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\begin{document}
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\begin{sloppypar}
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36
\title{MEASUREMENT OF CHERENKOV RINGS WITH MULTIANODE PHOTOMULTIPLIERS}
37
\author{S.Korpar$^{1,2}$, R.Pestotnik$^{2}$, P.Kri\v zan$^{3,2}$,
38
        A.Gori\v sek$^2$, A.Stanovnik$^{4,2}$
39
\\$^1${\it \small Faculty of Chemistry and Chemical Engineering,
40
                  University of Maribor, Slovenia}
41
\\$^2${\it \small Jo\v zef Stefan Institute, Ljubljana, Slovenia}
42
\\ $^3${\it \small Faculty of Mathematics and Physics,
43
                   University of Ljubljana, Slovenia}
44
\\ $^4${\it \small Faculty of Electrical Engineering,
45
                   University of Ljubljana, Slovenia} }  
46
 
47
\maketitle
48
 
49
%Contents:
50
%1. Introduction
51
%2. Position sensitive photomultipliers: Hamamatsu R5900-M16 and R5900-L16
52
%3. Experimental setu-up
53
%4. Measurement  
54
%* HV plateau
55
%* Threshold scan
56
%* Cross-talk
57
%* Diffraction pattern
58
 
59
\section*{Abstract}
60
The present paper describes a laboratory course to be held at the
61
Danube School on Instrumentation in Elementary Particle \& Nuclear
62
Physics in Novi Sad, Serbia. It is a continuation and upgrade of
63
similar courses held in
64
Bogota, Colombia in 2013,
65
Bariloche, Argentina in 2010,
66
Itacuru\c{c}a, Brasil in 2003 \cite{Icfa},
67
Istanbul in 1999 and 2002 and
68
in Faure, South Africa in 2001.
69
The main purpose of this exercise is to introduce the student to the
70
Ring Imaging CHerenkov technique. The student will work with multianode
71
photomultipliers (Hamamatsu, R5900-M16 and R5900-L16 PMT's), with which
72
measurements requiring position sensitive detection of single photons
73
will be performed. The first exercise is a measurement of the diffraction
74
pattern by counting individual photons passing through a slit, and the
75
second is a measurement of Cherenkov rings produced by cosmic muons in
76
an aerogel radiator.
77
 
78
\section{Introduction}
79
Photomultiplier tubes (PMTs), or photomultipliers (PMs) for short, are
80
sensitive detectors of weak light signals capable of detecting even single
81
photons \cite{Knoll,Leo}. The photomultiplier consists of an evacuated
82
glass vessel containing a photocathode, from which incident photons may eject
83
an electron, and a system of electrodes (dynodes) in which this photoelectron
84
is multiplied to give a measurable electrical signal at the anode. The
85
photocathode, the dynodes and the anode have leads through the glass to the
86
outside of the vessel, enabling connections of high voltage and allowing the
87
signals to be further processed by suitable electronics. The photomultiplier
88
is thus plugged into a photomultiplier base, which consists of a resistor
89
chain providing appropriate voltages for the dynodes and a
90
load resistor, on which the signal appears. In some cases, potentiometers are
91
provided for adjusting the voltage on the electrodes for focusing the
92
photoelectrons to the first dynode and capacitors or Zener diodes to stabilize
93
the voltage on the last dynodes in case of high rate and high gain operation
94
(Fig.~\ref{fig1}).
95
 
96
\begin{figure}[hbt]
97
\centerline{\epsfig{file=\epsdir fp.eps,width=8cm,angle=0.0}}
98
\caption{Voltage divider.}
99
\label{fig1}
100
\end{figure}
101
 
