\chapter{The H1 Detector}
\label{Ch1detector}

%An important contribution to the systematic error of structure
%function measurements come from the uncertainty of the electron energy
%and scattered angle measurements. The resolution of $x$ is strongly
%affected by the energy measurement in particular at high
%values of $x$. Similarly at large scattering angles the $Q^2$ resolution is
%very sensitive to the angular resolution

The data sample of this analysis were collected in the year $2000$ by
the H1 detector at the {\small HERA} collider. In this chapter
an overview of the HERA accelerator and the H1 detector is
presented. Special emphasis is given to the H1 subdetector components
used to measure the proton structure function for low values of $Q^2$. 

\section{HERA Storage Ring}

The ``Hadron-Elektron-Ring-Anlage'' {\small HERA} at DESY is the first
machine constructed to collide electrons or positrons with protons,
where {\it both} electrons and protons are accelerated. In
Fig. \ref{Fighera} a schematic layout of {\small HERA} and the  
pre-accelerator complex is shown. 

\begin{figure}[t]
\begin{center}
\includegraphics[width=12.cm]{./detector/figures/HERAfig.eps}
\caption{Schematic view of {\small HERA} (left) and the preaccelerator
system (b)}
\label{Fighera}
\end{center}
\end{figure}

{\small HERA} consists of two independent accelerators, with a
circumference of $6,3\,$km. Electrons are injected 
with an initial energy of $12\,$GeV, while the
protons are injected with an energy of $40\,$GeV into a ring of
superconducting dipole magnets. 
In the year $2000$, {\small HERA} delivered positrons \footnote{during
the following description the term ``electron'' is 
used to describe generically electrons or positrons}  and protons with
a final energy of $27.5\,$GeV and $920\,$GeV respectively. 

In {\small HERA} proton and electron beams are composed of packets of
particles called ``bunches''. The {\small HERA} rings can store
maximally 220 bunches of particles. 
The electron bunches are short and the
profile in beam direction is approximatly of Gaussian shape, the protons
have a more complex structure with a central (main) bunch of
high intensity, which is surrounded by additional bunches of much less
intensity called ``satellite bunches''. 

The electron and proton bunches cross the North and South interaction
regions every $96\,$ns, where the H1 and Zeus detectors are 
installed. In order to directly determine the beam induced
background in the interaction region, some electron and proton
bunches are {\it not} filled. Therefore in addition to the {\it
  colliding bunches} 
there are a number of non colliding bunches ({\it empty bunches}) and
also the so called {\it electron and proton pilot bunches}. Electron bunches  
not having a colliding proton bunch are known as {\it electron-pilot}
bunches, in analogy proton bunches without a corresponding  
colliding electron bunch are known as {\it proton pilot} bunches.
Thus, from the 220 bunches that
{\small HERA} can fill, in average only $174$ collide, $24$ are empty bunches
and $7,15$ correspond to proton and electron pilot bunches,
respectively \cite{olaf}. 
 
%The non-colliding packets are used to estimate the beam
%induced background, especially important for the luminosity measurement.

\section{The H1 Detector}

The H1 detector is a multipurpose detector, designed to study 
inclusive and exclusive final states of $ep$ interactions. 

In Fig. \ref{FigH1detector} a three dimensional view of the H1
detector is shown, where the sub-detector components are marked with
\fbox{numbers}. The H1 detector is situated concentrically around the beam
axis \fbox{1}. The interaction point (marked in red) defines the origin of 
the H1 coordinate system. The direction of the incoming proton defines
the positive $z$ direction of the coordinate system. Since the centre
of mass energy of the $ep$ collisions is boosted along the proton
direction, the H1 detector is more massive and finer segmented in that
direction. 

