%\documentstyle[12pt]{article}
%\begin{document}

\section{Forward Detector} \label{sec:fcal}

The forward region is defined as polar angles $|\cos\theta| > 0.99$ ($\theta<$ 140mrad)
forward of the SiD Endcap ECAL. The angular coverage is completed by two
detectors, the Luminosity Calorimeter (LumiCal) and the Beam Calorimeter
(BeamCal). The physics missions in this region are:

\begin{itemize}
\item precision measurement of
the integrated luminosity using small-angle Bhabha scattering (LumiCal).
To measure cross section of an event sample $O(10^6)$ expected for
$e^+e^- \rightarrow
W^+W^-$ in 5 years with 500 fb$^{-1}$, the goal is to measure the luminosity
with an accuracy better than $10^{-3}$.

\item precise determination of the luminosity spectrum by measuring
the acolinearity angle of Bhabha scattering (LumiCal).
Due to the beamstrahlung emission the colliding beams loose energies
before collision, and the center-of-mass energy is no longer monochromatic.
The luminosity spectrum affects mass measurement and threshold scan.

\item extend the calorimeter hermeticity into the small angles for physics
searches (LumiCal and BeamCal). An excellent hermeticity is essential
as many new-physics reactions are accompanied with a large missing energy.

\item instantaneous luminosity measurement using beamstrahlung
pairs (BeamCal).

\item two photon veto for new particle searches (BeamCal).
\end{itemize}

The detector challenges are good
energy resolution, radiation hardness, interfacing with the final focus
elements, high occupancy rate requiring special readout, and performing the
physics measurements in the presence of the very high background in the
forward direction.

\subsection{Design criteria}

\subsubsection{LumiCal Physics Requirements}
The lowest order Bhabha cross-section for {\it t} channel one photon
exchange is given by:

$$ \frac{d\sigma}{d\Omega} = \frac{\alpha^2}{8E^2} \left( \frac{1+\rm{cos}^2\theta/2}{\rm{sin}^4\theta/2}\right) $$

We use this simple formula to estimate the polar angle coverage needed,
although the complete electro-weak {\it s} and {\it t} channel cross-section
will later be needed in order to do the physics. The number of Bhabha events
per bunch crossing for a detector with minimum and maximum polar angle coverage
$\theta_{min}$ and $\theta_{max}$ (in mrad) is:

$$ N = 0.5\rm{pb}\frac{L}{R}\int\limits_{\theta_{min}}^{\theta_{max}}\frac{d\rm{cos}\theta}{\rm{sin}^4\theta/2} \sim 8 \left( \frac{1}{\theta_{min}^2}-\frac{1}{\theta_{max}^2}\right) $$

\noindent
for $\sqrt{s}$=0.5 TeV, L=2$\times10^{34} \rm{cm}^{-2}\rm{s}^{-1}$, and bunch crossing rate
R=$1.4\times10^4 \rm{s}^{-1}$. Our goal is to measure the luminosity normalization
with an accuracy of several $10^{-4}$ for $\sqrt{s}$=0.5 TeV. To do this one needs
$\approx 10^8$ events collected
over $\approx10^7$ s, or about ten events per second. One can then calculate the
absolute luminosity with $\approx10\%$ statistical error every several minutes
during the run. With a bunch crossing rate of $1.4\times10^4 \rm{s}^{-1}$, we need
$>10^{-3}$ events per bunch crossing.
To achieve this statistical accuracy, we start the fiducial region for the
precision luminosity measurement well away from the beamstrahlung pair edge at
$\theta_{min}$=20mrad, with a fiducial region beginning at 30mrad, which gives
$\approx 10^{-2}$ events per bunch crossing.

