.  Time fitting 
algorithms matched to the chamber pulse shape can be employed to provide a 
time resolution of $\sim$2~ns (amounting to $\sim$20\% of the time bin width).  
This timing information from the cathode signals will significantly aid in 
resolving hits from multiple tracks passing through the chamber volume.

The primary design issue for the front-end electronics for the FDC
system is to maintain a signal-to-noise ratio of better than 100:1 in 
the presence of a large detector capacitance.  Capacitance measurements 
in detectors are very important because they serve to determine the
performance of the detector in terms of the charges induced on the cathodes,
gain variations, detector efficiency, etc.  They also play an important
role in determining the characteristics of the readout electronics.
For the FDC chambers the dominant contribution
to the capacitance seen by the preamplifiers will be the strip-to-strip
capacitance.  The capacitance between adjacent strips is given approximately
by~\cite{csc-phenix}:

\begin{equation}
C (pF/cm) = 0.12 t/w + 0.09(1+k)log_{10}(1 + 2w/s + w^2/s^2),
\end{equation}

\noindent
where $t$ is the strip thickness, $w$ is the strip width, $s$ is the
strip separation, and $k$ is the dielectric constant of the backing
material (here it is envisioned to be kapton).  For the FDC design
that is presently considered, this capacitance is roughly 1~pF/cm.  
Accounting for the total capacitance of the system then forms a basic 
requirement for the input capacitance for the front-end electronics 
performance.  An additional concern for this design is the coupling of 
the signals between adjacent strips.  Studies of the PHENIX CSCs have 
shown that appropriate setting of the integration times of the electronics 
is important to decrease sensitivity to distortions in the induced charge 
distribution due to inter-strip coupling.

\subsection{Resolution Effects}

Resolution degradation of cathode chambers comes primarily from two sources,
tracks inclined from the normal to the face of the chamber and Lorentz
angle effects. In both cases the spatial resolution is degraded because 
the avalanche charge is distributed non-uniformly along the anode wire due 
to the energy loss fluctuations in the gas.  The cathode position resolution 
is optimum when the avalanche is formed at a single point along the wire.  A 
finite spatial extent of the anode charge results in a resolution degradation 
{$\cal{D}$}.  Studies of the PHENIX cathode chamber~\cite{csc-phenix} have shown 
that {$\cal{D}$} goes as:

\begin{equation}
{\cal{D}} = 0.16 d \tan \theta,
\end{equation}

\noindent
where $d$ is the anode-to-cathode spacing and $\theta$ is the angle 
from the normal to the face of the chamber. 

Skewed or non-local charge distributions along the anode wire can also
be caused by a Lorentz force along the anode wire from the presence of 
magnetic field components that are not collinear with the electric field 
of the chambers.  The Lorentz effect itself does not result in a systematic 
shift of the measured coordinate in the cathode plane.  It simply results
in a degradation of the resolution because of the spread of the charge along 
the wire.

\subsection{Gas Considerations}

There are several basic requirements that need to be met by the chamber
gas that will be used for the FDC system.  These include a high drift
velocity (50-60~$\mu$m/ns), low Lorentz angle ($< 10^{\circ}$), and
for safety, we much prefer a non-flammable mixture.  It is important to
understand that the performance of a cathode chamber in terms of cathode
position resolution is reasonably insensitive to the exact values of the 
gas parameters.  Here variations of the drift velocity or non-uniform
drift velocities as a function of $E/p$ (i.e. electric field/pressure) are 
relatively unimportant.  For the same reason, the cathode readout operation 
is immune to modest variations of temperature and pressure.  Variations in 
gas gain on the order of 20\% do not strongly affect the cathode resolution 
since a relative charge measurement in adjacent strips is involved.  

However, the gas mixture and its control are essential to consider
carefully for the operation of the MWDC.  In order to enable accurate 
calibrations of the drift times, it is essential that the gas mixture 
is stable, which amounts to constructing a gas handling system that 
carefully controls the gas mixture, as well as hall controls to fix the 
temperature and relative humidity as much as possible.  A gas system for
the FDC prototype is currently under design by Brian Kross of the JLab
Detector Group.

Detailed studies of chamber performance will be performed with
our prototype cathode chamber employing various gas mixtures.
A number of gas mixtures have been studied by various groups
that have proven suitable for cathode chambers.  Most of these
gases contain CF$_4$ in combination with isobutane (C$_4$H$_{10}$)
or CO$_2$.  The Lorentz angle is similar for each gas and is about
5$^{\circ}$ at 0.5~T magnetic field.  One chamber-safe gas mixture 
that has worked well with the PHENIX cathode chambers consists of
30\% argon, 50\% CO$_2$, and 20\% CF$_4$.

\section{Cathode Chambers}
\label{generic_csc}

Cathode chambers are not a new technology to nuclear and particle
physics experiments, and many of the design choices in the 
construction of the small-scale prototype were based on existing designs.
The small-scale FDC prototype chamber has the same electrode configuration
as planned for the full-scale prototype, but is square in design with
an active area of 20~cm $\times$ 20~cm (see Section~\ref{fdc_prototype}).