\begin{figure}[p]
\begin{minipage}{0.8\textwidth}
\begin{center}
\includegraphics[height=14.5cm]{./detector/figures/h1_3d_box.eps}
\end{center}
\end{minipage}
\begin{minipage}{0.8\textwidth}
\setcaptionwidth{\textwidth}
\label{FigH1detector}
\caption{Three dimensional view of the H1 detector, the \fbox{numbers} denote:}
\begin{center}
\begin{tabular}{l l l l}
\framebox[1cm][c]{1} & Beam pipe and beam magnets & \framebox[1cm][c]{9} & Muon Chambers \\
\framebox[1cm][c]{2} & Central tracking chambers & \framebox[1cm][c]{10} & Instrumented iron yoke \\
\framebox[1cm][c]{3} & Forward tracking chambers & \framebox[1cm][c]{11} & Forward muon toroid \\
\framebox[1cm][c]{4} & Electromagnetic LAr calorimeter & \framebox[1cm][c]{12} & Backward calorimeter Spacal \\
\framebox[1cm][c]{5} & Hadronic LAr calorimeter & & and backward drift chamber \\
\framebox[1cm][c]{6} & Superconducting coil ($1.16$T) & \framebox[1cm][c]{13} & Forward plug calorimeter \\
\framebox[1cm][c]{7} & Compensating magnet & \framebox[1cm][c]{14} & Concrete shielding \\
\framebox[1cm][c]{8} & Helium supply for \fbox{7} & \framebox[1cm][c]{15} & Liquid Argon cryostat \\
\end{tabular}
\end{center}
\end{minipage}
\end{figure}

The interaction point is surrounded by the central and
backward silicon trackers (not visible in
Fig. \ref{FigH1detector}). The central and forward trackers \fbox{2,3}
enclose the silicon detectors and the beam pipe. They are used to
identifies charged particles and to measures their momenta. The liquid
argon calorimeter (LAr) surrounds the tracking devices \fbox{4,5} and is
used to measure the 
energy and momenta of high energetic particles. The superconducting coil
\fbox{6} surrounds both the tracking devices and the LAr calorimeter,
producing a constant magnetic field of $1.16\,$T parallel to the beam
axis. The compensating magnet \fbox{7} provides a longitudinal field
equal in size and opposite in direction to that of the superconducting
coil. The magnetic field
configuration of H1 is designed to  
not disturb the circulating beams of {\small HERA}. 

Muons are detected in a streamer tube system placed inside the iron of
the return yoke \fbox{10}. The muons are recognised since they can
penetrate large quantities of material almost without
deflection, meanwhile other particles are absorbed. In order to
recognise muons produced in the forward direction, the forward muon
spectrometer \fbox{11} is used. 

%Thus, the backward detectors of H1 are specially
%important for analysis at low $Q^2$.
%One of the main task of the backward devices is to identify the
%scattered electron and separate it from the hadronic final state.
Particles scattered into the backward direction deposit their energy in
the SpaCal calorimeter \fbox{12}. In front of the SpaCal,
the backward drift chamber BDC is located. Using the SpaCal calorimeter and the
BDC chamber, it is possible to identify the scattered electron coming
from DIS events for values of $2<Q^2<100\,$GeV$^2$. In
Fig. \ref{Figspazview} a schematic $r-z$ view of the backwards
detectors is shown. The essential subdetector components used in the
low $Q^2$ analysis are: 

\begin{itemize}
  \item the {\bf{SpaCal}} calorimeter since it provides trigger
  information, identify the scattered electron and measure their
  energy.
  \item the {\bf{Central Trackers}} devices (CTD) which measure the position
  of the interaction point (vertex) and the momenta of particles
  belonging to the final state. 
  \item the {\bf{Backward Drift Chamber}} (BDC) provide information of
  the exact position of the scattered electron in the radial direction  and
  measure the angle of the scattered electron, together with the CT devices. 
  \item the {\bf{Backward Silicon Trackers}} (BST) measures precisely the
  vertex position and the angle of the scattered electron.
  \item the {\bf{Liquid Argon}} calorimeter measures the momenta of particles
  coming from the hadronical final state.
  \item the {\bf{Luminosity system}} measures the luminosity.  
\end{itemize} 

In the following sections, these subdetectors components will be
explained in detail.