\subsubsection{Luminosity precision and detector alignment}
The integrated luminosity, L is measured using the number of Bhabha
events N and the Bhabha scattering cross section $\sigma$ in the
detector fiducial region as $L = N/\sigma$. Since the Bhabha cross
section is $\sigma \sim 1/\theta^3$, the luminosity precision can be
expressed as

$$\frac{\Delta L}{L} = \frac{2\Delta\theta}{\theta_{min}},$$

\noindent
where $\Delta\theta$ is a systematic error (bias) in polar angle measurement
 and $\theta_{min}$ is the minimum polar angle of the fiducial region.
Because of the steep angular dependence, the precision of the minimum polar
angle meaurement determines the luminosity precison.
To reach the luminosity precision goal of $10^{-3}$,
the polar angle must be measured with a precision
$\Delta\theta <$ 0.02 mrad and the radial positions of the sensors
must be controlled within 30 $\mu$m relative to the IP.

\subsubsection{Monitoring the Instantaneous Luminosity with BeamCal}
The colliding electron and positron bunches at the ILC experience
intense electromagnetic fields as they pass each other. These fields
generate large Lorentz forces, which cause radiation of gammas
called beamstrahlung. A small fraction of the beamstrahlung gammas
convert in pairs. Under the ILC Nominal beam parameters at
$\sqrt{s}$ = 0.5 TeV, approximately 75k $e^+/e^-$ are generated. The
BeamCal intercepts $\approx 3\times10^4$ beamstrahlung pairs of
average energy $\approx$0.7 GeV per bunch crossing when the bunches
have maximum overlap. Since the number of pairs is directly
proportional to the beam overlap, the instantaneous luminosity can
be monitored by detecting pairs in the BeamCal. Our goal is at the
ten percent level per beam crossing.

The Detector Integrated Dipole (DID)\cite{did} plays an important role in controlling
the beamstrahlung pairs. The DID is a pair of coils wound on the
detector solenoid, which creates sine-like transverse field. In the so-called
Anti-DID configuration, the DID field effectively compensates the crossing
angle for the outgoing beam and directs the low energy pairs into the
extraction aperture, reducing the total pair energy hitting the BeamCal
from 20 TeV to 10 TeV.

\subsubsection{Detector Hermeticity}
By hermeticity we mean an accurate measurement of the transverse
momentum ($P_T$) balance in the event, which is achieved by good
energy resolution, avoiding cracks, dead areas, and by covering down
to small polar angles. The measurement of $e^+e^- \rightarrow
slepton~pairs$ in the presence of two photon background has been
given as the performance detector design criteria for
hermeticity\cite{stau}. In the stau production and decay,
$$e^+e^- \rightarrow \bar{\tau} \bar{\tau} \rightarrow \tau^+ \chi^0 \tau^- \chi^0$$
the $\chi^0$ is the LSP and escapes the detector. Under the SUSY dark matter
scenario, the mass difference between stau and the LSP becomes less than 10
GeV, the missing $P_T$ is less and the measurements become more difficult.
The main background comes from the two-photon process $e^+e^-\rightarrow e^+e^-X$, where X is
$ee$, $\mu\mu$, or $\tau\tau$ for the slepton search. This background process has
no missing $P_T$; however, if we miss both electrons then the missing $P_T < 2\theta_{min}E_{beam}$. This is the kinematic limit. Generally one photon is on-shell, so
usually the missing $P_T<\theta_{min}E_{beam}$. The search region in the missing $P_T$ is
determined by how small angle the two-photon electrons are detected and
thereby vetoed. The electron detection must be made in the BeamCal where the
beamstrahlung pairs deposit 10 TeV of energy.


\subsubsection{Dynamic range and mip sensitivity}
While minimum ionizing particles (MIP) deposit 93 keV in a 320
$\mu$m-thick Si layer, a 250 GeV electron can deposit up to 160 MeV
or 1700 MIP equivalents in a single cell near shower maximum. If we
want a 100\% MIP sensitivity, the S/N ratio for MIP should be
greater than 10, and the dynamic range of electronics need to be at
least 17,000. This dynamic range can be achieved using 10 bits ADC
with two gains.