Cathode strip chambers (CSC) are typically multiwire proportional
chambers (MWPCs) with a symmetric drift cell in which the 
anode-cathode spacing $d$ is equal to the anode wire pitch $s$ (see
Fig.~\ref{fig:csc_schem}).  In these chambers the spatial resolution 
of the anode readout is limited to roughly $s/\sqrt{12}$ (RMS).  In a 
CSC the precision coordinate is obtained by measuring the charge induced 
on a segmented cathode by the electron avalanche formed on the anode wire 
as shown in Fig.~\ref{fig:csc_work1}.  However, CSCs can also be used to 
measure a three dimensional space point on a track by rotating the 
opposing cathode plane strips at an angle with respect to each other.  
For the case of multiple tracks, a second segmented cathode can also help 
to reduce multi-hit ambiguities as shown in Fig.~\ref{fig:csc_work2}.
The stereo technique is superior to the alternative of reading out only
one cathode plane and a hit wire number in that multiple hits on a single
wire may be resolved.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{5.0cm}
\special{psfile=csc_schem.eps hscale=100 vscale=100 hoffset=40 voffset=10}
\caption{Schematic diagram of a generic cathode strip chamber defining
the geometry described in the text.}
\label{fig:csc_schem}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=csc_fig1.eps hscale=115 vscale=115 hoffset=20 voffset=0}
\caption{Illustration of the cathode readout in a typical MWPC.}
\label{fig:csc_work1}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=csc_fig2.eps hscale=110 vscale=110 hoffset=65 voffset=-10}
\caption{Illustration of the resolution of ambiguities within a CSC for two 
particle hits in a typical MWPC.}
\label{fig:csc_work2}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The optimum cathode readout pitch $w$ is determined by the width of the
induced charge distribution.  It has been shown by several groups that
minimal differential non-linearity ($\sim$1\%) is achieved when
$w/d \approx 1$ (e.g. \cite{fenker}).  This ratio is employed in the 
current FDC design.

Simulations from Ref.~\cite{fenker} have shown that resolutions of
25~$\mu$m could be achieved for minimum-ionizing tracks if the
electronics and readout could be provided with noise and
inter-channel gain variations of less than 0.5\% of the nominal pulse
height.  The primary factor limiting the spatial resolution of a
cathode chamber is the electronic noise of the preamplifier.  Other
factors such as the uncertainty in the gain calibrations and cathode
plane distortions should also be considered as well.  The precision in
the determination of the position of the induced charge depends 
linearly on the signal-to-noise ratio.  Note that preamplifier noise
is dominated by the input capacitance and that optimal capacitive
coupling requires that the inter-strip capacitance be much larger than
the capacitance of a strip to ground~\cite{csc-atlas}.  Operation within 
a realistic experimental environment will result in resolutions much 
closer to our design goal of 150--200~$\mu$m.

An interesting question regarding cathode chambers regards the change
in system resolution when they are also employed as drift chambers
(MWDCs), specifically horizontal drift chambers.  The principles
of operation of a MWDC are such that the best position 
resolution is achieved when the first electrons that reach the anode 
wire drift along field lines in the plane of the wires.  If we
consider a GARFIELD calculation~\cite{garfield} of the field lines 
for such a chamber (see Fig.~\ref{fig:csc_garfield}(a)), the first 
electrons to reach the anode wire will most certainly arise from other 
locations within the drift cell.  This gives rise to non-linearities in 
the space-time correlation that strongly degrade the position resolution,
especially in a strong magnetic field.  In order to improve the field 
configuration for the MWDC operation, field-shaping wires can be included 
within the anode plane between each anode wire.  This can clearly improve 
the field configuration as shown in Fig.~\ref{fig:csc_garfield}(b).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=csc_garfield.eps hscale=70 vscale=70 hoffset=20 voffset=0}
\caption{GARFIELD calculations of electric field lines (for a $B$=0 field
configuration) within a square drift cell for a 90\% argon - 10\% CO$_2$ 
gas mixture for electrode configurations without (a) and with (b) 
field-shaping wires.}
\label{fig:csc_garfield}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The basic algorithm to determine the cathode position of the 
charged track is to fit the charge distribution across the cathode
plane.  This amounts to determining the position of the center of
gravity using the ratio of the first and second moments of the
charge distribution on the plane of the strips from~\cite{csc-atlas}:

\begin{equation}
x_{c.g.} = \frac{\sum_{i=1}^{N} x_i q_i}{\sum_{i=1}^{N} q_i},
\end{equation}

\noindent
where $x_i$=$iw$ and $w$ is the pitch of the cathode readout.  If the
charges $q_i$ are measured with an RMS error of $\sigma$, then
the uncertainty in $x_{c.g.}$ is given by:

\begin{equation}
\sigma_{c.g.} = \frac{\sigma}{Q}\sqrt{2 \sum_i x_i^2}
\end{equation}

\noindent
or

\begin{equation}
\sigma_{c.g.} = \frac{\sigma}{Q}\sqrt{2w^2 + 2(4w^2) + 2(9w^2) + \ldots}~.
\end{equation}

\noindent
Therefore the resolution depends on the number of strips used.  Our Monte
Carlo simulations and prototype studies, as well as operational experience 
from different groups have shown that the optimum number lies between three 
and five strips.  The position resolution is poor when only one or two strips 
are present as there is not enough information, while it increases slowly 
when more than five strips are used.  The resolution function in this case also
includes the additional electronic noise from each strip.  Here there
must be an optimization of chamber resolution factoring in the desire
to minimize the number of readout channels to contain costs.

One of the central questions that we have been investigating through our 
R\&D program for the FDC system regards the optimal electrode structure in 
our cathode chambers.  Specifically we are seeking to fully understand the 
trade-offs between timing resolution from the wire planes and spatial resolution
from the cathode planes.  The main question is how the inclusion of field-shaping
wires affects the cathode position resolution.  The results from our prototype
studies, indicate that we can meet the design specifications for resolution in 
cathode coordinates with the inclusion of the field wires.  This is a novel
aspect of our chamber design.