%The energy of the scattered electron is measured with the 
%SpaCal calorimeter, meanwhile the electron track can be reconstructed
%with the central tracking devices or with the backward silicon
%detector. Such detector components will be described in the following
%sections. 
%The data used for this analysis result from a short data taking period
%where the ep collision vertex was shifted by 70cm in the proton beam
%direction with respect to the nominal vertex position to increase the
%acceprance for the electrons scattered through small angles
%For nominal position of the electron proton scattering 

\subsection{SpaCal Calorimeter}
\label{Secspacalcalorimeter}

\begin{figure}[t]
\begin{center}
\includegraphics[width=14.0cm]{./detector/figures/position.eps}
\caption{$z-r$ view of the backward devices of the H1 detector. The
  interaction point (IAP) is surrounded by the central silicon
  tracker (CST). In front of the Backward silicon tracker (BST) are
  localised the Backward Drift Chamber (BDC) and the SpaCal
  calorimeter. Some modules of the electromagnetic section of the LAr 
  calorimeter labelled as BBE, CB1E, CB2E are also shown.} 
\label{Figspazview}
\end{center}
\end{figure}

%The scintillating fibres are mounted on a lead matrix.
The SpaCal is a sampling calorimeter which uses lead as convertor material 
and scintillating-fibre as active material
\cite{Appuhn:1996na}. The SpaCal is localised at $z=-160\,$cm and has a
diameter of $160\,$cm, having an angular acceptance of $168
^{\circ}<\theta_e<177.8 ^{\circ}$ for electrons scattered from the
nominal vertex position. The SpaCal 
calorimeter is divided into two sections, one electromagnetic and one
hadronic. In Fig. \ref{Figspazview} an $r-z$ view of the
electromagnetic section of the SpaCal
calorimeter is shown.  

\begin{figure}[p]
\centering
\subfigure[$r-\phi$ view of the electromagnetic section of the SpaCal calorimeter. The border of the
  16-cell modules are drawn with bold lines.]{\epsfig{figure=./detector/figures/elm_xy.ps,width=0.7\textwidth}}\quad
\subfigure[The 2-cell module configuration showing lead fibre matrix,
  fibre bundles and the light mixers.]{\epsfig{figure=./detector/figures/submodul.eps,angle=90,width=0.6\textwidth}}\quad
\subfigure[$r-\phi$ drawing of the insert module]{\epsfig{figure=./detector/figures/insert_b.eps,width=0.35\textwidth}}
\caption{The geometry of the SpaCal calorimeter and its basic
  components \cite{Appuhn:1996na}.}
\label{Figspamodul}
\end{figure}

The electromagnetic part of the SpaCal calorimeter consists of 1192
cells, each cell has an active cross section area of $40.5 \times
40.5\,$mm$^2$ and a depth of $250\,$mm. The SpaCal cells are made of
grooved lead plates and scintillating fibres with a lead-fibre ratio
of $2.27\!:\!1$. The electromagnetic SpaCal corresponds to
$27.47$ radiation lengths ($X_0$) and one hadronic interaction
length. A drawing of the SpaCal calorimeter in the $r-\phi$ view is
shown in Fig. \ref{Figspamodul}(a).

The smallest construction unit of the detector are 2-cell modules. They
consist of a stack of 52 lead plates each containing 90 fibres (see
Fig. \ref{Figspamodul}(b)). The fibres ends are arranged into two fibre 
bundles of $70\,$mm length. The scintillation light of each cell is
converted to a electric pulse using photomultipliers tubes, which
operates in the magnetic field of $1.16\,$T and reach an amplification
gain of $\approx 10^{4}$ \cite{janoth}. 

Groups of 2-cell modules are combined to form a $16-$cell module, which
represent the main building block of the electromagnetic section (see
Fig. \ref{Figspamodul}(a)). The
innermost module is called the insert module and has the same size as
the other $16-$cell modules (see Fig. \ref{Figspamodul}(c)). The cells of
the insert module are not of rectangular shape due to the space needed
for the beam pipe. The cells closest to the beam pipe are of ring
shape and are called ``veto cells'' (see Fig \ref{Figspamodul}(c)). A
$2\,$mm thick tantalum layer protects the detector against synchrotron
radiation. 

Due to the small diameter of the fibres, an relative energy resolution
of $7 \% / \sqrt{E[GeV]} \oplus 1\%$ is achieved. The designed energy
resolution 
of the SpaCal calorimeter is $2\%$ for electron energies
of $30\,$GeV, and the angular resolution achieved 
is $2\,$mrad. The time resolution of the SpaCal calorimeter is $1\,$ns and
is used to reject beam related background (beam-gas and
beam-wall) events. The time of the SpaCal is used for trigger purposes.

