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\begin{document}
\begin{sloppypar}
\title{MEASUREMENT OF CHERENKOV RINGS WITH MULTIANODE PHOTOMULTIPLIERS}
\author{S.Korpar$^{1,2}$, R.Pestotnik$^{2}$, P.Kri\v zan$^{3,2}$,
A.Gori\v sek$^2$, A.Stanovnik$^{4,2}$
\\$^1${\it \small Faculty of Chemistry and Chemical Engineering,
University of Maribor, Slovenia}
\\$^2${\it \small Jo\v zef Stefan Institute, Ljubljana, Slovenia}
\\ $^3${\it \small Faculty of Mathematics and Physics,
University of Ljubljana, Slovenia}
\\ $^4${\it \small Faculty of Electrical Engineering,
University of Ljubljana, Slovenia} }
\maketitle
%Contents:
%1. Introduction
%2. Position sensitive photomultipliers: Hamamatsu R5900-M16 and R5900-L16
%3. Experimental setu-up
%4. Measurement
%* HV plateau
%* Threshold scan
%* Cross-talk
%* Diffraction pattern
\section*
{Abstract}
The present paper describes a laboratory course to be held at the
Danube School on Instrumentation in Elementary Particle \& Nuclear
Physics in Novi Sad, Serbia. It is a continuation and upgrade of
similar courses held in
Bogota, Colombia in 2013,
Bariloche, Argentina in 2010,
Itacuru\c{c}a, Brasil in 2003 \cite{Icfa},
Istanbul in 1999 and 2002 and
in Faure, South Africa in 2001.
The main purpose of this exercise is to introduce the student to the
Ring Imaging CHerenkov technique. The student will work with multianode
photomultipliers (Hamamatsu, R5900-M16 and R5900-L16 PMT's), with which
measurements requiring position sensitive detection of single photons
will be performed. The first exercise is a measurement of the diffraction
pattern by counting individual photons passing through a slit, and the
second is a measurement of Cherenkov rings produced by cosmic muons in
an aerogel radiator.
\section{Introduction}
Photomultiplier tubes (PMTs), or photomultipliers (PMs) for short, are
sensitive detectors of weak light signals capable of detecting even single
photons \cite{Knoll,Leo}. The photomultiplier consists of an evacuated
glass vessel containing a photocathode, from which incident photons may eject
an electron, and a system of electrodes (dynodes) in which this photoelectron
is multiplied to give a measurable electrical signal at the anode. The
photocathode, the dynodes and the anode have leads through the glass to the
outside of the vessel, enabling connections of high voltage and allowing the
signals to be further processed by suitable electronics. The photomultiplier
is thus plugged into a photomultiplier base, which consists of a resistor
chain providing appropriate voltages for the dynodes and a
load resistor, on which the signal appears. In some cases, potentiometers are
provided for adjusting the voltage on the electrodes for focusing the
photoelectrons to the first dynode and capacitors or Zener diodes to stabilize
the voltage on the last dynodes in case of high rate and high gain operation
(Fig.~\ref{fig1}).
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir fp.eps,width=8cm,angle=0.0}}
\caption{Voltage divider.}
\label{fig1}
\end{figure}
An important parameter of a photomultiplier is the quantum
efficiency (QE), defined as the ratio of the number of photoelectrons ejected
from the photocathode to the number of photons incident on the
photomultiplier. Clearly, this parameter is a function of the energy (or
wavelength) of the incident photons and is a product of the probability for
the photoelectric effect and the probability for the electron to escape from
the photocathode. The most common photocathode materials are
semiconductors containing alkali elements. The quantum efficiency
QE($\lambda$) is connected to the photocathode radiant sensitivity
S($\lambda$), which is defined as the photocathode current divided by the
incident photon power:
$$S(\lambda ) = QE(\lambda ){e_0 \lambda \over h c}$$
The quantum efficiency is cut off on the low
energy side by the vanishing probability for the
photoelectron to escape into the vacuum and on the high energy
side by photon absorption in the PM glass window.
The photoelectrons ejected from
the photocathode are focused to the first dynode, where they eject more
electrons. The electron multiplication is given by the secondary emission
factor, which depends on the incident electron energy as well as on the dynode
material.
Usually, there are several dynodes (10 to 12) leading to an overall
amplification of about 10$^6$ to 10$^7$.
In experimental physics, photomultipliers are most often used as detectors of
scintillations, which charged particles, neutrons or gamma rays produce when
depositing some or all of their energy in special scintillating materials.