\section{Small-Scale FDC Prototype Chamber}
\label{fdc_prototype}

The FDC prototype cathode chamber has been designed primarily to provide 
us experience with cathode strip chambers.  Through detailed study of
this prototype we have been able to make design decisions on which electrode
structure and layout will fulfill the design requirements for the final
FDC chambers.  The prototype has also provided important insights
into the mechanical design, tolerances, construction and assembly 
techniques, noise immunity, and calibrations that will be important for 
the final FDC detector design.  Some of the elements of the FDC
prototype design have descended from the cathode chambers employed in
the original LASS spectrometer~\cite{csc-slac}.

A schematic of the FDC prototype chamber is shown in an exploded view in
Fig.~\ref{fig:exploded}.  The basic chamber layout consists of two cathode planes
with strips oriented at $\pm$45$^{\circ}$ sandwiching a single wire plane.  
The gas volume is defined by two outer aluminum frames that each include an 
aluminized mylar window.  The active area of the prototype chamber is
roughly 20~cm $\times$ 20~cm, and the chamber is about 8~cm thick.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{10.0cm}
\special{psfile=fdc_exploded.ps hscale=58 vscale=58 hoffset=40 voffset=295 angle=-90}
\caption{Schematic representation of the FDC prototype chamber in an exploded 
view showing the wire plane, two cathode planes, and the two aluminum window 
frames.}
\label{fig:exploded}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The test chamber has purposefully been designed to act as a test bed for any
number of electrode configurations.  So far we have tested wire planes
consisting only of anode wires and planes consisting of alternating anode
and field-shaping wires.  We have also designed cathode planes of varying
rotation angle
%, varying cathode strip pitch, 
and varying cathode strip
separations.  Each configuration has been studied in order to come to an 
understanding of the optimal electrode structure for our purposes.

The $U$ and $V$ cathode planes are mirror symmetric with respect to each 
other.  The cathode planes are copper-clad Kapton sheets ($\sim$2~mil 
thickness) mounted onto 5-mm thick G10 frames.  The chamber is designed 
to operate with the anode wires at positive high voltage, the field wires 
at negative high voltage, and the cathode strips at ground.

The printed circuit board for the wires was designed to capacitively decouple 
high voltage from the signals and to route the signals to the output connector.  
The printed circuit board for the cathodes routes the signals directly to the 
output connector.  The basic circuits on the boards are shown in
Fig.~\ref{fig:csc_elec}.  Small signal routing circuit boards attach to the 
output connectors on the wire and cathode circuit boards, and contain the 
preamplifiers for each readout channel.  The output connects to a shielded
twisted-pair line that routes the signals to the readout electronics.  The 
signal readout boards used for the cathode readout are different than those 
for the wire readout in order to account for the polarity difference in these 
signals. 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=csc_elec.eps hscale=48 vscale=48 hoffset=120 voffset=5}
\caption{Circuit board electronics for the sense and field wires, along 
with the cathode strips.}
\label{fig:csc_elec}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Each readout channel has its own associated ``SIP'' preamplifier.  These 
single-channel transimpedance preamplifiers were originally designed 
for the Hall B CLAS detector.  They have complementary outputs 
designed to amplify signals by a factor of 2.25~mV/$\mu$A.  Besides high gain, 
characteristics of the SIPs include: fast rise and fall times (3 to 4~ns), wide 
frequency bandwidth, wide dynamic range, and low noise and power dissipation 
(65~mW).  The power requirement for a single SIP is 5~VDC at 13~mA, and is 
supplied by a low-voltage power supply.
 
In total the chamber includes 16 sense wires, separated by 1~cm.  The cathode 
planes are located 5~mm away from the wire plane.  They each include 32 copper 
strips with a pitch of 5~mm.  Three different sets of $U$ and $V$ cathode planes 
have been designed with strip separations of 0.25~mm, 0.50~mm, and 0.75~mm to 
allow for the optimal configuration to be determined.  Studies from the
prototype chamber indicate no differences in cathode resolution or noise levels
among the different configurations.  Our nominal strip gap choice is 1~mm.
Presently the chamber is operating with a 90\% argon - 10\% CO$_2$ gas mixture.  
Photographs of the prototype cathode chamber and the cathode plane itself are shown
in Fig.~\ref{fig:fdc-proto}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{14.8cm}
\special{psfile=fdc_proto.eps hscale=75 vscale=75 hoffset=90 voffset=5}
\caption{(Top) Photograph of the prototype FDC cathode chamber constructed to 
optimize the chamber structures. (Bottom) Photograph of a cathode 
plane showing the cathode strips.}
\label{fig:fdc-proto} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