\subsubsection{Radiation hardness}
The beamstrahlung pairs will hit the BeamCal, depositing 10 TeV of
energy every bunch crossing. Sensor electronics could be damaged by
the energy deposition, and sensor displacement damage could be
caused by neutrons. The radiation dose varies significantly with
radius, and a maximum dose of up to 100 MRad/year is expected at
near the beampipe. The main source of neutrons is from secondary
photons in the energy range 5-30 MeV, which excite the giant nuclear
dipole resonance. The number of neutrons produced in one
$0.5\rm{cm}\times0.5\rm{cm}$ BeamCal detector segment per year is
approximately $5\times10^{13}\rm{n}/\rm{cm}^2$


\subsubsection{Occupancy}
The issue here is how ``deep'' we need to make the readout buffer to
hold one train of events for the LumiCal. The LumiCal occupancy is
studied for the beamstrahlung pairs and two-photon events. The
occupancy from the pairs still dominates. In the far LumiCal just
outside the pair edge, the number of hits will reach 120 hits per
bunch train. The number of hits per bunch train decreases to four at
approximately $R\sim$10 cm in the near LumiCal.

\subsection{Baseline Design}
The layout of the forward region is illustrated in Figure
\ref{fcal:1}. The LumiCal covers the polar angles from 40 mrad to 90
mrad, and the BeamCal from 3 mrad to 40 mrad. The conical mask made
of 3cm-thick tungsten is located between the LumiCal and BeamCal.
When the beamstrahlung pairs hit the BeamCal, low energy secondary
particles are generated. The mask shields the SiD central detectors
from low energy photons backscattered from the BeamCal. The Low-Z
mask made of 13cm-thick Borated-Polyethylene is located in front of
the BeamCal. The Low-Z mask reduces the low energy electron and
positron albido from the BeamCal by more than an order of magnitude.
Borated-Polyethylene also absorbs low energy neutrons produced in
the BeamCal and directed toward the IP.

\begin{figure}[h]
\center{\includegraphics[height=3in]{Subsystems/Forward/fcal_1.eps}}
\caption{\label{fcal:1} Forward region.}
\end{figure}

The beam pipe at the IP is made of beryllium to minimize multiple scattering.
The inner radius is 1.2 cm, and the thickness is 400 $\mu m$. The conical
section starts at R=1.2 cm, Z=6.25 cm, and flares to 103 mrad, which is outside
of the LumiCal fiducial region. The flared beam pipe design allows particles
to exit the beam pipe at normal incidence before entering the LumiCal. The
cylindrical beam pipe inside the LumiCal is 6 cm in radius, and is centered
on the extraction beam line to accommodate the 14 mrad crossing angle.
The beam pipe does not intercept the beamstrahlung pairs which are confined
within 4 cm radius by the SiD 5 Tesla solenoid.


The entire forward region is supported by the support tube which is
cantilevered from the QD0 cryostat. There is a 1 cm gap between the support
tube and the endcap door to facilitate the door opening. To minimize the
electromagnetic energy loss due to the gap, the LumiCal is 10 cm
closer to the IP relative to the ECAL.

The LumiCal consists of two cylindrical C-shaped modules surrounding the beam pipe.
The inner radius is 6 cm centered on the extraction beam line
with a horizontal offset of $\Delta x$ = 1.0 cm (158 cm $\times$ 0.007).
The inner radius is dictated by the requirement that no detector
intercepts the intense beamstrahlung pairs, which are confined within 4 cm
radius by the 5 Tesla solenoid field.
The longitudinal structure follows the ECAL design,
consisting of 30 alternating layers of tungsten and silicon. The first 20
layers of tungsten each have thickness equivalent to 2.5 mm (or 5/7
radiation length) of pure tungsten. The last 10 layers have double this
thickness, making a total depth of about 29 radiation length.
The silicon sensors will be made from 6 inch wafers, and the segmentation is
illustrated in Figure \ref{fcal:2}.
The sensor is segmented in a $R-\phi$ geometry. A fine
radial segmentation with 2.5 mm pitch is used to reach the luminosity
precision goal of $10^{-3}$. The azimuthal division is 36 with each sensor
covering 10 degrees. Table \ref{fcal-table:1} summarizes the LumiCal parameters.