The hadronic section of the SpaCal calorimeter has a structure similar to
the electromagnetic section. The diameter of the scintillation fibres
is $1\,$mm being two times bigger than the electromagnetic ones. The
lead-to-fibre ratio for the hadronic part of the SpaCal calorimeter is
$3.4\!:\!1$. The calorimeter consists of 136 modules 
surrounding the beam pipe, each module has a cross section area of
$119.3 \times 119.0\,$mm$^2$ and a depth of $250\,$mm, corresponding
 to one nuclear interaction length.

\begin{figure}[t]
\begin{center}
\includegraphics[width=10cm]{./detector/figures/bdc2frame.eps}
\caption{Schematic drawing of the Backward Drift Chamber \cite{BDC}.}
\label{Figbdc}
\end{center}
\end{figure}

\subsection{Backward Drift Chamber}
\label{Secbdc}

The scattering angle measurement of the SpaCal can be improved using
the Backward Drift Chamber (BDC) \cite{BDC}. The BDC is placed in
front of the SpaCal calorimeter (see Fig. \ref{Figspazview}). The
chamber is built of four double layers, which are divided into eight
octants. Each octant comprises $32$ drift cells 
with sense wires. The radial wire spacing is $1\,$cm for the inner
$16$ cells and $3\,$cm for the outer cells. Each double layer is
consequently revolved by $11.25^{\circ}$ to enable the azimuthal
$\phi$ angle measurement. A schematic view of the chamber is shown in
Fig. \ref{Figbdc}.

In order to optimise the polar angle measurement, the wires of
the BDC are oriented in the azimuthal direction like a spiderweb. In
that way the drift in the cells takes place in the radial direction.
The BDC has the same angular acceptance as the SpaCal and provides a
polar angle measurement with a resolution of $0.5\,$mrad.

\subsection{Tracking Devices}
\label{Sectracker}

\begin{wrapfigure}[18]{r}{0.6\textwidth}
\begin{center}
\epsfig{figure=./detector/figures/cjccut.ps,width=0.7\textwidth}
\begin{minipage}{0.4\textwidth}
\setcaptionwidth{\textwidth}
\caption{Radial view of the tracking detectors \cite{Abt:1996xv}}
\label{Figctd}
\end{minipage}
\end{center}
\end{wrapfigure}

%\begin{figure}[t]
%\begin{center}
%\includegraphics[width=10cm]{./detector/figures/cjccut.ps}
%\caption{Radial view of the tracking detectors \cite{Abt:1996xv}.}
%\label{Figctd}
%\end{center}
%\end{figure}
The track reconstruction in the central region of the H1 detector is
based on two large 
concentric drift chambers CJC1 and CJC2 (detector \fbox{2} in
Fig. \ref{FigH1detector}), having wires strung 
parallel to the beam axis. The drift cells are inclined with respect
the radial direction. From the
signals recorded in those chambers the transverse track momentum is
determined and in addition the specific energy loss $dE/dx$ is used to
perform particle identification. A transversal view of the tracking
devices of the H1 detector is shown in Fig. \ref{Figctd}
The chambers allow the measurement of the $z$ position
comparing the signals in the read out from both wire ends. 

The central inner $z-$chamber (CIZ) and the central outer $z-$chambers
(COZ) measure the $z$ coordinate with better accuracy than CJC1 and
CJC2. They deliver track elements with a resolution in $z$ of $300 \mu
m$, which is combined with the measurement of the CJC. The 
CIZ is placed inside CJC1, while the COZ is located between CJC1 and
CJC2. The polar angles covered by CIZ and COZ are $16^{\circ} < \theta
< 25^{\circ}$ and $25^{\circ} < \theta < 156^{\circ}$
respectively. 

\begin{figure}[t]
\begin{center}
\includegraphics[width=15cm]{./detector/figures/zVertexHistogram.eps}
\caption{The trigger of the $z$ position of the interaction vertex \cite{zvertex}.}
\label{Figzvertex}
\end{center}
\end{figure}

In the central and forward regions, combinations of pad hits in the
central inner proportional chamber (CIP), central outer proportional
chamber (COP) and the forward proportional chambers (FWPC) are used to
trigger on tracks coming from a nominal interaction vertex.
The principal task of the trigger of the proportional chambers is the
determination of the vertex in the $z$ axis. Fig. \ref{Figzvertex}
illustrates the concept to determine the vertex. For each $ep$ collision,
the hits in the chambers are connected by a straight line which is
extrapolated to the beam 
axis. The interception of the line tracks with the beam axis make an entry
in a $z$-histogram. One expects that the maximum of the histogram
corresponds to the position of the vertex. The vertex histogram is
constructed with 16 bins in an interval in $z$ from $-43.9\,$cm to
$43.9\,$cm \cite{Abt:1996xv}. 

