The simulations of the TPCD were carried out using HDGeant a physics simulation program developed at UConn.  In a HDGeant simulation, 300 million photons were produced by a coherent bremsstrahlung generator and directed on a computer model of an 8-quadrant tungsten pin-cushion detector at different beam offsets from nominal alignment.
\par
The vertical and horizontal coordinates of the beam position on the TPCD (with the origin at the center of the TPCD) was constrained to a square that extended 6.0 cm horizontally and 6.0 cm vertically from the origin.  Because of the symmetry properties of the TPCD, covering the square in the upper right hand quadrant gives enough information to describe the current response over the entire surface of the TPCD.   
\par
The beam was scanned across a grid of ten thousand points each separated by
0.06 cm.  For a total of 300 million simulated beam gammas and 10,000 grid
points, approximately 30,000 showers were recorded at each point.  Some of the results of this simulation are shown in fig.~\ref{PlateCurrentPic}.  By comparing the simulated beam spectrum with the calculated flux from a coherent bremsstrahlung source, it was observed that 30,000 gammas corresponds to 7.00$\pm$0.04 $\mu$s of beam time, assuming 1.0 $\mu$A of 12.0 GeV electrons on a 10$^{-4}$ diamond radiator. 
\par
Every time a gamma ray creates a shower in the tungsten plates, information about the secondaries is recorded, such as the plate where the secondary was produced and the charge excess created on the plate due to escaping secondaries.  The current is obtained by dividing the magnitude of the charge excess by the beam run time of the simulation.  These quantities are stored in an ntuple and analyzed by the physics analysis program PAW.  In PAW, histograms of beam position versus current for each of the eight plates are made and used to measure the performance of the TPCD. 
\par
Given measurements of current I$_{j}^{(m)}$ from the detector plate j, these
simulated plots of plate current versus beam position I$_{j}$(x,y) can be used to
estimate beam position using the method of maximum likelihood.  $\chi^{2}$ is
defined as
\begin{equation}
\chi^{2}(x,y)=\sum_{j=1}^{8}\left(\frac{i_{j}(x,y)-i_{j}^{(m)}}{{{\delta}i_{j}^{(m)}}}\right)^{2}
\label{eq1}
\end{equation}


\begin{displaymath}
where \;\;\;
i_{j}^{(m)}=\frac{I_{j}^{(m)}}{\sum_{k=1}^{8}I_{k}^{(m)}}\;,\;\;\;
i_{j}(x,y)=\frac{I_{j}(x,y)}{\sum_{k=1}^{8}I_{k}(x,y)}\;\;\; and\;\;\;
{\delta}i_{j}^{(m)}=\frac{{\delta}I_{j}^{(m)}}{\sum_{k=1}^{8}I_{k}^{(m)}} 
\end{displaymath}

and $\delta$I$_{j}^{(m)}$ is defined as the uncertainty in I$_{j}^{(m)}$.
The minimization was done using the CERNLIB package MINUIT.  MINUIT employs multiple strategies, including a variable metric Gauss-Newton gradient search and a simplex search, to find the values of parameters which minimize the user-defined $\chi^{2}$.