\begin{table}[h]
\begin{center}
\begin{tabular}{|c|c|} \hline
z    & 158 - 173 cm            \\ \hline
Inner radius      & 6 cm            \\ \hline
Outer Radius      & 20 cm     \\ \hline
Fiducial      & 46-86 mrad \\ \hline
Tungsten thickness      & 2.5 mm (20 layers), 5.0 mm (10 layers)  \\ \hline
Silicon sensor thickness      & 320 $\mu$m  \\ \hline
Radial division      & 2.5 mm pitch  \\ \hline
Azimuthal division      & 36  \\ \hline
\end{tabular}
\end{center}
\caption{LumiCal Parameters}
\label{fcal-table:1}
\end{table}

\begin{figure}[h]
\center{\includegraphics[height=3in]{Subsystems/Forward/fcal_2.eps}}
\caption{\label{fcal:2} LumiCal sensor and segmentation.}
\end{figure}

The BeamCal consists of two cylindrical C-shaped modules split in half
horizontally to accommodate the incoming beam line.
The inner radius is 2 cm centered on the extraction beam line and the outer
radius is 13.5 cm. The longitudinal structure consists of 50 alternating
layers of tungsten and silicon. The tungsten thickness is 2.5 mm, making a
total depth of 36 radiation lengths. The silicon sensor design based on a 6 inch
wafer is shown in
Figure \ref{fcal:3}. The inner region less than $R<7.5$ cm is the area where the
beamstrahlung pairs would hit. The segmentation in this region is approximately
$5\rm{mm}\times5\rm{mm}$ with about a half a Moli$\grave{e}$re radius. This segmentation
is optimized so that two-photon electron/positron can be detected in the high
beamstrahlung pair background.
The outer region $R>7.5$ cm is the far LumiCal and has the same geometrical
segmentation as shown in Figure \ref{fcal:2}.

\begin{figure}[h]
\center{\includegraphics[height=3in]{Subsystems/Forward/fcal_3.eps}}
\caption{\label{fcal:3}BeamCal sensor and segmentation.}
\end{figure}

Currently two electronic readout chips are being developed. The KPiX chip
with 1024 channels is designed primarily for the ECAL. The chip has four
hits per bunch train to be stored for each channel. The FCAL chip with 64
channels is designed to handle the 100\% occupancy in the BeamCal. The chip
has 2820 buffer space so that a complete bunch train can be stored.
Although the LumiCal
occupancy is not 100\%, the LumiCal region smaller than about 10 cm will
have more than four hits per bunch train. Therefore, the LumiCal will use
the FCAL chip in the inner region and the KPiX chip in the outer region.

\subsection{Expected Performance}
The detector performance has been studied using EGS5 \cite{egs},
FLUKA \cite{fluka},
 and GEANT4 \cite{g4}
simulation packages. The ILC Nominal beam parameters at $\sqrt{s}$=500 GeV are used.
Bhabha scattering is simulated using BHWIDE \cite{bhwide}, and beamstrahlung pairs
are generated using GUINEA-PIG \cite{guinea}.
The magnetic field map for the SiD 5 Tesla solenoid
and the Anti-DID field are used.

\subsubsection{Energy containment and energy resolution in LumiCal}
One of the most important requirements for the LumiCal is the energy
containment. If the energy of Bhabha events is not fully contained,
some events will be classified as radiative Bhabhas and fail Bhabha
event selection criteria, introducing a systematic error. Figure
\ref{fcal:4}(a) shows the deposited energy (scaled by the incident
energy) distribution as a function of the silicon layer from 1 GeV
to 500 GeV electrons. At lower energies, the energy is mostly
contained in the front 20 layers. Even at 500 GeV a significant
deposition is in the front 20 layers, and the back 10 layers with
double tungsten thickness accomplish the energy containment. Figure
\ref{fcal:4}(b) shows the energy resolution parameter $\alpha$ in
$\Delta E/E = \alpha / \sqrt{E}$ as a function of energy. The energy
resolution improves at the lower energies, reaching $15\%/\sqrt{E}$
at 1 GeV, and still maintains $20\%/\sqrt{E}$ at 500 GeV.