\subsection{BST}
\label{Secbst}

The Backward Silicon Tracker (BST), is one of the two silicon
detectors placed close to the beam pipe. The BST serves for the
precise measurement and identification of the scattered electron in
the backward region. A schematic view of the detector is shown in
Fig \ref{Figbst}.

The detector consists of two subdetector parts BST1 and BST2, each one
is arranged perpendicularly to the beam axis between $z=-35.8\,$cm
and $-95.7\,$cm. Both BST1 and BST2 are composed of two symmetric
shells, each containing 8 planes of active sensors called
{\it{wafers}} (see Fig. \ref{Figbst}(a)).

Each plane of the BST is made of $16$ so called $r$ sensors and $1$ $u$
sensors. The $u$ sensor is a single metal sided silicon, which is
located on each plane at $45^{\circ} < \phi < 67.5^{\circ}$. Combining the
information from the $r$ and $u$ sensors it is possible to measure the
momentum and the charge of a track with the BST.

The active sensors or the wafers are made of 250 $\mu$m thick n-type
silicon. A single minimizing ionization particle creates about 22000
electron-hole pairs, which
is sufficient to produce a signal. Each wafer provides 640 readout
channels, the signals are collected with an integrated front-end
system \cite{Arkadov}. 

The BST provides a polar angle measurement independent of the central
tracking devices, covering the interval $164^{\circ} < \theta  <
176^{\circ}$ with an accuracy of about $0.2\,$mrad. Through the
extrapolation of the reconstructed track to the beam line a
measurement of the z-vertex position is also possible. 
%The $z$ vertex measurement has a precision of $20\,\mu$m.

\begin{figure}[t]
\begin{center}
\subfigure[Three dimensional view of the backward silicon tracker. The
  label $1$ and $2$ represent the detectors BST1 and BST2.]
{\epsfig{figure=./detector/figures/bst4.eps,width=0.45\textwidth}}\quad
\subfigure[The structure of the silicon sensors (a)$r$ and (b)$u$. ]
{\epsfig{figure=./detector/figures/bstsensors.eps,width=0.45\textwidth}}
\caption{The Backward Silicon Tracker in its configuration in the year
  2000 \cite{Arkadov}.}
\label{Figbst}
\end{center}
\end{figure}

\subsection{Liquid Argon Calorimeter}
\label{Seclar}

The Liquid Argon calorimeter (LAr) is the biggest calorimeter of the
H1 detector (see \fbox{4} and \fbox{5} in Fig. \ref{FigH1detector}). It is
divided in an electromagnetic and an hadronic section. 
The LAr is a sampling calorimeter which uses liquid argon as
active material, and lead as absorber material in the electromagnetic
section and steel in the hadronic section.
In order to keep the liquid argon fluid, the calorimeter is placed in
a cryostat. Cooling down to liquid argon temperature
is achieved by circulating helium gas cooled in an external and
movable liquid nitrogen heat exchanger. Fig. \ref{Figlar} shows the LAr
calorimeter in the $r-z$ view. 

The calorimeter is build of absorber plates supplemented by high
voltage and read out electrodes. The interspaces between the plates
are filled with liquid argon.
To obtain a uniform energy resolution, the orientation of the plates
is arranged such that the 
angle of incidence of particles coming from the interaction point is
always larger than $45^{\circ}$. 
%Plates of lead are used as absorber
%material in the electromagnetic section, meanwhile plates of steel are
%used as absorber material in the hadronic part.
The absorption length of the
electromagnetic part varies between 20 and 30 radiation lengths
$X_{0}$. 