PMs may also be used as
position sensitive detectors of single photons, especially for the Ring
Imaging Cherenkov (RICH) counters in high energy physics experiments
\cite{Debbe,Krizan,Arino,Akopov}.
The present laboratory course will introduce two such photomultiplier
tubes produced by Hamamatsu Photonics K.K.; the R5900-M16 and the R5900-L16
multianode photomultipliers.
\section{Position sensitive photomultipliers}
The R5900 series M16 and L16
multianode photomultipliers are shown in
Fig.~\ref{fig2}. The M16 is divided into 4 x 4 = 16 anode outputs, each
covering a pad size of 4.5 x 4.5 mm$^2$. The
L16 anode, on the other hand, is divided into 16 strips of 16 mm length and
1 mm pitch. The exact dimensions of the photomultipliers and the locations
of the electrode pin connectors are given in the data sheets \cite{Hama}.
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir pmt2.eps,width=9cm}}
\caption{Hamamatsu multianode photomultipliers (L16, M16, M16 from left
to right).}
\label{fig2}
\end{figure}
The quantum efficiency and the radiant sensitivity given by the
manufacturer for L16 photomultipliers are shown in Fig.~\ref{fig3}.
It seems that allowance has to be made for an additional
efficiency factor due to less than perfect collection and transmission
($\sim$»80\%) of the photoelectrons by the dynode system \cite{Krizan}.
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir L16.eps,width=7.5cm}}
\caption{Typical spectral response of L16 PMT \cite{Hama}.}
\label{fig3}
\end{figure}
The dynode system in these multianode
photomultipliers differs considerably from those in conventional
photomultipliers. It consists of foils with specially shaped
perforations or channels. On the walls of these channels, secondary emission
takes place thus multiplying the number of electrons (Fig.~\ref{fig4}). With
10-12 such dynode foils, gains above 10$^6$ are reached. The anode dark
current is mainly below 200 nA \cite{Hama}.
Attention must be paid not to exceed the maximum allowed voltage
of 900~V for L16 and 1000~V for M16 PMT and the maximum allowed current of 0.01 mA \cite{Hama}.
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir MCtype.eps,width=8cm}}
\caption{Metal channel type PMT \cite{Hama-web}.}
\label{fig4}
\end{figure}
Of special interest
e.g. in Cherenkov ring imaging is the position resolution, which is mainly
given by the anode pad size. The cross-talk to
adjacent channels is small and the response
across the photocathode surface seems to be uniform to the level of some 10\%
\cite{Krizan,Hama}.
For the M16 photomultipliers, measurements have been made
of single photoelectron pulse height distributions showing a well resolved
single electron peak corresponding to a plateau on the
rate-versus-voltage curve \cite{Krizan}. Tests with rates of
3 MHz/channel during 30 days \cite{Krizan} and two years of experience with the
HERA-B photon detector \cite{Arino}, show that these photomultipliers operate
smoothly even in otherwise hostile environments as are characteristic of the
new high energy colliders. According to specifications \cite{Hama}, the pulse
rise time is 0.8 ns with a transit time spread of 0.3 ns, so they could also
be used for timing purposes.
\section{Experimental set-up}
The exercise is divided into three parts. The first consists of measuring the
high voltage plateau and the position dependence of the M16 count rate
for a pencil beam. The second part consists of measuring Cherenkov rings
with an array of sixteen M16 PMTs. The third part of this
exercise represents a measurement of a diffraction pattern by counting single
photons with the L16 position-sensitive photomultiplier.
\subsection{M16 - HV plateau and position dependence of the count rate}
The experimental set-up for measuring the M16
photomultiplier is shown in Fig.~\ref{fig5}. Light from the LED source
is collimated by two pinholes,
defining an illuminated spot of about 0.5 mm diameter on the
photocathode.
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir skica1.eps,height=7.5cm,angle=-90.0}}
\caption{The experimental set-up for measuring the characteristics of M16 PMT.}
\label{fig5}
\end{figure}
The photomultiplier is plugged into a PM base and both are
enclosed in a light-tight box together with the light source and collimators.