\begin{figure}[h]
\center{\includegraphics[height=3in]{Subsystems/Forward/fcal_4.eps}}
\caption{\label{fcal:4} (a) Deposited energy in Si layers (b) Energy
resolution}
\end{figure}

\subsubsection{Luminosity precision and LumiCal segmentation}
The polar angle bias ($\Delta\theta$) and achievable luminosity
precision have been studied as a function of sensor segmentation.
Each silicon layer is segmented equally in the radial and azimuthal
directions, and energy depositions in individual cells are
calculated. The polar angle is reconstructed by taking a weighted
average of the polar angle $\theta_i$ of individual cells with a
weight $W_i$ as

$$\theta = \frac{\sum_i\theta_i W_i}{\sum_i W_i}.$$

It is well known that the electromagnetic shower development is non-linear and
the weight in linear energy introduces a large bias in coordinate measurements\cite{loge} .
The bias can be reduced by using so-called logarithmic weight,

$$W_i = \rm{max}\{0, C+\ln(E_i/E_{total})\},$$

\noindent
where $E_i$ is energy deposition in each cell, $E_{total}$ total energy deposition,
and $C$ is a constant. The constant provides an effective energy threshold,
and only cells with a large enough energy deposition are used in the polar
angle reconstruction.

The LumiCal is fully simulated using 250 GeV electrons with a $1/\theta^3$
angular distribution. The reconstructed polar angle, $\theta_{rec}$ is compared
with the generated one $\theta_{gen}$. The polar angle bias $\Delta\theta$ is
calculated by an average value of $\theta_{rec} - \theta_{gen}$, and the angular
resolution by the rms value. Table \ref{fcal-table:2} shows the angular
bias, angular resolution
and the luminosity precision as a function of the radial segmentation.
The azimuthal segmentation is fixed to 32. The luminosity precision
improves as the radial segmentation decreases, and the luminosity
precision goal of $10^{-3}$ can be reached when the radial segmentation is smaller
than 3 mm. The dependence on the azimuthal segmentation is studied using a
fixed 2.5 mm radial segmentation. Table \ref{fcal-table:3} shows the result.
The luminosity
precision improves as the azimuthal segmentation is decreased, but the
improvement is small. Finer azimuthal segmentation would be beneficial for
cluster separation.

\begin{table}[h]
\begin{center}
\begin{tabular}{|c|c|c|c|} \hline
$\hspace{0.5cm}\Delta r (mm) \hspace{0.5cm}$ & $\hspace{0.5cm} \Delta\theta
(mrad)\hspace{0.5cm}$ & $\hspace{0.5cm}\sigma(\theta) (mrad)\hspace{0.5cm}$&
$\hspace{1cm}\Delta L/L  \hspace{1cm}$ \\ \hline
2.0    & 0.008 & 0.042 & $3.3\times10^{-4}$ \\ \hline
2.5    & 0.017 & 0.046 & $7.9\times10^{-4}$ \\ \hline
3.0    & 0.023 & 0.050 & $1.0\times10^{-3}$ \\ \hline
4.0    & 0.036 & 0.058 & $1.7\times10^{-3}$  \\ \hline
5.0    & 0.049 & 0.069 & $2.2\times10^{-3}$  \\ \hline
\end{tabular}
\end{center}
\caption{Radial segmentation}
\label{fcal-table:2}
\end{table}