The LAr calorimeter is divided along the $z-\,$direction into eight
self supporting wheels named according to its position with respect to
the proton beam, 
Backward Barrel (BB), Central Barrel (CB), Forward Barrel (FB1,FB2)
and Outer Forward (OF) and Inner Forward (IF). The BBE consists only of
an electromagnetic section and the OF of two hadronic sections. In
$\phi$ direction each wheel is further segmented into eight
identical units, the so called octants.

The energy resolution of the electromagnetic part of the calorimeter
is $\sigma_{E}/E \approx 11 \% / \sqrt{\textstyle{E/GeV}} \oplus 1\%$
while the hadronic part has a resolution energy of $\sigma_{E}/E
\approx 50 \% / \sqrt{E/GeV} \oplus 2\%$.  The LAr calorimeter covers
the tracking system and has an angular acceptance of $5^{\circ}\,< \theta <
\,154^{\circ}$.

\begin{figure}[t]
\centering
\epsfig{figure=./detector/figures/h1calolong.eps,bb=63 329 487 503, clip=,width=0.9\textwidth}
%\subfigure[]{\epsfig{figure=./detector/figures/calo-quer.eps,bb=313 404 544 641, clip=,width=0.35\textwidth,angle=270}}
%\subfigure[]{\epsfig{figure=./detector/figures/f2h.eps,bb=1 16 323 330,clip=,width=0.35\textwidth}}
\caption{$r-z$ view of the LAr calorimeter. The modules are labelled
  according to its position with 
  respect the interaction point (WWP) either central (CB) backward (B) or
  forward (IF,OF). The modules corresponding to the electromagnetic
  and hadronic section are in addition labelled with a $E$ or a $H$
  \cite{Abt:1996xv,LArnim}.} 
\label{Figlar}
\end{figure}

\subsection{The Luminosity system}
\label{Seclumi}

The luminosity in the H1 experiment is derived
from the rate of the Bethe-Heitler events $ep \rightarrow ep
\gamma$. In such a process the electron and the proton interact
elastically and in addition a photon is emitted.

\begin{figure}[t]
\begin{center}
\includegraphics[height=12.cm,angle=270]{./detector/figures/lumid.eps}
\caption{Luminosity system \cite{Abt:hi,lumigroup1}.}
\label{Figlumi}
\end{center}
\end{figure}

The luminosity system consist of two arms, the electron
tagger (ET) and the photon detector (PD). Since the angular
separation between the electron 
and the photon are of the order or $16 \mu$rad, the detectors are placed
far away from the H1 interaction point. A schematic view of the
luminosity system is shown in Fig. \ref{Figlumi}. 

The on-line luminosity is obtained measuring the rate of 
Bethe-Heitler events detected in coincidence.
The scattered electron is 
deflected by quadrupoles and a bending magnet, being detected with
the ET located at 
$z=-33.4\,$m. The bremsstrahlung photon is detected in the PD located
at $-z=102.9\,$m. In order to protect the PD from the high synchrotron
flux, a filter of Pb with 2$X_{0}$ followed by a 1$X_{0}$
water Cerenkov counter is located in front of the PD.
The main source of background are
bremsstrahlung events originating from collisions between the
beam electron and the residual gas ({\it $e^{+}$gas}) in the beam pipe
leading to the same event signature. The contribution of such events
is estimated using the electron pilot bunches. 

%The on-line 
%measurement of the luminosity using the coincidence method has
%an uncertainty of $4\%$ \cite{lumigroup1,lumigroup2}.
A more precise luminosity calculation is performed ``off-line'' using
the energy 
spectrum of the brem\-strahlung photons coming from the Bethe-Heitler
process. To minimise the systematic errors, it is important to
understand in detail the energy spectrum of the photon and the influence of the
acceptance of the PD. In addition the $e^{+}$gas background is taken
into account and the effect that more than one photon at the same buch
crossing (photon pile-up effect) is produced and detected in the PD \cite{cisserver}.
The luminosity calculation needs to consider also
contribution coming from the satellite bunches \cite{lumizeus}. The
resulting uncertainty of the measured luminosity is within $2.2\%$ \cite{levonian}.

%Apart from the luminosity measurement, the ET is also used to study
%the ``photoproduction'' processes for very low values of $Q^2$ (see
%Section \ref{Secphotoproduction}). In
%addition photons emitted collinearly by the incoming electron can be
%investigated using the PD (see Section \ref{Secloweanalysis}).

