\documentclass[preprint2]{aastex}
\begin{document}
\title{ \bf TPCino test for the Harp experiment.}
\author { {\bf Alejandro Castillo Ram\'irez} \\
Supervisor \\ {\bf Juan Jos\'e G\'omez Cadenas} \\
Technical Supervisor\\ {\bf Valeri Serdiouk}}
\affil{CERN \vskip 1 cm}
\email{acastill@mail.cern.ch}
\email{gomez@mail.cern.ch}
\email{Valeri.Serdiouk@cern.ch}
\begin{abstract}
The following is a contribution to the harp experiment, in particular
in the TPCino analysis, it consists on a series of plots that describe part
of the behaviour of the detector. This project was part of the
summer student program in CERN.
\vskip 1cm
\end{abstract}
\section{Introduction}
The HARP\footnote{Hadron research production, for the neutrino factory
and for the atmospheric neutrino flux} experiment is a programme of
measurements of secondary hadrons over the full solid angle,
for this the TPC has a special role. It has been planed not only to
determine the momentum of the tracks but also to identify pions, kaons
and protons at low momenta.
In order to achieve this the HARP collaboration has decided to modify the
TPC90\footnote{The so called TPC90 is the ALEPH prototype TPC\cite{TPC}}.
In section \ref{des}, we make simple description on the TPCino
configuration\ref{des2}, \ref{des3}, and we mention some of the physic
characteristics of the chamber\ref{des1}.
In section \ref{meas} we describe the procedure to acquire the Data.
On the last section \ref{future} we mention the next goals on future
projects which include a slow simulation of the
TPC\footnote{this is a project on geant4, to
develop a further understanding on the Harp TPC}.
\section{The TPCino detector}
\label{des}
The TPCino is a small TPC chamber with the geometry similar to the real
design, created to understand the electronics\footnote{The preamplifiers,
the shapers etc.}, and the wire chambers of the HARP Time projection
chamber, so one of the purposes of this device is to find the best
configuration of wire grids for the readout wire chambers to use in
the TPC\cite{one} \cite{two}, and to understand the behaviour of the drift
and diffusion parameters. In \ref{des1} we only mention the
potential of a wire grid, in order to get an idea of the form of the
fields there\footnote{for more information see\cite{one}, and the analysis
of the harp group on the TPC read out\cite{set}}, the drift velocity and the
diffusion.
\subsection{Wire Grids}
\label{des1}
In the TPC as in many drift chambers the electric field must do two things,
drift the electrons and produce the amplification. Near the sense wires the
cylindrical electric field provides directly the fields strengths needed
for the amplification, the drift must be produced by a suitable arrangement
of electrodes at right potentials\footnote{in the next sections we make the
description of this arrangements.\cite{one}}
Taking a reference system with the x-y plane coincident with the conducting
plane (pad plane) and the y axis on the direction of the wires of the grid.
The potential function is:
\begin{equation}
\phi(U) =-\frac{\lambda}{2\pi\epsilon_0}
{\sum_\infty^\infty ln\frac{U-U_k'}{U-U_k''}}
\end{equation}
were $U=x+iz$, $U'= x'-iz'$ and $U_k'$ is la coordinate of the
K's wire, making the summation we get to the following real potential:
\vskip .5cm
$V(x,z)=\phi(U)=$
\begin{equation}-\frac{\lambda}{2\pi\epsilon_0}
{ln\frac{sin^2[(\pi)(x-x_0)]+sinh^2[(\pi)(z-z_0)}
{sin^2[(\pi)(x-x_0)]+sinh^2[(\pi)(z+z_0)}}
\end{equation}
The behaviour of the drift chamber depends crucially on the drift of the
electrons and ions created either by the particles measured or in the
avalanches at the electrodes.\footnote{in addition to the electric field,
there is a magnetic one, but in our case the measurements were done in
absence of it} The electrons and ions, are scattered by the gas molecules,
so their movement is randomised in each collision, but they acquire a
constant drift velocity $u$ in the direction of the E field. We can neglect
thermal motion, and make the statistic to get
\begin{equation}
u^2=\frac{eE}{mN\sigma}\sqrt{\frac{\lambda}{2}}
\end{equation}
As the electrons are scattered on the gas molecules, the drift velocity
deviates from the average, this ones are taken to be Gaussian, the same in
all directions, and point-like. Using the expression for mobility we find
that the energy determines the diffusion width of an electron cloud which
after a starting point-like has travelled a distance L\cite{one} is
\begin{equation}
\label{diffusion}
\sigma^2=2Dt=\frac{2DL}{\mu E}\end{equation}
% due to the conditions of chamber, and the knowledge gained in the TPC90,
%we only need some simple measurements to test the behaviour of the TPC
%under the planned modifications\cite{HARP}\cite{six}.