A set of 19 wire chambers have been borrowed from IUCF in order
to put together a cosmic ray test stand at Jefferson Laboratory.  This
test stand is being used to define tracks through the FDC prototype 
chamber.   This system employs multiple layers 
of drift chambers above and below the FDC prototype chamber to precisely 
define the trajectory of an incident charged particle track that can be used to
compare against the position measured in the FDC prototype.  This
position difference represents a convolution of the resolution of the
test stand and of the FDC prototype.  The configuration of the test stand 
includes two $X$ layers and two $Y$ layers above the FDC prototype and a 
matching set of four layers below.  This system is capable of defining a track 
to roughly 200~$\mu$m at the location of the FDC prototype.  A photograph of 
the test setup is shown in Fig.~\ref{tstand}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.5cm}
\special{psfile=fdc_cosmicray.ps hscale=60 vscale=60 hoffset=55 voffset=-115}
\caption{Photograph of the cosmic ray test stand set up at Jefferson Laboratory 
to study resolution characteristics of the FDC cathode strip chambers.}
\label{tstand}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Fig.~\ref{gar1} shows the results of a GARFIELD calculation~\cite{garfield} 
of the electric field line and equipotentials for the case for our nominal 
electrode configuration where the high voltage on the sense and field wires 
is 1650~V and -300~V, respectively, the cathode planes are grounded, and the 
gas mixture in the chamber consists of a mixture of 90\% argon and 10\% carbon 
dioxide.  This voltage setting was chosen to give an equal number of field 
lines from the anode wires terminating on both the cathode surface and the 
field wires in order to optimize the coordinate resolution from both the cathode 
strips and the drift time measurement.  The field strength near the wires and 
the surface charge density for this configuration are listed in Table~\ref{gar2}.  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{7.5cm}
\special{psfile=s1650_f300.epsi hscale=45 vscale=45 hoffset=105 voffset=-70}
\caption{GARFIELD calculation result showing the electric field lines
and equipotential contours for our nominal cell configuration at voltage
settings of $V_s$=1650~V and $V_f$=-300~V.}
\label{gar1}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}
\begin{center}
\begin{tabular}{cccccc}
  & Charge  & Surface field  &  Field at 2$r$  & Surface pot.&  Pot. at 2$r$\\ 
 &   & (kV/cm) & (kV/cm) & (volts)& (volts) \\
\hline
Sense wire  &  263.68  & 263.68  & 131.84  & 1650.0  & 1467.2 \\
Field wire  & -113.49  & 16.21   & 8.11    & -300.0  & -221.3
\end{tabular}
\end{center}
\caption{Charge, surface electric field, electric field at twice the wire 
radius, surface potential, and potential at twice the wire radius for the
wire plane with +1650 V on the sense wires and -300 V on the field wires.}
\label{gar2}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

GARFIELD results for other high voltage combinations are described in 
Ref.~\cite{carman1}.  Fig.~\ref{drift_times} illustrates that the 
long-time edge of the drift time distribution is poorly defined when 
the field wires are absent but the distribution becomes sharper when 
the field wires are present, especially when the magnitude of the voltage 
on the field wires is increased.  The effect of changing the field wire 
high voltage on the position resolution derived from the cathode strip 
data is described in Section \ref{fs_results}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{12.0cm}
\special{psfile=s_drift.ps hscale=32 vscale=35 hoffset=20 voffset=120}
\special{psfile=fs_drift_f0v.ps hscale=32 vscale=35 hoffset=250 voffset=120}
\special{psfile=fs_drift_f-300v.ps hscale=32 vscale=35 hoffset=140 voffset=-55}
\caption{FDC prototype drift distributions for the sense wire only plane 
with the sense wires at +1750 V (top left), the field+sense wire plane with 
the field wires at zero potential and the sense wires at 1650~V,
(top right), and the field+sense wire plane with the field wires at -300~V
and the sense wires at 1650~V (bottom).}
\label{drift_times}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Anode-Cathode Separation}

The gain of the FDC chambers depends critically on the separation between 
the cathode planes and the wire plane (referred to as the ``half-gap'').  
Our early cathode plane samples suffered from noticeable folds and wrinkles 
that lead to local variations in the half-gap and hence the gain.  In our 
small-scale prototype we did not attempt to pretension the cathode planes 
before they were attached to their frames to remove the defects.  Thus the 
resolution measurements reported in this document should represent an
upper limit from our design.  We have been in contact with the circuit 
board manufacturers regarding the defects and they will able able to
work with us to eliminate these problems.  For the full-scale cathode
planes our nominal flatness specifications for the cathodes are 50~$\mu$m.

Beyond local distortions in the cathode due to folds and wrinkles, there
is another important distortion effect that must be considered in the
design of the full-scale cathodes.  When high voltage is applied to the 
wires, the grounded cathode planes are deflected toward the wires dues to 
electrostatic pressure as described in Ref.~\cite{taylor1}. This distortion
is largest at the center of the cathodes and uniformly decreases to zero
at the perimeter.  Kapton by itself offers little resistance to this 
deflection.  In the small-scale prototype, given its small size, this
deflection does not present a serious problem.  We are currently
investigating two techniques to mitigate this electrostatic distortion to
optimize the chamber resolution.  The first approach is to pretension
the cathode planes and to attach the pretensioned planes to a support
frame.  The second approach is to laminate the cathode plane to a
rigid backing.  Both approaches, which are described further below, have
advantages and disadvantages.

The effect of decreasing the half-gap on cathode signals was studied by the 
ATLAS group for a cathode strip chamber similar to our prototype.  
Fig.~ \ref{atlas_csc} shows the relative change of the cathode signals as a 
function of the change in the half-gap.   Assuming these results can be 
generalized to our geometry, we have set a flatness goal of $\pm$50~$\mu$m, 
corresponding to a change in the cathode signals of $\pm$5\%.

To illustrate the issue at hand, the gain $\cal{G}$ in a proportional 
counter is given in general by:

\begin{equation}
{\cal{G}} = K e^{CV}.
\end{equation}

\noindent
For an operational voltage $V$, the gain is dependent on the capacitance
of the detector $C$.  Thus any variation on the flatness of the cathode
plane changes the capacitance of the detector and hence the gain.  It 
also creates field non-uniformities that affect the cathode position
resolution.  For gain variations of less than 5\%, a rough calculation
shows that the cathode plane must have less than a $\pm$5~mil flatness
variation.