High voltage is provided by a HV power supply from which a cable leads to the
PM base inside the light-tight box. Cables from four anode
pads connect each signal first to an amplifier, then discriminator and
finally to a scaler. The plate on which the PMT is fastened, may
be displaced in a direction transverse to the light beam by means
of a screw thread (1 mm/turn), which could be operated from the outside of
the box. The height of the beam is set in order to be centered on one
of the four rows with four pads. After observing the set-up the box
is closed and the count rate at given threshold is recorded as a function
of high voltage (see Fig.6). The voltage is then set on the plateau
and count rates of the four pads are measured as a function of the PM
position relative to the light spot (Fig.7). From the results of this
measurement one may study the position resolution, the cross talk between
adjacent pads, the uniformity of pad response and the response variation
across a given pad, which reflects the structure of the dynode channels,
as also seen in Fig.~\ref{fig2}.
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir M16hv.eps,width=11.5cm}}
\caption{Plateau curves for 4 channels of the M16 PMT.}
\label{fig6}
\end{figure}
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir M16pos.eps,width=11.5cm}}
\caption{Count rate on 4 channels of the M16 PMT depending on the light
spot position.}
\label{fig7}
\end{figure}
\clearpage
\subsection{Array of M16 PMT's - Cherenkov rings}
When the velocity $v = \beta c$ of a charged particle in a medium exceeds
the speed of light $c/n$ in that medium (c is the speed of light in vacuum
and n is the refractive index of the medium), the particle emits light at an
angle with respect to it's direction of motion. This Cherenkov angle
is determined by the relation
$$\cos \theta _{c} = {1 \over {\beta n}}$$
and the threshold velocity for emission of Cherenkov
light is at $\beta _{th} = 1/n$.
With a position sensitive detector of single photons, one may detect
a Cherenkov ring image \cite{Nappi}, from which the Cherenkov angle and thus
the particle velocity may be determined. As the particle momentum is
measured by other components of a detector system, one may use the velocity
measurement to calculate the particle mass. Thus, Cherenkov detectors are
usually refered to as particle identification devices. Most large detector
systems operating at the high energy accelerators and colliders, include such
a Ring Imaging Cherenkov detector (RICH) \cite{Eingedi}.
In the literature \cite{Nappi} we find
that the number of detected photons is given by:
$$N = N_0 \cdot L \cdot \sin ^2 \theta _{c}.$$
$N_0$ is a figure of merit of the particular Cherenkov detector, which depends
mainly on the efficiency of photon detection and the loss of photons
between emission and detection. $L$ is the length of the radiator and
$\theta _{c}$ is the Cherenkov angle.
In the present exercise, we shall measure the Cherenkov photons radiated by
high energy muons in an aerogel radiator.
The muons are produced by cosmic rays in the upper layers of
the atmosphere so are mainly incident from above onto the apparatus shown
in Fig.~\ref{fig11}.
The muon first gives a trigger signal in a scintillation counter and then
enters two, 2 cm thick aerogel layers (n$_1$ = 1.0485, n$_2$ = 1.0619),
where a $\beta \simeq 1$ muon would radiate Cherenkov photons at
$\theta _c$ = $\arccos$(1/n) = 305(343) mrad. The Cherenkov photons are
refracted into air and are detected by the photon detector lying
$\simeq$16 cm below the aerogel radiator entrance surface.
The hits are distributed
on the circumference of a ring of aproximately 5 cm radius
(for $\beta \simeq 1$ particles). The radiator thickness leads to an
uncertainty in the emission point, which translates into a $\approx$7~mm
uncertainty in the hit position
on the photon detector. This uncertainty and the shortage of readout
channels resulted in four adjacent anode pads of the M16 PMT
being connected into one $9 \times 9$ mm$^2$ pixel.
The PMT array consists of sixteen M16 PMT's on a $30 \times 30$ mm$^2$
grid, so the geometrical acceptance of the photocathodes ($18 \times 18$
mm$^2$) is 36 \%. From this geometrical acceptance and the photocathode
quantum efficiency ($\simeq 20\%$ over $\Delta$E $\simeq$ 1 eV),
we estimate the figure of merit to be $N_0 \sim 15$ cm$^{-1}$. One may thus
expect on average about 3 detected Cherenkov photons per full muon ring.
As the number of photons is distributed statistically,
a larger number (say 5 or 6) will be occasionally detected, allowing an
estimate of the ring radius and thus the charged particle velocity.
The PMT anode signals are led through a discriminator to a 64 channel
multihit TDC unit (CAEN V673A) (Fig.~\ref{fig11}). The TDC is read out through
the VME system into the computer (using WIENER PCI-VME interface), where
appropriate algorithms reconstruct the hit maps displaying the Cherenkov ring
images.