\subsection{The Trigger system}

The principal task of the trigger system is to separate real physic events
from background events.
The trigger system in H1 in the year 2000 selected events in three levels,
in the following denoted as {\small{L1,L2}} and {\small{L4}},
respectively. 

During the latency time of the first trigger level L1, all subdetector
components store their 
data in pipelines \cite{dwhc}. The pipeline is designed such that 
the decision if the event is accepted (or not) has to be taken within
$2.3\,\mu$s.  
In order to take this decision selected subdetector components deliver
their 
trigger information to the central trigger. 
The central trigger receives up to 256 trigger elements {\small{(TE)}}, which
through logical combinations define 
the 128 subtrigger elements {\small{(SE)}}. If one of those SE
accepts the event, the so called L1-keep signal is generated
the pipeline system is stopped, causing from that moment and dead time
of the detector.

The second trigger level {\small{(L2)}} calculates its decision within
$20\mu$s. The decision of {\small{L2}} is based on two 
systems, the topological trigger {\small{(L2TT)}} and the
neuronal trigger {\small{(L2NN)}}. Both use the information
of several subdetector components. In case the event is accepted 
by {\small{L2}}, the full detector data for the triggered event are
readout and sent to L4. After that, the pipelines are enabled again.

The level $4$ system {\small (L4)} consist of a group of 30 farm
computers working in parallel. These computers run a optimised version
of the H1 reconstruction program. Based on the result of the
reconstruction the decision of the early trigger levels is
verified. In addition each event gets assigned to various classes of
physics. The event will be rejected if does not match the selection of
any class.

The capacity of the L4 input has a fixed bandwidth of $50\,$Hz
and has to be distributed over all active SE. Since the rates of the
SE might be different, the bandwidth of L4 is not equally distributed over
all SE. 

In addition to the trigger conditions, also the beam conditions can
influence the rate of the various SEs. It is possible that several
subtriggers accept so often events that the rate of the SEs exceeds the
input rate of L4. Therefore it is necessary to introduce prescale 
factors. If one subtrigger element $j$ (SE-j) has a prescale-factor
$k$, then it will cause an L1-keep only every $k$-time. On analysis
level the events triggered by the subtriger SE-j have to have a
weight corresponding to the prescale factor $k$
\cite{hrick,Schultz-Coulon:tx}. 

The prescale factors are calculated with a prescale program. It is an
automatic tool which analyses the rate of the different subtriggers and
performs a prediction on the future behaviour of the rate of the
triggers. Using a complicated strategy the distribution of the
bandwidth can be optimised. 

\section{Run selection}

The time during which the electron and proton beams collide is known as
luminosity fill and its duration is limited due to the lifetime of the
electron beam. This luminosity fills are divided into
``runs'', having an average duration of $1-2$ hours,
depending on the beam and background conditions. Thus, on analysis
level is important to perform a selection of the usable runs. 

The selection of the runs is based in the following criteria:

\begin{itemize}
\item {\it Run quality.} Each run is clasified as ``good'' ``medium''
  or ``poor'' depending on the status of the subdetectors
  components. A run can be poor if one of the main components is not
  available over the whole
  time. Here will be used only runs which were clasified as ``good'' and
  ``medium''. 
\item {\it Readout status.} For each run there is information
  available over the status of the readout of the subdetector
  components. Since an inclusive DIS cross section measurement
  requires the identification of the electron and the hadronical final
  state, only runs where SpaCal, BDC, BST, CIP, COP, CIZ, CJC and LAr
  in the readout are considered.  
\item {\it Trigger phase and prescale.} At the beginning of the
  luminosity fill, the trigger phase $2$ is declared if the current of
  the electron and proton beams is high and the background conditions
  allows turn on the central tracker devices.
  Since the statistic error of the measurement is calculated through
  the quadrat of the prescales $\sigma^2=\sum_i w_i$, only runs with
  prescale less than 3 will be considered. 
  The trigger used in this analysis is based on energy depositions on
  the SpaCal calorimeter 
  of particles coming from the interaction point. In section
  \ref{Sectriggerfiducuts} a dissusion of the trigger efficiency will
  be presented. 
\end{itemize} 