Various schemes have been employed by different groups to provide
mechanical support for the cathode planes in large area chambers.  For
example, in the so-called {\it Plug Chambers} used in the LASS
experiment~\cite{csc-slac}, polyurethane spacers were epoxied onto
the cathodes to fix the anode-cathode gap spacing.  Our approaches,
discussed below, have been designed to allow for the easiest and most
robust system to establish and maintain the mechanical tolerances.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\vspace{8.0cm}
\special{psfile=csc_gap_data.ps hscale=25 vscale=25 hoffset=150 voffset=20}
\caption{Cathode signal dependence on the half-gap from ATLAS CSC data.
This figure is taken from Ref.~\cite{oconnor}.}
\label{atlas_csc}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Cathode Plane Tensioning}

Our first approach in order to maintain the cathode plane flatness
to our specifications is to pretension the cathode planes.  This
method has the advantage of reducing the amount of material within
the detector, but suffers from the lateral distortions it induces on
the cathode planes.  Brian Kross of the JLab Detector Group has designed 
a tensioning mechanism for the cathode planes of the small-scale prototype.
This system, illustrated in Fig.~\ref{stretcher}, is based on two
concentric rings.  The cathode plane (labeled ``film'' in the diagram) is 
epoxied face down to the top plate and pulled over the ridge in the bottom 
plate by using a set of screws at various places around the circumference 
of the top plate.  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{6.2cm}
\special{psfile=stretcher.ps hscale=50 vscale=50 hoffset=30 voffset=170 angle=-90}
\caption{Side view of apparatus for tensioning the cathode planes.}
\label{stretcher}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

A set of tensioned cathode planes was installed in the small-scale 
prototype.  The tensioning was performed at a level to reduce the size
of the folds and wrinkles to our predetermined flatness specifications.
However the lateral distortions of the cathode strips in the tensioned
planes were deemed unacceptable for the final detector design.  In
spite of this, we have installed a set of these tensioned planes in the
small-scale prototype to compare against the untensioned planes.  The
final resolution results for the wrinkled planes were comparable to the
tensioned planes (see Section~\ref{fs_results}).

Brian Kross has made adjustments to the design of the tensioning system
given our experiences with the small-scale prototype cathode planes.
The design of the tensioning system for the 1.2~m planes is complete and
the parts have been ordered.  We expect that a combination of improved 
quality of the cathode planes from the manufacturer coupled with 
improvements to the tensioning system will allow for a final decision to 
be made on this approach.

\subsection{Cathode Plane Backing}

Our second approach for establishing and maintaining the flatness
of the 1.2~m cathode planes is to attach the Kapton planes to backing 
material made out of Rohacell, a very low density foam 
($\rho$=0.032 g/cm$^3$).  A sketch of the various components of a single 
layer of a package with this design is shown in Fig.~\ref{sandwich}.
This approach is attractive in that the flatness tolerance for our
cathodes can more easily be met without any worries of cathode plane
lateral distortion.  The drawback is the increased material thickness
and the worsened momentum resolution.  In this scheme we are working
to include the backing while striving to minimize the overall material
thickness.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{11.5cm}
\special{psfile=layers.eps hscale=50 vscale=50 hoffset=100 voffset=10}
\caption{Sketch of the proposed structural components for one 
cathode-anode-cathode layer of the FDC.  The structure repeats six times 
per FDC package.}
\label{sandwich}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

To date we have obtained samples of the Rohacell foam and are studying
its properties.  Several groups
at JLab have extensive experience with this material.  It is used
in Hall B to provide a backing for the mirrors in the {\v C}erenkov
counters being designed for the CLAS12 detector~\cite{youri}.  The material is
fully machinable and its surface can be polished to a flatness well
beneath those required for the FDC.  Pieces of Rohacell that can be
used for our 1.2~m cathode planes are now on order and a design has
been completed to construct a cathode-Rohacell-ground plane-Rohacell-cathode
``sandwich'' using minimal epoxy layers.  This will enable us to finalize
our construction procedure for the full-scale prototype detector.  We are also 
devising a scheme to quantify the flatness of the ``sandwich''.  Based
on these experiences, we will converge on a final design and a final
set of quality control techniques.

We are also aggressively working to complete full GEANT Monte Carlo 
simulations of the FDC system to make final choices on the allowable 
material budget in order to achieve the design coordinate resolution 
values for the FDC.  Our initial studies from a fast parametric Monte
Carlo (HDFast) have indicated that our nominal sandwich design should 
allow us to achieve the design resolution for this system.  We continue 
to hone the design to minimize the overall material thickness.

\section{Chamber Resolution Studies}
\label{fs_results}

This report presents the first results for the field+sense wire 
configuration of the anode plane.  Fig.~\ref{efficiency} shows the 
wire plane efficiency in a 90\% argon - 10\% CO$_2$ gas environment as a 
function of the voltage applied to the sense wires, with the field wires 
at zero potential.  The efficiency is defined to be the ratio of the number 
of events that have one peak in each cathode view matched to a sense wire 
relative to the number of triggers.  A narrow plateau occurs above about 1600~V.   
The setting we used for normal operation was 1650~V.  Fig.~\ref{gain_curve} 
shows the anode charge (deduced from the cathode strip data) as a function of 
the sense wire high voltage.  The trend is well-characterized by Sauli's gain 
function (eq.31 in Ref.~\cite{Sauli}).  Fig.~\ref{res_0} demonstrates that the 
position resolution improves with increasing sense wire voltage (and hence 
gain). It is not feasible to run the chamber with the sense wires at 1700~V 
because the wires start drawing too much current.  However, with the sense 
wires set at 1650~V, the good resolution obtained at 1700~V can be recovered 
by increasing the magnitude of the voltage on the field wires, as 
demonstrated in Fig.~\ref{res_0_400v}.  A plot of the wire positions 
reconstructed from the cathode data when the sense wires are at +1650~V and 
the field wires are at -300~V is shown in Fig.~\ref{xpos}.  The average position 
resolution under these conditions was $158.2\pm3.1\ \mu$m.  This improves upon 
the typical resolution of $182.6\ \mu$m obtained with the sense wire only 
configuration~\cite{taylor2}.  These studies indicate that the electrode
structure of our nominal prototype design can achieve the required resolution
for this tracking system.  Additional results of these studies can also be
found in Refs.~\cite{taylor3,taylor5}.