\subsection{The TPCino field cage}
\label{des2}
The TPCino field cage is composed of copper strips 1.25 mm wide, 0.25 mm
between strips etched on the 1.15 thick Fiberglas PCB The rectangular cross
section of the field cage is $33 mm$ (a long the wires of the readout chamber)
and $14.5 mm$ perpendicular to them. The height of the field cage
(along drift direction) is 47.5 mm. The voltage divider consist of
31 resistors$0.5mhoms$ ${\pm}$ 10 Kohms i.e. 15.5 Mohms.
For the initial stage of TPCino testing two potentiometer are put to define
the voltage between the last strip of the field cage (0.66 Mohms) and the
grating grid plane ( 2m gap) and 1.66 mohms between gating grid and
cathode plane (5mm gap). The drift voltage of 800 v corresponds to drift
field 150 v/cm.
At the moment a gamma source Fe-55 (5.9 kev) collimated with a 1 mm hole
collimator is installed on one of the walls of the field cage.
The distance between the axes of the collimator and the gating
grid is about 20 mm. On the opposite side of the field cage is
installed a wire counter with a hole at the level of the collimator;
This gives a possibility of triggering the TPC if using a charged source
like an $\alpha$ alpha\ref{Tpcino}.
\subsection{Readout wire Chamber}
\label{des3}
The TPCino readout wire Chamber is formed by the frame of the readout
chamber, two sense anode planes, a cathode plane and a mother board.
The frame of the readout chamber is made from stesalite it has a glued
print circuit for wire soldering.
The two sense anode planes are prepared. one with 4 mm pitch, anode wires
of 20 mkmof diameter (constructed with gold covered by a layer
of tungsten\footnote{this is also know as gold plated}).
The last wires (guard wires) in the plane are of 50 mkm of diameter
to smooth the gain.
The second frame is formed by repeating the following pattern:
{\bf\sf field - sense - field - sense wires}
The field wires are made from an alloy of copper- beryllium and have a
diameter of 100 microns, while the sense wires are made of tungsten and
gold and have a diameter of 20 microns.
The Cathode plane is formed with: 1 mm pitch, 70 micron copper - beryllium
wires.
The grating grid plane is formed with: 2 mm pitch, 70 micron copper
beryllium wires.
The frame width of 5 mm define the gaps between gating grid, cathode,
anode and pad planes.
The active surface of the chamber is about 70 by 70 square mm.
in the absence of the motherboard a copper plate is installed for testing
the chamber and the whole setup\ref{Tpcino}.
\begin{figure}[t]
\plotone{fig10.eps}
\caption{Schematic diagram of the TPCino detector.}\label{Tpcino}
\end{figure}
\section{Measurements}\label{meas}
The work performed on the TPCino, was to measure the time widths, in order
to understand by comparison, the behaviour of the longitudinal diffusion
$DL$, as well as measurements of the gating grid to find a good operation
point. In the \ref{meas1} we describe the conditions of those measurements
and we present some plots\footnote{The plots and data analysis were done
using Root 2.23}of the diverse FWHM\footnote{Full width at half of maximum},
and base widths and amplitude response, and some of the gating grid plateau
measurements.
\subsection{Setup}
\label{meas1}
There are many parameters on the TPCino, we worked on the
following:high voltage,drift voltage, Grating grid offset potential $V^0$,
trigger level. We perform measurements fixing most of those and varying
only one\footnote{the different plots are available on request} , to check
the response of both the pad and the cathode. we find a extreme sensitivity
on the value of the trigger level, being the chamber to sensitive to cosmic
rays with trigger levels (tl) above 20mv.\footnote{in this report thus we
only show the plots with a tl of 10 mv}
The data was acquired using a Lecroy oscilloscope model 9450 A. On
CERN-- Previssine in a temperature controlled room. The low voltage was
settled at $\pm$ 8v for the buffer, and the preamplifiers at
$\pm$ 3v.\footnote{two different set of preamplifiers were used,
we show only the set of plots correspondent to the second one}
The range of operation were for the drift voltage $0 \rightarrow 800$ volts,
the high voltage $0 \rightarrow 1500$ volts and the
$V^0$ was $0 \rightarrow 135$volts. The gas was premixed in the right
proportions\footnote{see also
http://r.home.cern.ch/r/rjd/www/Harp/gas.html} \cite{set}.
