The simulations were used for three tests of the TPCD design.  The first test
measured the magnitude of the observed plate currents to find out the
sensitivity requirements for the TPCD data acquisition equipment.  The second
test of the TPCD measured the sensitivity of the detector to changes in beam
position.  The final test determined the TPCD's ability to reproduce the beam position from detector currents. 
\par
In the first test, the simulated gamma ray beam was directed on the
TPCD face and the current in each plate was recorded.
Table~\ref{PlateCurrents} shows the values of plate current when the beam is centered on the origin (x,y) = (0.0,0.0) and at (0.2,0.2) cm.  The detector current at these points ranged
between a maximum of approximately 1.0 nA and minimum of
2.0 pA for the nominal beam power of 1.4 W on the collimator face.  Currents in this range will be difficult to detect in a high radiation environment but possible with the use of sensitive pre-amplifiers.	 
\par
To test beam sensitivity the beam was positioned on the TPCD face at four
locations: the origin, (0.05,0.05), (0.1,0.1) and (0.2,0.2).  The values of
the plate current at each of these locations were used to calculate the
deviation d$_{n}$ from the plate currents at the (0.0,0.0) beam position.  Defined exactly, the deviation is given as
\begin{equation}
d_{n}=\sum_{j=1}^{8}\left(\frac{i_{j}^{(n)}-i_{j}^{(0)}}{{i_{j}^{(0)}}}\right)^{2}\;\;\;where\;\;\;
n=1,2,3
\label{eq2}
\end{equation}

\begin{displaymath}
where\;\;\;i_{j}^{(m)}=\frac{I_{j}^{(m)}}{\sum_{k=1}^{8}I_{k}^{(m)}}\;\;\;for\;\;\;m=0,1,2,3
\end{displaymath}


where $I_{j}^{(0)}=$current on the j-th plate
for position (0.0,0.0),
$I_{j}^{(1)}=$current on the j-th plate
for position (0.05,0.05), $I_{j}^{(2)}=$current on the j-th plate
for position (0.1,0.1), $I_{j}^{(3)}=$current on the j-th plate
for position (0.2,0.2), and ${\delta}I_{j}^{(1)}=$current error on the j-th
plate for position (0.05,0.05), ${\delta}I_{j}^{(2)}=$current error on the
j-th plate for position (0.1,0.1), ${\delta}I_{j}^{(3)}=$current error on the
j-th plate for position (0.2,0.2) The fractional change in the deviation between (0.1, 0.1) and (0.2, 0.2) cm was 2.61$\pm$0.42.  The values of the deviation for (0.05,0.05), (0.1,0.1) and (0.2,0.2) are shown in Table~\ref{Deviation}.  Plots of the plate currents at each of these four beam locations demonstrate the sensitive dependence of the individual plate currents on beam position (fig.~\ref{CurrentCompare}).       
\par
	The most important test of the design is the ability to estimate beam
position based on the plate currents.  This test involved first learning how
the current varies with beam position for each plate, and then using this
knowledge to find a method for converting currents to beam position.  A
$\chi^{2}$ function that depends on beam position and the observed currents
can be calculated using Eq. 1~\ref{eq1}.  The minimum of the $\chi^{2}$ function with
respect to position yields the best estimate of beam position.  Estimated
values of beam position are determined by running simulations in HDGeant with
a known and fixed beam position.  The actual and estimated values of beam
position are compared in Table~\ref{PositionComparison}.  The correspondence between actual and
estimated position is good when $|$x$|$$<$3.0 cm and $|$y$|$$<$3.0 cm.  Outside this region, the beam misses the tungsten pins and the resolution rapidly degrades.