102
An important parameter of a photomultiplier is the quantum
103
efficiency (QE), defined as the ratio of the number of photoelectrons ejected
104
from the photocathode to the number of photons incident on the
105
photomultiplier. Clearly, this parameter is a function of the energy (or
106
wavelength) of the incident photons and is a product of the probability for
107
the photoelectric effect and the probability for the electron to escape from
108
the photocathode. The most common photocathode materials are
109
semiconductors containing alkali elements. The quantum efficiency
110
QE($\lambda$)  is connected to the photocathode radiant sensitivity
111
S($\lambda$), which is defined as the photocathode current divided by the
112
incident photon power:
113
$$S(\lambda ) = QE(\lambda ){e_0 \lambda \over h c}$$
114
The quantum efficiency is cut off on the low
115
energy side by the vanishing probability for the
116
photoelectron to escape into the vacuum and on the high energy
117
side by photon absorption in the PM glass window.
118
 
119
The photoelectrons ejected from
120
the photocathode are focused to the first dynode, where they eject more
121
electrons. The electron multiplication is given by the secondary emission
122
factor, which depends on the incident electron energy as well as on the dynode
123
material.
124
Usually, there are several dynodes (10 to 12) leading to an overall
125
amplification of about 10$^6$  to 10$^7$.
126
 
127
In experimental physics, photomultipliers are most often used as detectors of
128
scintillations, which charged particles, neutrons or gamma rays produce when
129
depositing some or all of their energy in special scintillating materials.
130
PMs may also be used as
131
position sensitive detectors of single photons, especially for the Ring
132
Imaging  Cherenkov (RICH) counters in high energy physics experiments
133
\cite{Debbe,Krizan,Arino,Akopov}.
134
 
135
The present laboratory course will introduce two such photomultiplier
136
tubes produced by Hamamatsu Photonics K.K.; the R5900-M16 and the R5900-L16
137
multianode photomultipliers.
138
 
139
\section{Position sensitive photomultipliers}  
140
The R5900 series M16 and L16
141
multianode photomultipliers are shown in
142
Fig.~\ref{fig2}. The M16 is divided into 4 x 4 = 16 anode outputs, each
143
covering a pad size of 4.5 x 4.5 mm$^2$. The
144
L16 anode, on the other hand, is divided into 16 strips of 16 mm length and
145
1 mm pitch.  The exact dimensions of the photomultipliers and the locations
146
of the electrode pin connectors are given in the data sheets \cite{Hama}.
147
 
148
\begin{figure}[hbt]
149
  \centerline{\epsfig{file=\epsdir pmt2.eps,width=9cm}}
150
  \caption{Hamamatsu multianode photomultipliers (L16, M16, M16 from left
151
         to right).}
152
  \label{fig2}
153
\end{figure}  
154
 
155
The quantum efficiency and the radiant sensitivity given by the
156
manufacturer for L16 photomultipliers are shown in Fig.~\ref{fig3}.
157
It seems that allowance has to be made for an additional
158
efficiency factor due to less than perfect collection and transmission
159
($\sim$‚»80\%) of the photoelectrons by the dynode system \cite{Krizan}.
160
 
161
\begin{figure}[hbt]
162
  \centerline{\epsfig{file=\epsdir L16.eps,width=7.5cm}}
163
  \caption{Typical spectral response of L16 PMT \cite{Hama}.}
164
  \label{fig3}
165
\end{figure}
166
 
167
The dynode system in these multianode
168
photomultipliers differs considerably from those in conventional
169
photomultipliers. It consists of foils with  specially shaped
170
perforations or channels. On the walls of these channels, secondary emission
171
takes place thus multiplying the number of electrons (Fig.~\ref{fig4}). With
172
10-12 such dynode foils, gains above 10$^6$  are reached. The anode dark
173
current is mainly below 200 nA \cite{Hama}.
174
Attention must be paid not to exceed the maximum allowed voltage
175
of 900~V for L16 and 1000~V for M16 PMT and the maximum allowed current of 0.01 mA \cite{Hama}.
176
 
