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2\documentclass{icrc}
3
4\usepackage{times}
5\usepackage{graphicx} % when using Latex and dvips
6%                       % (the latter best with option -Pcmz, if available,
7%                       % to invoke Type 1 cm fonts)
8%\usepackage[pdftex]{graphicx} % when using pdfLatex (preferred)
9
10\begin{document}
11
12\title{Detailed Monte Carlo studies for the MAGIC telescope}
13\author[1]{O. Blanch}
14\affil[1]{IFAE, Barcelona, Spain}
15\author[2]{J.C.  Gonzalez}
16\affil[2]{Universidad Complutense Madrid, Spain}
17\author[3]{H. Kornmayer}
18\affil[3]{Max-Planck-Institut f\"ur Physik, M\"unchen, Germany}
19
20\correspondence{O.Blanch (blanch@ifae.es), H. Kornmayer (h.kornmayer@web.de)}
21\affil[ ]{ }
22\affil[ ]{\large (for the MAGIC Collaboration)}
23
24
25
26\firstpage{1}
27\pubyear{2001}
28
29% \titleheight{11cm} % uncomment and adjust in case your title block
30                     % does not fit into the default and minimum 7.5 cm
31
32\maketitle
33
34\begin{abstract}
35For understanding the performance of the MAGIC telescope a detailed
36simulation of air showers and of the detector response are
37indispensable. Such a simulation must take into account the development
38of the air showers in the atmosphere, the reflectivity of the mirrors,
39the response of photo detectors
40and the influence of both the light of night sky and the light of 
41bright stars.
42A detailed study is presented.
43\end{abstract}
44
45\section{Introduction}
46
47The $17~\mathrm{m}$ diameter
48Che\-ren\-kov telescope called MAGIC
49is presently in the construction stage \cite{mc98}.
50The aim of this
51detector is the observation of $\gamma$-ray sources in the
52energy region above $\approx 30~\mathrm{GeV}$ in its first phase.
53The air showers induced by cosmic ray particles (hadrons and gammas)
54will be detected with a "classical" camera consisting of 576
55photomultiplier tubes (PMT). The analog signals of these PMTs will
56be recorded by a FADC system running with a frequency of
57$f = 333~\mathrm{MHz}$.
58The readout of the FADCs will be started
59by a dedicated trigger system containing
60different trigger levels.
61
62The primary goal of the trigger system is the selction of showers.
63For a better understanding of the MAGIC telescope and its different
64systems (trigger, FADC) a detailed Monte Carlo (MC) study is
65neccessary. Such a study has to take into account the simulation
66of the air showers, the effect of absorption in the atmosphere, the
67behaviour of the PMTs and the response of the trigger and FADC
68system.
69 
70An important issue for a big telescope like MAGIC
71is the light of the night sky.
72There will be around 50 stars with magnitude $m \le 9$ in the
73field of view of the camera.
74Methods have to be developed which allow to
75reduce the biases introduced by the presence of stars.
76The methods can be tested by using Monte Carlo data.
77
78
79Here we present the first results of such an investigation.
80
81\section{Generation of MC data samples} 
82
83The simulation is done in several steps:
84First the
85air showers are simulated with the
86CORSIKA program \citep{hk95}.
87In the next step we simulate the reflection of the
88Cherenkov photons on the mirror dish.
89Then the behaviour of the PMTs is simulated and the
90response of the trigger and FADC system is generated.
91In the following subsections
92the various steps are described in more details.
93
94\subsection{Air shower simulation}
95
96The simulation of gamma and of hadron showers in the
97atmosphere is done with
98the CORSIKA program, version 5.20.
99As the had\-ro\-nic interaction model 
100we use the VENUS model.
101We simulate showers
102for different zenith angles
103($\Theta = 0^\circ, 5^\circ$, $ 10^\circ, 15^\circ,
10420^\circ, 25^\circ $) at fixed azimuthal angle $\Phi$.
105Gammas are assumed to originate from point sources
106in the direction ($\Theta$,$\Phi$)
107whereas the hadrons are simulated isotropically
108around the given ($\Theta$,$\Phi$) direction in a
109region of the solid angle corresponding to the FOV
110of the camera.
111The trigger probability for hadronic showers with
112a large impact parameter $I$ is not negligible.