In Fig.~\ref{fig11.a} six events with high number of Cherenkov photons reconstructed are shown. They were taken at the ICFA Instrumentation School in Istanbul in 2002.
\vspace{1.0cm}
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir aerogel_rich.eps,width=11.0cm}}
\caption{RICH counter for cosmic muons: the set-up.}
\label{fig11}
\end{figure}
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir compilation1.eps,width=11.0cm}}
\caption{Reconstructed hits on the photon detector as obtained with the setup in Fig.~\ref{fig11}. Six events with high number of hits were selected. The two red circles define the maximal and minimal rings which correspond to Cherenkov photons irradiated at the beginning and at the end of the aerogel radiator, correspondingly. 2x2 PMT channels were connected together in one readout channel, to simplify the readout electronics.}
\label{fig11.a}
\end{figure}
\clearpage
\subsection{L16 - Diffraction pattern}
The schematic diagram of this experimental set-up is shown in
Fig.9. The light source is a light emitting diode
(Fig.10). This light is passed through a slit of width D, on which
diffraction occurs. The diffraction pattern is given by
$$j(\vartheta ) = j_0 {\sin ^2 \alpha \over {\alpha}^2}$$
where $\alpha = {\pi D \sin \vartheta \over \lambda}$
and $\vartheta$ is the diffraction angle with respect to the beam direction. In
terms of the distance x from the central maximum and the distance L between
the slit and the photomultiplier, this angle is given by
tg $\vartheta = x / L$ (see Fig.~\ref{fig9}). The first minimum in the
diffraction pattern occurs at $\sin {\vartheta}_{min} = \lambda / D$. Assuming
that the diffraction angle ${\vartheta}_{min}$ is small, the x-position of
the minimum will be given by $x_{min}/L = \lambda / D$. In the present
exercise one measures the position of the minimum and thus determines the slit
width $D = \lambda \cdot L / x_{min}$.
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir skica2.eps,height=7.5cm,angle=-90.0}}
\caption{The experimental set-up for measuring diffraction with the L16 PMT.}
\label{fig8}
\end{figure}
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir spektri_mod.eps,height=6cm,angle=0.0}}
\caption{Spectra of three different LED sources.}
\label{fig8}
\end{figure}
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir skica3.eps,width=9.5cm}}
\caption{Geometric parameters for the diffraction measurement.}
\label{fig9}
\end{figure}
From the 16 anode strips, the signals are led through amplifiers into CAMAC
discriminators and then to a 16 channel CAMAC scaler. The counting time is
set by removing the veto pulse on the discriminator. This is performed via
a CAMAC input/output register and a NIM timing unit.
The register and the scaler are
connected via CAMAC and GPIB to a personal computer, which runs a data acquisition
programme and displays the diffraction histogram.
With the 16 channels at 1 mm pitch only a 16 mm portion of the diffraction
pattern could be measured simultaneously.
In order to cover a broader range of diffraction angles, the photomultiplier may be displaced relative to the light beam by
means of a screw thread (1mm/turn) operated from the outside of the
light-tight box.
A diffraction pattern is first demonstrated
by using a light beam from a laser pointer and slits made
from razor blades.
The slits are then inserted onto the
rails in front of the light emitting diode, the distance $L$ is measured and
the box is closed. The high voltage on the PMT is set to approximately 800 V
and the current through the LED is adjusted for an acceptable count rate.
The diffraction pattern is then measured in
at least two different positions of the PMT relative to the light beam
and the results are appropriately connected.
From the distribution (Fig.~\ref{fig10}), one determines the position of the
first minimum and then calculates the slit width D from the above equation.
At this point the student may be reminded of the analogy between
this experiment and the measurement of nuclear sizes by the so called
diffraction scattering.
\begin{figure}[hbt]
\centerline{\epsfig{file=\epsdir L16dif.eps,width=12cm}}
\caption{Measured diffraction distribution.}
\label{fig10}
\end{figure}
In this exercise, the pedagogical problem of wave-particle duality is
stressed. With sufficiently low
counting rate one may in principle simultaneously observe the
count increment of individual channels and the appearance of the diffraction
histogram (Fig.~\ref{fig10}). The individual hit is a manifestation of the
particle nature of the photon, while the diffraction distribution speaks of
its wave properties.
\clearpage
\section*{Acknowledgment}
We are grateful to Hamamatsu Photonics K. K. for donating some of the
multianode photomultipliers used in the present laboratory course.
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%\item
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\end{thebibliography}
\end{sloppypar}
\end{document}