177
\begin{figure}[hbt]
178
  \centerline{\epsfig{file=\epsdir MCtype.eps,width=8cm}}
179
  \caption{Metal channel type PMT \cite{Hama-web}.}
180
  \label{fig4}
181
\end{figure}
182
 
183
Of special interest
184
e.g. in Cherenkov ring imaging is the position resolution, which is mainly
185
given by the anode pad size. The cross-talk to
186
adjacent channels is small and the response
187
across the photocathode surface seems to be uniform to the level of some 10\%
188
\cite{Krizan,Hama}.
189
 
190
For the M16 photomultipliers, measurements have been made
191
of single photoelectron pulse height distributions  showing a well  resolved
192
single electron peak corresponding to a plateau on the
193
rate-versus-voltage curve \cite{Krizan}. Tests with rates of
194
3 MHz/channel during 30 days \cite{Krizan} and two years of experience with the
195
HERA-B photon detector \cite{Arino}, show that these photomultipliers operate
196
smoothly even in otherwise hostile environments as are characteristic of the
197
new high energy colliders. According to specifications \cite{Hama}, the pulse
198
rise time is 0.8 ns with a transit time spread of 0.3 ns, so they could also
199
be used for timing purposes.
200
 
201
\section{Experimental set-up}
202
The exercise is divided into three parts. The first consists of measuring the
203
high voltage plateau and the position dependence of the M16 count rate
204
for a pencil beam. The second part consists of measuring Cherenkov rings
205
with an array of sixteen M16 PMTs. The third part of this
206
exercise represents a measurement of a diffraction pattern by counting single
207
photons with the L16 position-sensitive photomultiplier.
208
 
209
\subsection{M16 - HV plateau and position dependence of the count rate}
210
The experimental set-up for measuring the M16
211
photomultiplier is shown in Fig.~\ref{fig5}. Light from the LED source
212
is collimated by two pinholes,
213
defining an illuminated spot of about 0.5 mm diameter on the
214
photocathode.
215
\begin{figure}[hbt]
216
\centerline{\epsfig{file=\epsdir skica1.eps,height=7.5cm,angle=-90.0}}
217
\caption{The experimental set-up for measuring the characteristics of M16 PMT.}
218
\label{fig5}
219
\end{figure}
220
The photomultiplier is plugged into a PM base and both are
221
enclosed in a light-tight box together with the light source and collimators.
222
High voltage is provided by a HV power supply from which a cable leads to the
223
PM base inside the light-tight box. Cables from  four anode
224
pads connect each signal first to an amplifier, then discriminator and
225
finally to a scaler. The plate on which the PMT is fastened, may
226
be displaced in a direction transverse to the light beam by means
227
of a screw thread (1 mm/turn), which could be operated from the outside of
228
the box. The height of the beam is set in order to be centered on one
229
of the four rows with four pads. After observing the set-up the box
230
is closed and the count rate at given threshold is recorded as a function
231
of high voltage (see Fig.6). The voltage is then set on the plateau
232
and count rates of the four pads are measured as a function of the PM
233
position relative to the light spot (Fig.7). From the results of this
234
measurement one may study the position resolution, the cross talk between
235
adjacent pads, the uniformity of pad response and the response variation
236
across a given pad, which reflects the structure of the dynode channels,
237
as also seen in Fig.~\ref{fig2}.
238
\begin{figure}[hbt]
239
\centerline{\epsfig{file=\epsdir M16hv.eps,width=11.5cm}}
240
\caption{Plateau curves for 4 channels of the M16 PMT.}
241
\label{fig6}
242
\end{figure}
243
 
244
\begin{figure}[hbt]
245
\centerline{\epsfig{file=\epsdir M16pos.eps,width=11.5cm}}
246
\caption{Count rate on 4 channels of the M16 PMT depending on the light
247
         spot position.}
248
\label{fig7}
249
\end{figure}
250
 