113Therefore we
114simulate hadrons with $I < 400~\mathrm{m}$ and gammas
115with $I < 200~\mathrm{m}$.
116The number of generated showers can be found in table
117\ref{tab_showers}.
118%
119%
120%
121\begin{table}[b]
122\begin{center}
123  \begin{tabular}{|c||r|r||}
124    \hline
125    zenith angle & gammas & protons \\
126    \hline \hline
127        $\Theta = 0^\circ$  &  $\approx 5 \cdot 10^5$ &  $\approx 1 \cdot 10^6$ \\
128        $\Theta = 5^\circ$  &  $\approx 5 \cdot 10^5$ & $\approx 1 \cdot 10^6$  \\
129        $\Theta = 10^\circ$ &  $\approx 5 \cdot 10^5$ & $\approx 1 \cdot 10^6$  \\
130        $\Theta = 15^\circ$ &  $\approx 2 \cdot 10^6$    &  $\approx 5 \cdot 10^6$  \\
131        $\Theta = 20^\circ$ &  in production   &  in production  \\
132        $\Theta = 25^\circ$ &  in production   &  in production  \\
133    \hline
134  \end{tabular}
135\end{center}
136\caption {Number of generated showers.}
137\label{tab_showers}
138\end{table}
139%
140%
141%
142For each simulated shower all
143Cherenkov photons hitting a horizontal plane at the
144observation level
145close to the telescope position are stored.
146
147\subsection{Atmospheric and mirror simulation}
148
149The output of the air shower simulation is used
150as the input to this step.
151First the absorption in the atmosphere is taken into
152account.
153Using the height of production and the
154wavelength of each Cherenkov photon the effects of Rayleigh
155and Mie scattering are calculated.
156Next the reflection at the mirrors is simulated. 
157We assume a reflectivity of the mirrors of around 85\%.
158Each Cherenkov photon hitting a mirror is propagated
159to the camera plane of the telescope. This procedure
160depends on the orientation of the telescope relative
161to the shower axis.
162All Cherenkov photons reaching the camera plane will be
163kept for the next simulation step.
164
165\subsection{Camera simulation}
166
167The simulation comprises the behaviour of the PMTs and the
168electronics of the trigger and FADC system.
169We take the wavelength dependent quantum
170efficiency (QE) for each PMT into account.
171In figure \ref{fig_qe} 
172the QE of a typical MAGIC  PMT is shown.
173%
174%
175%
176\begin{figure}[hb]
177 \vspace*{2.0mm} % just in case for shifting the figure slightly down
178 \includegraphics[width=8.3cm]{qe_123.eps} % .eps for Latex,
179                                            % pdfLatex allows .pdf, .jpg, .png and .tif
180 \caption{quantum efficency of the PMT for pixel 123}
181 \label{fig_qe}
182\end{figure}
183%
184%
185%
186For each photo electron (PE) leaving the photo cathode we
187use a "standard" response function to generate 
188the analog signal of that PMT - separatly for the
189trigger and the FADC system.
190At present these response functions are gaussians with
191a given width in time.
192The amplitude of the response function is chosen randomly
193according to the distribution shown in figure \ref{fig_ampl}
194(\cite{ml97}).
195 
196By superimposing all photons of one pixel and by taking
197the arrival times into account the response
198of the trigger and FADC system for that pixel is computed
199(see also figure \ref{fig_starresp}).
200This is done for all pixels in the camera.
201
202The simulation of the trigger electronic starts by checking
203whether the generated analog signal exceeds the discriminator
204threshold.
205In that case a digital output
206signal of a given length (6 nsec.)
207for that pixels is generated.
208By checking next neighbour conditions (NN) at a given time
209the first level trigger is simulated.
210If a given NN condition (multiplicity, topology, ...)
211is fullfilled, a first level trigger signal is generated and
212the
213content of the FADC system is written to disk.
214%
215%
216%
217\begin{figure}[t]
218 \vspace*{2.0mm} % just in case for shifting the figure slightly down
219 \includegraphics[width=8.3cm]{ampldist.eps} % .eps for Latex,
220                                            % pdfLatex allows .pdf, .jpg, .png and .tif
221 \caption{The distibution of the amplitude of the standard response
222 function.}
223 \label{fig_ampl}
224\end{figure}
225%
226%
227%
228
229\subsection{Starlight simulation}
230
231Due to the big mirror area MAGIC will be sensitive to stars up to a
232magnitude of 10.