\begin{table}[h]
\begin{center}
\begin{tabular}{|c|c|c|c|} \hline
$\hspace{0.5cm}N\phi \hspace{0.5cm}$ & $\hspace{0.5cm} \Delta\theta
(mrad)\hspace{0.5cm}$ & $\hspace{0.5cm}\sigma(\theta) (mrad)\hspace{0.5cm}$&
$\hspace{1cm}\Delta L/L  \hspace{1cm}$ \\ \hline
16    & 0.017 & 0.046 & $7.7\times10^{-4}$ \\ \hline
32    & 0.017 & 0.046 & $7.9\times10^{-4}$ \\ \hline
48    & 0.017 & 0.045 & $7.6\times10^{-3}$ \\ \hline
64    & 0.014 & 0.045 & $6.6\times10^{-3}$  \\ \hline
\end{tabular}
\end{center}
\caption{Azimuthal segmentation}
\label{fcal-table:3}
\end{table}

\subsubsection{Bhabha scattering}
The LumiCal performance is studied using Bhabha events at
$\sqrt{s}$=0.5 TeV. A sample of 10,000 Bhabha events is generated in
the CM system by the BHWIDE event generator\cite{bhwide}. Each event
is transferred to the laboratory system with the 14 mrad crossing
angle, and then processed through the LumiCal simulation. After
energy and angle reconstructions, the event is transferred back to
the CM system to understand the characteristics of Bhabha events.
Figure \ref{fcal:5}(a) shows the total energy distribution of the
reconstructed $e^+$ and $e^-$. The distribution has a peak at 500
GeV as expected, and has a long tail of radiative Bhabha events. The
current cluster finder can reconstruct shower above 25 GeV. Figure
\ref{fcal:5}(b) shows the correlation between the reconstructed
$e^-$ and $e^+$ polar angles. The 14 mrad crossing angle has been
properly taken care of. The radial segmentation is visible at small
angles.

\begin{figure}[h]
\center{\includegraphics[height=3in]{Subsystems/Forward/fcal_5.eps}}
\caption{\label{fcal:5} (a) Total energy distribution (b)
Correlation of e+ and e- polar angles}
\end{figure}

\subsection{High energy electron detection in BeamCal}
We have studied the ability to identify and reconstruct high energy electron in
the presence of beamstrahlung pair background in the BeamCal\cite{uriel}.
The analysis consists of three parts:
\begin{enumerate}
\item A lookup table which would correlate the energy and position of a
shower on the BeamCal to an incident particle energy. This accounts for the
$\theta$ and $\phi$ dependence of shower energy introduced by energy loss down
the beampipe, and also incorporates the sampling fraction of the detector.
\item A lookup table of average beamstrahlung depositions which would be used 
to subtract the expected beamstrahlung energy from the shower of interest.
\item A cluster algorithm which would analyse the total signal on the BeamCal
and attempt to isolate the part of the signal that is due to the high energy
electron. 
\end{enumerate}
BeamCal signals are created by overlaying a high energy electron shower and
one bunch crossing of beamstrahlung backgrounds randomly selected from the
10,000 crossings. After subtracting the average beamstrahlung energy, the 
cluster algolithm reconstructs the high energy electron if the subtracted
energy is greater than three sigma of the beamstrahlung energy variation.
As the beamstrahlung energy has a strong radial and azimuthal dependence,
the detection efficiency is calculated as a function of the distance 
from the extraction beam axis
at three azimuthal angles (0, 90, and 180 degrees).
Figure \ref{fcal:6} shows the detection efficiency as a function
of radius in the BeamCal for 50, 100, and 150 GeV electrons.   
The inefficiency between 30 and 50 mm at phi=$180^\circ$ is due to the incomming 
beam hole. Since the beamstrahlung background energy is the highest at phi
$\approx$ $90^\circ$ (and $270^\circ$), the detection efficiency is lower
 at this angular region. The efficiency to detect more than
150 GeV electrons is almost 100\% up to 8 mrad from the beam axis.

\begin{figure}[h]
\center{\includegraphics[height=3in]{fcal_6.eps}}
\caption{\label{fcal:6} Efficiency to reconstruct high energy electrons
at three azimuthal angles}
\end{figure}