251
\clearpage
252
 
253
\subsection{Array of M16 PMT's - Cherenkov rings}
254
When the velocity $v = \beta c$ of a charged particle in a medium exceeds
255
the speed of light $c/n$ in that medium (c is the speed of light in vacuum
256
and n is the refractive index of the medium), the particle emits light at an
257
angle with respect to it's direction of motion. This Cherenkov angle
258
is determined by the relation
259
$$\cos \theta _{c} = {1 \over {\beta n}}$$
260
and the threshold velocity for emission of Cherenkov
261
light is at $\beta _{th} = 1/n$.
262
 
263
With a position sensitive detector of single photons, one may detect
264
a Cherenkov ring image \cite{Nappi}, from which the Cherenkov angle and thus
265
the particle velocity may be determined. As the particle momentum is
266
measured by other components of a detector system, one may use the velocity
267
measurement to calculate the particle mass. Thus, Cherenkov detectors are
268
usually refered to as particle identification devices. Most large detector
269
systems operating at the high energy accelerators and colliders, include such
270
a Ring Imaging Cherenkov detector (RICH) \cite{Eingedi}.
271
In the literature \cite{Nappi} we find
272
that the number of detected photons is given by:
273
$$N = N_0 \cdot L \cdot \sin ^2 \theta _{c}.$$
274
$N_0$ is a figure of merit of the particular Cherenkov detector, which depends
275
mainly on the efficiency of photon detection and the loss of photons
276
between emission and detection. $L$ is the length of the radiator and
277
$\theta _{c}$ is the Cherenkov angle.
278
 
279
In the present exercise, we shall measure the Cherenkov photons radiated by
280
high energy muons in an aerogel radiator.
281
The muons are produced by cosmic rays in the upper layers of
282
the atmosphere so are mainly incident from above onto the apparatus shown
283
in Fig.~\ref{fig11}.
284
The muon first gives a trigger signal in a scintillation counter and then
285
enters two, 2 cm thick aerogel layers (n$_1$ = 1.0485, n$_2$ = 1.0619),
286
where a $\beta \simeq 1$ muon would radiate Cherenkov photons at
287
$\theta _c$ = $\arccos$(1/n) = 305(343) mrad. The Cherenkov photons are
288
refracted into air and are detected by the photon detector lying
289
$\simeq$16 cm below the aerogel radiator entrance surface.
290
The hits are distributed
291
on the circumference of a ring of aproximately 5 cm radius
292
(for $\beta \simeq 1$ particles). The radiator thickness leads to an
293
uncertainty in the emission point, which translates into a $\approx$7~mm
294
uncertainty in the hit position
295
on the photon detector. This uncertainty and the shortage of readout
296
channels resulted in four adjacent anode pads of the M16 PMT
297
being connected into one $9 \times 9$ mm$^2$ pixel.
298
The PMT array consists of sixteen M16 PMT's on a $30 \times 30$ mm$^2$
299
grid, so the geometrical acceptance of the photocathodes ($18 \times 18$
300
mm$^2$) is 36 \%. From this geometrical acceptance and the photocathode
301
quantum efficiency ($\simeq 20\%$ over  $\Delta$E $\simeq$ 1 eV),
302
we estimate the figure of merit to be $N_0 \sim 15$ cm$^{-1}$. One may thus
303
expect on average about 3 detected Cherenkov photons per full muon ring.
304
As the number of photons is distributed statistically,
305
a larger number (say 5 or 6) will be occasionally detected, allowing an
306
estimate of the ring radius and thus the charged particle velocity.
307
 
308
The PMT anode signals are led through a discriminator to a 64 channel
309
multihit TDC unit (CAEN V673A) (Fig.~\ref{fig11}). The TDC is read out through
310
the VME system into the computer (using WIENER PCI-VME interface), where
311
appropriate algorithms reconstruct the  hit maps displaying the Cherenkov ring
312
images.
313
 