233These stars will contribute locally to the noise in the
234camera and have to be taken into account.
235A program was developed to simulate the star light together
236with the generated showers.
237This program considers all stars in the field of view of the camera
238around a chosen direction. The light of these stars is traced up to
239the camera taking the wavelength of the light into account.
240After simulating the response of the photo cathode, we
241get the number of emitted photo electrons per pixel and
242time.
243
244These number are used to generate a noise signal for all the pixels.
245%
246%
247%
248\begin{figure}[h]
249 \vspace*{2.0mm} % just in case for shifting the figure slightly down
250 \includegraphics[width=8.3cm]{signal.eps} % .eps for Latex,
251                                            % pdfLatex allows .pdf, .jpg, .png and .tif
252 \caption{The response of a pixel due to a star with magnitude
253 $m=7$ in the field of view. On the left plot the analog signal that goes into
254 the trigger system is plotted while on the right plot the content in the
255 FADC system is shown.}
256 \label{fig_starresp}
257\end{figure}
258%
259%
260%
261In figure \ref{fig_starresp} the response of the trigger and the
262FADC system can be seen for a pixel with a star of
263magnitude $m = 7$.
264These stars are typical, because there will
265be on average one $7^m$ star in the trigger area of the camera.
266
267
268\section{Results}
269
270
271
272\subsection{Trigger studies}
273
274The trigger system will consist of different
275trigger levels.
276The discriminator of each channel is called the
277zero-level-trigger.
278If a given signal exceeds the discriminator threshold
279a digital output signal of a given length is produced.
280So the important parameters of such a system are the
281threshold of each discriminator and the length of the
282digital output.
283
284The first-level-trigger checks in the digital output of the
285271 pixels of the trigger system for next neighbor (NN)
286conditions. 
287The adjustable settings of the first-level-trigger
288are the mulitiplicity, the topology and the minimum required
289overlapping time.
290
291The second-level-trigger of the MAGIC telescope will be based
292on a pattern-recognition method.
293This part is still in the design phase.
294All results presented here refer to the
295first-level-trigger. If not stated explicitly otherwise,
296the MC data are produced with "standard"
297values (discriminator threshold = 4 mV, gate length = 6 nsec,
298multiplicity = 4, topology of NN = {\sl closed package}).
299
300
301 
302\subsubsection{Trigger collection area}
303
304
305
306The rigger collection area is defined as the integral
307\begin{equation} 
308  A(E,\Theta)  = \int_{F}{ T(E,\Theta,F) dF}
309\end{equation} 
310where T is the trigger probablity. F is a plane perpendicular
311 to the telescope axis. 
312The results for different zenith angles $\Theta$ and
313for different discriminator thresholds are shown in figure
314\ref{fig_collarea}.
315%
316%
317%
318\begin{figure}[h]
319 \vspace*{2.0mm} % just in case for shifting the figure slightly down
320 \includegraphics[width=8.3cm]{collarea.eps} % .eps for Latex,
321                                            % pdfLatex allows .pdf, .jpg, .png and .tif
322 \caption{The trigger collection area for gamma showers as a function
323 of energy $E$.}
324 \label{fig_collarea}
325\end{figure}
326%
327%
328At low energies ($ E < 100 ~\mathrm{GeV}$), the trigger collection
329area decreases with increasing zenith angle , and it decreases with
330increasing discriminator threshold.
331 
332
333\subsubsection{Energy threshold}
334
335The threshold of the MAGIC telescope is defined as the peak
336in the $dN/dE$ distribution for triggered showers.
337This value is determined
338for all different trigger settings.
339The energy threshold could
340depend among other variables on the background conditions,
341the threshold of the trigger discriminator and the zenith angle. We
342check the dependence on these three variables.
343
344For both, gammas and protons, some different background conditions
345have been simulated (without any background light, diffuse light,
346and light from Crab Nebula field of view).
347No significant variation of the energy threshold is observed.
348It should be stressed that this is based only on first level
349triggers.
350Most likely some effects will be seen after the second
351level trigger and the shower reconstruction.