The cathode resolution as a function of $x$ and $y$ is shown in Fig.~\ref{xyres}.
Even with the relatively poor statistics in this study (acquired in a 
week--long run with incident cosmic ray muons), there is no indication of any 
strong
dependence of cathode resolution on strip length.  More detailed studies of the 
small-scale prototype are underway to better quantify the cathode resolution as 
a function of cathode strip length.  In the full-scale chamber, the lengths of 
the cathode strips will vary from $\sim$10~cm to 1.2~m.  The variation of the 
chamber resolution with strip length must be minimized.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=fs_plateau_f0.eps hscale=65 vscale=65 hoffset=40 voffset=-120}
\caption{Efficiency as a function of sense wire high voltage for the 
field+sense wire configuration of the small prototype.}
\label{efficiency}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=fs_gain_curve_f0v.eps hscale=65 vscale=65 hoffset=40 voffset=-120}
\caption{Chamber gain as a function of sense wire voltage with the field wires 
at zero potential.}
\label{gain_curve}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=fs_resolution_f0v.eps hscale=65 vscale=65 hoffset=40 voffset=-120}
\caption{Position resolution as a function of sense wire voltage with the
field wires at zero potential.}
\label{res_0}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=fs_xres_f0-400v.eps hscale=65 vscale=65 hoffset=40 voffset=-120}
\caption{Position resolution as a function of field wire voltage with the
sense wires at 1650~V.}
\label{res_0_400v}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=x_r130.eps hscale=65 vscale=65 hoffset=50 voffset=10}
\caption{Wire position from cathode data for sense HV=1650~V, field HV=-300~V.
The average cathode coordinate resolution from these data is
158.2$\pm$3.1~$\mu$m.}
\label{xpos}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=xyres_r130.eps hscale=65 vscale=65 hoffset=50 voffset=10}
\caption{Position resolution as function of position for sense HV=1650~V, 
field HV=-300~V.}
\label{xyres}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The purpose of the cathode tensioning exercise was to make the planes as 
flat as possible and to minimize electrostatic deflections, thereby 
minimizing local variations in the gain that could in principle affect 
the resolution of the device.  These tensioned planes replaced our original
untensioned planes that suffered from numerous folds and wrinkles.  
Comparisons between the position resolutions obtained for the two 
configurations as a function of sense high voltage (Fig.~\ref{compres0}) 
and field high voltage (Fig.~\ref{compres400}) revealed no significant 
difference between the two sets of planes.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=comp_res_f0v_old_new_planes.eps hscale=100 vscale=100 hoffset=-80 voffset=-260}
\caption{Comparison of position resolution as a function of sense wire high 
voltage (with the field wires at zero potential) between the tensioned cathode 
planes and the untensioned cathode planes.}
\label{compres0}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{8.0cm}
\special{psfile=comp_res_s1650v_old_new_planes.eps hscale=65 vscale=65 hoffset=30 voffset=-120}
\caption{Comparison of position resolution as a function of field wire high 
voltage (with the sense wires at +1650 V) between the tensioned cathode planes 
and the untensioned cathode planes.}
\label{compres400}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Monte Carlo Studies}