314
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.
315
 
316
 
317
\vspace{1.0cm}
318
 
319
 
320
\begin{figure}[hbt]
321
\centerline{\epsfig{file=\epsdir aerogel_rich.eps,width=11.0cm}}
322
\caption{RICH counter for cosmic muons: the set-up.}  
323
\label{fig11}
324
\end{figure}
325
 
326
\begin{figure}[hbt]
327
\centerline{\epsfig{file=\epsdir compilation1.eps,width=11.0cm}}
328
\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.}
329
\label{fig11.a}
330
\end{figure}
331
 
332
 
333
\clearpage
334
 
335
 
336
\subsection{L16 - Diffraction pattern}
337
The schematic diagram of this experimental set-up is shown in
338
Fig.9. The light source is a light emitting diode
339
(Fig.10). This light is passed through a slit of width D, on which
340
diffraction occurs. The diffraction pattern is  given by
341
$$j(\vartheta ) = j_0 {\sin ^2 \alpha \over {\alpha}^2}$$  
342
where $\alpha = {\pi D \sin \vartheta \over \lambda}$
343
and $\vartheta$ is the diffraction angle with respect to the beam direction. In
344
terms of the distance x from the central maximum and the distance L between
345
the slit and the photomultiplier, this angle is given by
346
tg $\vartheta = x / L$ (see Fig.~\ref{fig9}). The first minimum in the
347
diffraction pattern occurs at $\sin {\vartheta}_{min} = \lambda / D$. Assuming
348
that the diffraction angle ${\vartheta}_{min}$ is small, the x-position of
349
the minimum will be given by $x_{min}/L = \lambda / D$. In the present
350
exercise one measures the position of the minimum and thus determines the slit
351
width  $D = \lambda \cdot L / x_{min}$.
352
 
353
\begin{figure}[hbt]
354
\centerline{\epsfig{file=\epsdir skica2.eps,height=7.5cm,angle=-90.0}}
355
\caption{The experimental set-up for measuring diffraction with the L16 PMT.}
356
\label{fig8}
357
\end{figure}
358
 
359
\begin{figure}[hbt]
360
\centerline{\epsfig{file=\epsdir spektri_mod.eps,height=6cm,angle=0.0}}
361
\caption{Spectra of three different LED sources.}
362
\label{fig8}
363
\end{figure}
364
 
365
\begin{figure}[hbt]
366
\centerline{\epsfig{file=\epsdir skica3.eps,width=9.5cm}}
367
\caption{Geometric parameters for the diffraction measurement.}
368
\label{fig9}
369
\end{figure}
370
 
371
From the 16 anode strips, the signals are led through amplifiers into CAMAC
372
discriminators and then to a 16 channel CAMAC scaler. The counting time is
373
set by removing the veto pulse on the discriminator. This is performed via
374
a CAMAC input/output register and a NIM timing unit.
375
The register and the scaler are
376
connected via CAMAC and GPIB to a personal computer, which runs a data acquisition
377
programme and displays the diffraction histogram.
378
With the 16 channels at 1 mm pitch only a 16 mm portion of the diffraction
379
pattern could be measured simultaneously.
380
In order to cover a broader range of diffraction angles, the photomultiplier may be displaced relative to the light beam by
381
means of a screw thread (1mm/turn) operated from the outside of the
382
light-tight box.
383
 
384
A diffraction pattern is first demonstrated
385
by using a light beam from a laser pointer and slits made
386
from razor blades.
387
The slits are then inserted onto the
388
rails  in front of the light emitting diode, the distance $L$ is measured and
389
the box is closed. The high voltage on the PMT is set to approximately 800 V
390
and the current through the LED is adjusted for an acceptable count rate.
391
The diffraction pattern is then measured in
392
at least two different positions of the PMT relative to the light beam
393
and the results are appropriately connected.
394
From the distribution (Fig.~\ref{fig10}), one determines the position of the
395
first minimum and then calculates the slit width D from the above equation.
396
At this point the student may be reminded of the analogy between
397
this experiment and the measurement of nuclear sizes by the so called
398
diffraction scattering.
399
 