\subsubsection{Calorimeter hermeticity}
Calorimeter hermeticity is surveyed using 250 GeV electrons. Figure
\ref{fcal:8} shows the total energy deposition in Silicon layers as
a function of $\cos\theta$. The ECAL, LumiCal and BeamCal angular
coverages are indicated in the figure. Five sets of simulation are
made with different LumiCal Z locations. When the LumiCal is at the
same Z location as the ECAL, a significant energy is lost at
$\cos\theta\sim$0.993. To achieve calorimeter hermeticity, the
LumiCal is moved 10 cm closer to the IP.

\begin{figure}[h]
\center{\includegraphics[height=3in]{Subsystems/Forward/fcal_8.eps}}
\caption{\label{fcal:8} Energy deposition in Si layers as a functon
of $\cos\theta$}
\end{figure}

\subsubsection{Tungsten mask}
When the beamstrahlung pairs hit the BeamCal, a large number of
secondary photons are produced and about 35k photons per bunch
crossing are back scattered. The tungsten mask is to shield the
central detector from these low energy photons. Figure \ref{fcal:9}
shows the number of photons penetrating the tungsten mask as a
function of the mask thickness. To eliminate the photons, a mask
thicker than 6 cm is necessary. But such a thick mask takes up the
space and significantly increases the weight. The mask thickness of
3 cm is chosen. Although about 1000 photons are penetrating the
mask, they are low energy ($\sim$200 KeV) and are uniformly
distributed over the inner surface of Endcap HCAL.

\begin{figure}[h]
\center{\includegraphics[height=3in]{Subsystems/Forward/fcal_9.eps}}
\caption{\label{fcal:9} Number of photons penetrating the tungsten
mask as a function of the mask thickness}
\end{figure}

\subsection{R\&D}
The radiation level in the forward direction implies that one will
need to probably specify specialized Si material. One needs to
select the materials and expose them to radiation levels equivalent
to what will be seen at the ILC forward region over period of 5
years. Two possible radiation hard materials are oxygenated Float
Zone Si wafers and magnetic Czochralski Si wafers.

\begin{thebibliography}{99}
\bibitem{stau} ``Experimental implications for a linear collider of the
SUSY dark matter scenario,'' P. Bambade et al.,
arXiv:hep-ph/0406010v1, june 2004.

\bibitem{did} ``IR Optimization, DID and Anti-DID,'' A. Seryi, T. Maruyama and
B. Parker, SLAC-PUB-11662, Jan. 2006.

\bibitem{loge} ``A simple method of shower localization and identification in
laterally segmented calorimeters,'' Nucl. Instrum. Methods A, vol.
311, 130 (1992).
\bibitem{egs} ``The EGS5 code system,'' H. Hirayama, Y. Namito, A.F. Bielajew,
S.J. Wilderman and W.R. Nelson, SLAC-R-730 (2005)

\bibitem{fluka} ``FLUKA: a multi-particle transport code,'' CERN-2005-10 (2005), INFN/TC-05/11, SLAC-R-773.

\bibitem{g4} ``GEANT4 developments and applications,'' IEEE Transactions on
Nuclear Science, 53, 270 (2006)

\bibitem{bhwide} ``$O(\alpha)$ YFS exponentiated monte carlo for Bhabha scattering at wide angles for LEP/SLC and LEP2,'' Phys. Lett. B390, 298 (1997)

\bibitem{guinea} ``Study of Electromagnetic and Hadronic Background in the
Interaction Region of the TESLA Collider,'' D. Schulte, Ph.D Thesis,
Hamburg University 1996.

\bibitem{uriel} ``Electron Identification in the BeamCal of the Silicon Detector at ILC,'' G. Oleinik, J. Gill and U. Nauenburg, ILC-SID-TechNote-003. For details, see http://hep-www.colorado.edu/~uriel/Beamstrahl\_TwoPhoton-Process/grp\_results.html .


\end{thebibliography}

%\end{document}
\addcontentsline{toc}{section}{References}
