Subversion Repositories f9daq

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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.

\begin{thebibliography}{99}  

%\section{Bibliography}

%\begin{enumerate}

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%\item

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pattern by counting single photons,\\

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Vol. 536, p. 340-348

\bibitem{Knoll}

%\item

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\bibitem{Leo}

%\item

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Springer-Verlag, 1987

\bibitem{Debbe}

%\item

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\bibitem{Krizan}

%\item

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%\item

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\bibitem{Hama}

%\item

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\bibitem{Hama-web}

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%\item

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%\item

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%\end{enumerate}

\end{thebibliography}

\end{sloppypar}

\end{document}