400
\begin{figure}[hbt]
401
\centerline{\epsfig{file=\epsdir L16dif.eps,width=12cm}}
402
\caption{Measured diffraction distribution.}
403
\label{fig10}
404
\end{figure}
405
 
406
In this exercise, the pedagogical problem of wave-particle duality is
407
stressed. With sufficiently low
408
counting rate one may in principle simultaneously observe the
409
count increment of individual channels and the appearance of the diffraction
410
histogram (Fig.~\ref{fig10}). The individual hit is a manifestation of the
411
particle nature of the photon, while the diffraction distribution speaks of
412
its wave properties.
413
 
414
 
415
\clearpage
416
 
417
\section*{Acknowledgment}
418
We are grateful to Hamamatsu Photonics K. K. for donating some of the
419
multianode photomultipliers used in the present laboratory course.
420
 
421
 
422
\begin{thebibliography}{99}  
423
 
424
%\section{Bibliography}
425
 
426
%\begin{enumerate}
427
\bibitem{Icfa}
428
%\item
429
S.Korpar, P.Kri\v zan, A.Gori\v sek, A.Stanovnik,
430
Tests of a position sensitive photomultiplier and measurement of diffraction
431
pattern by counting single photons,\\
432
ICFA'99 Instrumentation School, Istanbul, Turkey, AIP Conference Proceedings,
433
Vol. 536, p. 340-348
434
\bibitem{Knoll}
435
%\item
436
G.F.Knoll, Radiation Detection and Measurement, John Wiley, 1989
437
\bibitem{Leo}
438
%\item
439
W.R.Leo, Techniques for Nuclear and Particle Physics Experiments,
440
Springer-Verlag, 1987
441
\bibitem{Debbe}
442
%\item
443
R. Debbe et al., In-beam tests of a Ring Imaging Cherenkov detector
444
with a multianode photomultiplier read-out,
445
Nucl. Inst. and Meth. in Phys. Res. {\bf A362}(1995)253-260
446
\bibitem{Krizan}
447
%\item
448
P.Kri\v zan et al., Tests of a Multianode PMT for the HERA-B RICH,\\
449
Nucl. Inst. and Meth. in Phys. Res. {\bf A394}(1997)27-34
450
\bibitem{Arino}
451
%\item
452
I.Arin\~ o et al., The HERA-B RICH, Nucl.Instr.Meth.Phys.Res.{\bf
453
A453}(2000)289-295
454
\bibitem{Akopov}
455
%\item
456
N.Akopov et al., The HERMES dual radiator ring imaging Cherenkov
457
detector, Nucl. Instr. Meth. Phys. Res. {\bf A479}(2002)511-530
458
\bibitem{Hama}
459
%\item
460
Hamamatsu Photonics K.K.,
461
Data Sheet of R5900-L16 and
462
Data Sheet of R5900-M16  
463
 
464
\bibitem{Hama-web}
465
http://www.hpk.co.jp/hp2e/products/Etd/PDFfiles/PMThd6E.pdf
466
 
467
\bibitem{Nappi}
468
%\item
469
E.Nappi, RICH detectors,
470
ICFA'99 Instrumentation School, Istanbul, Turkey, AIP Conference Proceedings,
471
Vol. 536, p. 60-86.
472
\bibitem{Eingedi}
473
%\item
474
Advances in Cherenkov Light Imaging Techniques and Applications,
475
eds. A.Breskin, R.Chechik, T.Ypsilantis,
476
Proceedings of the Third International Workshop on Ring Imaging Cherenkov
477
Detectors (RICH98), Ein Gedi, Dead Sea, Israel, November 15 -20, 1998,
478
Nucl. Instr. Meth. Phys. Res. {\bf A433}(1999)
479
%\end{enumerate}
480
 
481
\end{thebibliography}
482
\end{sloppypar}
483
\end{document}
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