The active area of the FDC will be limited by the requirement that the 
frames support the tension on the wires.  A study using the Hall-D 
GEANT-based Monte Carlo, HD-GEANT, was performed to assess the effect on 
the acceptance of reducing the active radii of the FDC packages.  Single 
muon tracks were thrown at all angles with respect to the direction of the 
beam with momenta in the range 0--9 GeV/c.  To be accepted the primary 
track was required to create at least 8 hits in a tracking detector (FDC 
or CDC).  Plots of the detector coverage for several choices of the FDC 
outer radius are shown in Figs.~\ref{accept1} and \ref{accept2}.  At an 
outer radius of about 49~cm and below, some events require hits in both 
the FDC and the CDC to be accepted because there is no longer an overlap 
between the two detectors.  At an outer radius of 33~cm and below, holes 
in the acceptance start to appear.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{20.0cm}
\special{psfile=acceptance_legend.eps hscale=60 vscale=60 hoffset=100 voffset=400}
\special{psfile=cdc_fdc_acceptance_61.eps hscale=32 vscale=40 hoffset=0 voffset=200}
\special{psfile=cdc_fdc_acceptance_57.eps hscale=32 vscale=40 hoffset=230 voffset=200}
\special{psfile=cdc_fdc_acceptance_53.eps hscale=32 vscale=40 hoffset=0 voffset=0}
\special{psfile=cdc_fdc_acceptance_49.eps hscale=32 vscale=40 hoffset=230 voffset=0}
%\special{psfile=cdc_fdc_acceptance_45.eps,width=2.5in}
%\special{psfile=cdc_fdc_acceptance_41.eps,width=2.5in}
%\special{psfile=cdc_fdc_acceptance_37.eps,width=2.5in}
%\special{psfile=cdc_fdc_acceptance_33.eps,width=2.5in}
%\special{psfile=cdc_fdc_acceptance_29.eps,width=2.5in}
\caption{Acceptance as function of momentum and angle for the FDC and CDC.
FDC outer radii for left column from top to bottom: $r$=61~cm, $r$=53~cm; radii 
for right column: $r$=57~cm, $r$=49~cm.}
\label{accept1}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{20.0cm}
\special{psfile=cdc_fdc_acceptance_45.eps hscale=32 vscale=40 hoffset=0 voffset=400}
\special{psfile=cdc_fdc_acceptance_41.eps hscale=32 vscale=40 hoffset=230 voffset=400}
\special{psfile=cdc_fdc_acceptance_37.eps hscale=32 vscale=40 hoffset=0 voffset=200}
\special{psfile=cdc_fdc_acceptance_33.eps hscale=32 vscale=40 hoffset=230 voffset=200}
\special{psfile=cdc_fdc_acceptance_29.eps hscale=32 vscale=40 hoffset=0 voffset=0}
\caption{Continuation of Fig.~\ref{accept1}.  Left column from top to 
bottom: $r$=45~cm, $r$=37~cm, $r$=29~cm;  right column from top to bottom:  
$r$=41~cm, $r$=33~cm.}
\label{accept2}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The initial specifications for the layout of the FDC system have been
studied within the framework of the HDFast Monte Carlo.  The goals
of the studies were twofold.  First the basic number of FDC chamber
packages within the solenoid was considered, as well as the number of
drift chamber layers within each package.  Secondly, the effect of the 
CDC design, specifically the 1-cm thick downstream endplate, was 
considered in its impact upon the resolution.
For these studies, pions with momenta between 0.25 and 4.0~GeV were
generated and the momentum uncertainty in the form of $\delta P/P$ was 
studied as a function of momentum.  Fig.~\ref{fig:fdc_mc1}(a) shows a 
typical result comparing a 3-package vs. a 4-package configuration 
(with packages equally spaced along the beam line).  Here the preliminary 
results make it apparent that the single track resolution, if all cathode 
and anode positions can be resolved to 150~$\mu$m, has improved resolution 
with the 4-package configuration.  Although the resolution decreases with 
increasing momentum, the resolution of the 4-package configuration 
worsens at a slower rate than the 3-package configuration.  The tracking 
system design parameters can be met with such a 4-package configuration.  
However, it is the redundancy that the fourth package provides that will 
be crucial in disentangling multiple charged particle hits and background 
within the readout time window.  Monte Carlo studies for the number of 
measurements (i.e. wire planes) within a single FDC package are 
continuing in order to optimize the design.  Preliminary studies however 
indicate that the 6-plane design is sufficient to meet the momentum 
resolution requirements for the tracking system.  Further information on
these studies in provided in Refs.~\cite{taylor4,taylor6}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\vspace{7.5cm}
\special{psfile=fdc_mc1.eps hscale=62 vscale=75 hoffset=0 voffset=0}
\caption{(a) Monte Carlo studies comparing the FDC resolution in a configuration 
with three packages vs. four packages. (b) Monte Carlo studies comparing the 
FDC resolution with and without a 1-cm thick aluminum CDC endplate.}
\label{fig:fdc_mc1} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Fig.~\ref{fig:fdc_mc1}(b) shows a comparison of the Monte Carlo
results with and without the 1-cm thick CDC endplate in position.
For the simulation, the endplate was aluminum, however the current design 
plans are based on employing the polymer Delrin.  The studies show that 
the resolution of the FDC system is worsened by roughly 10-15\% due to 
the presence of the endplate.

At the present time the Monte Carlo work is proceeding in earnest to
perform detailed systematic studies of the FDC design with realistic
backgrounds in the chambers.  This will enable final decisions to be
made regarding the number of chamber packages, the number of anode
planes, the optimal rotation between neighboring planes, and the optimal 
$z$-positions of the chambers.

\section{Other Aspects of Full-Scale Prototype}

There are several other aspects regarding the design and construction
of the full-scale FDC prototype that deserve mention here.  First the
design of the circuit boards for the wire planes is now underway.  This
design has no technical challenges of note as this layout will follow
standard practices in layouts of this sort.  Brian Kross, Simon Taylor,
and Daniel Carman will complete the initial design of this board.  Final
drawings and checks will be performed by Chris Cuevas of the JLab
Electronics Design Group.  Second, we have reached a tentative agreement
with Karen Kephart at Fermilab to wind the wire planes for the
detector.  We will also work with them to devise a scheme of quality
control and wire placement measurements to ensure that the wire positions
are within our design tolerances.  Final checks and all remaining aspects
of the detector assembly will be carried out by Daniel Carman, Simon Taylor, 
and Brian Kross.

\section{Conclusions}

Design and development studies for the full-scale FDC prototype chamber
are underway.  The design is based on lessons learned from the small-scale 
prototype cathode chamber that has been under study for nearly two years.
In conjunction with these studies, we are also pursuing an R\&D program
with the detector group at JLab.  We have identified the main areas of
risk associated with the design of a cathode strip chamber and the
mechanical constraints on the cathode planes.  The design and techniques 
that are under study have shown that our approach is sound and that
the resolution requirements for this system can be met.  Our design for
the chamber chamber and the electronics is based on the cathode chamber 
operating successfully in the ATLAS experiment at CERN.  Our work has
shown that the technical risks in the detector specifications are
minimal and that the basic design of the full-scale prototype will be
fully appropriate for the final design of the GlueX FDC system.