\subsection{Plots}
The drift velocities on the drift chambers is a very well studied phenomena.
in the measurements taken have the intension of showing the behaviour of the
TPCino, using the data book and making some modifications to the equation 4
we can relate the behaviour of the diffusion, with the Base with behaviour.
we performed a polynomial approximation to the data, being the behaviour of
the $D_l$ proportional to the second power of this polynomial,
plots: \ref{hw} y \ref{bw} show the behaviour of the FWHM width, and base
width signals respectively, the \ref{amppad} shows the dependence of the
Pad width vs the Drift voltage\footnote{the same analysis is available
for the Cathode plane}, the drift velocity on this conditions were found to
be $5.2cm/\mu s$, and the longitudinal diffusion to have and exponential
behaviour, with higher step.
\begin{figure}
\plotone{Tpcinohw.eps}
\caption{FWHM with of signal response from pad in function of drift voltage,
at 1450v of high voltage. trigger level at 10mv.}\label{hw}
\end{figure}[t]
\begin{figure}
\plotone{Tpcinobw.eps}
\caption{Base with of signal response in function of drift voltage from
pad, at 1450v of high voltage. trigger level at 10mv.}\label{bw}
\end{figure}
\label{meas2}
\begin{figure}[t]
\plotone{Tpcinoampad.eps}
\caption{Amplitude of signal response from pad against drift voltage,
at 1450v of high voltage. trigger level at 10mv.}\label{amppad}
\end{figure}
There are figures, showing the behaviour of the same parameters but
plotted against the High voltage available on request.
The following are presented to show the sensibility of the TPCino to the
trigger level and the drift voltage. we show a very low drift voltage in
order to appreciate the distortions in the shape of the signal, and the
lost of the plateau due to the mix of different signals\ref{pla350}.
\begin{figure}[t]
\plotone{plat350.eps}
\caption{effects of a very low drift voltage on the TPCino. we plot $V_0$
against amplitude of Pad..}\label{pla350}
\end{figure}
The following \ref{pla700} are presented to show the sensibility of the
TPCino to the drift voltage at the same trigger level that \ref{pla350}
we show a high drift voltage almost the point of operation, the idea is
to see which is the optimum voltage, and the point of operation ideal.
\begin{figure}[t]
\plotone{pla700.eps}
\caption{Diminution of the effects of signal mixture, thanks to the
augment of signal over noise due to the point of operation, 700 volts
drift voltage.}
\label{pla700}
\end{figure}
\section{TPC simulation}
The TPC of harp will have three major modifications respect to the TPC90,
the downstream iron end-cap of the flux return will be removed,
retaining the homogeneity of the solenoidal field inside the TPC volume,
the pad will be changed to a novel circular geometry, and the incorporation
of a cylindrical field cage that will surrounds the
target.\cite{set}\cite{six} A simulation of all this processes is visaged.
A montecarlo simulation and analysis of the chamber was the goal of the
second part of activities realized at CERN. This require the optimisation
of an existent program in geant4 designed by Juan Jos\'e Gomez y
Pedro Arce. The source code is not finished.
\label{future}
\section{Acknowledgements}
We would like to thank my two supervisors:{\bf Juan Jose Gomez y
Valeri Serdiouk} for all the time the expend with me, for their patience
and all. Also to Benoit R. who teach me how to convince root to play
attention to my macros, and the root discussion list for all the
good tips on the use of root.
\begin{thebibliography}{9}
\bibitem{one} W.Blum and Rolandi Particle Detection with Drift Chambers- Springer-Verlag, ISBN 3-540-56425-X
\bibitem{two} The Pad Response Function of the HARP TPC Juan Jos\'e G\'omez.
\bibitem{TPC}S.R. Amendiolia et al. Nucl. Instrum. Meth. A252(1986)392
\bibitem{three} http://Root.cern.ch/
\bibitem{four} http://wwwinfo.cern.ch/asd/geant4/geant4.html
\bibitem{five} http://alephwww.cern.ch/SUBDET/tpc.html
\bibitem{six} http://harp.web.cern.ch/harp
\bibitem{set}http://r.home.cern.ch/r/rjd/www/Harp/
\end{thebibliography}
\end{document}