\vfil
\eject

\section*{Appendix -- Nominal FDC Design Parameters}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[htbp]
\begin{center}
\begin{tabular} {||c|c||} \hline \hline
\rule{0mm}{4mm}
{\bf Parameter} & {\bf Value} \\ \hline \hline
\rule{0mm}{4mm}
Wire spacing $s$               & 10 mm (anode-anode) \\
 &  5 mm (anode-field) \\ \hline
\rule{0mm}{4mm}
Anode-cathode distance, $d$    & 5.0 mm \\ \hline
\rule{0mm}{4mm}
Cathode readout pitch, $w$     & 5.0 mm \\ \hline
\rule{0mm}{4mm}
Gap between cathode strips, $w_g$ & 1.0 mm \\ \hline
\rule{0mm}{4mm}
Width of cathode strips        & 4.0 mm \\ \hline
\rule{0mm}{4mm}
Capacitance between strips     & 21 pF/m \\ \hline
\rule{0mm}{4mm}
Total strip capacitance        & 56 pF/m + 8 pF \\ \hline
\rule{0mm}{4mm}
Resistance between strips      & $\sim$20 M$\Omega$ \\ \hline
\rule{0mm}{4mm}
Anode wire radius, $r_a$       & 0.010 mm \\ \hline
\rule{0mm}{4mm}
Wire capacitance per unit length, $C_0$  & $\sim$9 pF/m \\ \hline
\rule{0mm}{4mm}
Gas gain                       & 5$\times$10$^5$ \\ \hline
\rule{0mm}{4mm}
Operating voltage at nominal gain & 1800 V \\ \hline
\rule{0mm}{4mm}
Electric field at cathode, $E_c$  & $<$1 kV/cm \\ \hline
\rule{0mm}{4mm}
Electric field on anode wire surface & 280 kV/cm \\ \hline
\rule{0mm}{4mm}
Field-shaping wire radius      & 0.040 mm \\ \hline
\rule{0mm}{4mm}
Electric field on field-shaping wire surface & 15 kV/cm \\ \hline
\rule{0mm}{4mm}
Positive ion mobility, $\mu^+$ & 1.3 cm$^2$/V/s  \\ \hline
\rule{0mm}{4mm}
Total ion pairs                & 94/cm \\ \hline
\rule{0mm}{4mm}
Minimum wire tension           & 50 gm \\ \hline
\rule{0mm}{4mm}
Total charge collected         & $\sim$15.5 pC \\ \hline
\rule{0mm}{4mm}
Charge collected in 30 ns (\%) & $\sim$20\% \\ \hline
\end{tabular}
\end{center} 
\label{specs}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\vfil
\eject

\begin{thebibliography}{99}

\bibitem{fdc_web}
FDC homepage: http://www.jlab.org/Hall-D/detector/fdc/.

\bibitem{kadyk}
J.A. Kadyk, Nucl. Inst. and Methods A {\bf 300}, 436 (1991).

\bibitem{cathode}
S.B. Christo and M.D. Mestayer, ``Minimizing Cathode Emission in Drift 
Chambers'', CLAS-Note 92-016, (1992).

\bibitem{fnal}
Karen Kephart (FNAL), private communication.
 
\bibitem{csc-phenix}
{\it PHENIX Collaboration}.
\newblock PHENIX Internal Note PN125.

\bibitem{fenker}
H.~Fenker {\it et al.}, Nucl. Inst. and Meth. A {\bf 367}, 285 (1999).

\bibitem{csc-atlas}
{\it ATLAS Collaboration}.
\newblock ATLAS Technical Design Report, Chapter 6, June 1997.

\bibitem{garfield}
GARFIELD has been developed at the University of Mainz by R. Veenhof and
revised by M. Guckes and K. Peters.  See HELIOS-note 154, (1986).

\bibitem{csc-slac}
D.~Aston {\it et al.}~{\it (The LASS Collaboration)}.
\newblock SLAC Internal Note SLAC-298.

\bibitem{carman1}
D.~S.~Carman, ``FDC Garfield Studies � v1.0'', \\ 
(http://www.jlab.org/Hall-D/detector/fdc/design/garfield\_study.ps).

\bibitem{taylor1}
S. Taylor, {\it ``Deflections of Cathode Planes Due to Electrostatic 
Pressure''}, GlueX-doc-668-v1.

\bibitem{oconnor}
Figure taken from talk by Paul O'Connor.

\bibitem{youri}
Y. Sharabian, private communication.

\bibitem{Sauli}
F. Sauli, ``Principles of Operation of Multiwire Proportional and Drift 
Chambers'', CERN 77-09.

\bibitem{taylor2}
S. Taylor and D.S. Carman, {\it ``Update on FDC Algorithm Development''},
GlueX-doc-601-v2.

\bibitem{taylor3}
S. Taylor and D.S. Carman, {\it ``Update on Studies of the FDC Prototype and 
Test Stand Setup''}, GlueX-doc-526-v1.

\bibitem{taylor5}
S. Taylor and D.S. Carman, {\it ``FDC Prototype Studies''}, GlueX-doc-453-v1.

\bibitem{taylor4}
S. Taylor, {\it ``Further HDFast simulations of the FDC''}, GlueX-doc--514-v1.

\bibitem{taylor6}
S. Taylor, {\it ``HDFast Simulation Study of the FDC''}, GlueX-doc-418-v2.

\end{thebibliography}

\end{document}