352
353MAGIC will do observations in a large range of zenith angles,
354therefore it is worth studying the energy threshold as function of
355the zenith angle (see figure \ref{fig_enerthres}).
356Even though larger statistic is needed, the energy
357threshold increases slowly with the zenith angle, as expected.
358\begin{figure}[hb]
359 \vspace*{2.0mm} % just in case for shifting the figure slightly down
360 \includegraphics[width=8.3cm]{enerthres.eps} % .eps for Latex,
361                                            % pdfLatex allows .pdf, .jpg, .png and .tif
362 \caption{On the left upper plot the energy threshold for diffrent
363 zenith angles is plotted while on the left bottom plot the energy
364threshold is plotted for several values of the trigger discriminator
365threshold. On the right plot a characteristic fit for $dN/dE$ is shown
366(for showers at $10^\circ$ with discriminator at 4 mV and diffuse NSB
367of 0.09 photo electrons per ns and pixel)}
368 \label{fig_enerthres}
369\end{figure}
370
371If one lowers the threshold of the trigger discriminator, then less
372photons in the camera plane are needed to trigger the telescope,
373and it helps the low energy showers to fulfil the required trigger
374conditions.
375In figure  \ref{fig_enerthres} one can see that the threshold
376energy decreases when lowering the discriminator threshold.
377It is 29 GeV for 3 mV and 105 GeV  for 7 mV.
378Since we are aiming for a low energy threshold,
379a low discriminator value is  preferred.
380However, for 3 mV the expected rate due to protons together with night
381sky background light increases a
382lot (see section ~\ref{sec-rates}), while it is kept
383under control at 4 mV.
384Therefore, the threshold of the discriminator should be kept
385around 4 mV, which yields an energy threshold of 45 GeV.
386
387\subsubsection{Expected rates}\label{sec-rates}
388
389Using the Monte Carlo data sample, it is possible to estimate
390the expected rates for proton showers  taking into account the
391background light.
392
393The numbers quoted in this section are calcuated for a zenith angle
394of $10^\circ$.
395The results for $0^o$ and $15^o$ were found to be similar.
396We estimated the rate for the first level trigger
397with the "standard" trigger conditions. 
398The first level trigger rate due to proton showers without any
399background is $143 \pm 11~\mathrm{Hz}$.
400This rate will increase by $\approx 25$\% if heavier nuclei (He,
401Li,...) are included.
402 
403
404However, to get a more reliable rate one must take into account
405a realistic background situation.
406From the total mirror area, the integration time, the FOV of a pixel
407and the QE of the PMTs one obtains a value of 0.09 photo electrons per
408ns and pixel \citep{ml94} due to the diffuse night sky background.
409Added to this are the contributions from the star field around the
410Crab nebula.
411Under these more realistic conditions the first level trigger
412background rate (protons and light of night sky) is $396 \pm 88$ Hz.
413
414The dependence of the first level trigger rate on the discriminator
415threshold is shown in figure \ref{fig_rates}
416The trigger rate decreases
417with increasing discriminator threshold as expected.
418The rate for the discriminator threshold of 3 mV is more than 100
419times larger than that for higher thresholds.
420\begin{figure}[hb]
421 \vspace*{2.0mm} % just in case for shifting the figure slightly down
422 \includegraphics[width=8.3cm]{rates.eps} % .eps for Latex,
423                                            % pdfLatex allows .pdf, .jpg, .png and .tif
424 \caption{Estimated trigger rates as a function of trigger discriminator for $10^\circ$ zenith angle with 0.09 photo electrons of diffuse NSB and the Crab Nebula star field.}
425 \label{fig_rates}
426\end{figure}
427
428Some improvement in the trigger rate reduction is needed to lower the
429discriminator that the MAGIC telescope will use, below 4 mV. This value
430corresponds to a threshold of about 8 photo electrons.
431
432It has to be stressed, that these results are based on
433the first level trigger. There is a big potential in optimizing the
434settings. I.e. the background rate can be reduced by
435increasing the discriminator threshold for a few dedicated pixels,
436that have a star in their field of view. Studies in this direction are
437ongoing and will be presented on the conference.
438
439\section{Conclusion}
440
441We presented the actual status of Monte Carlo simulation for the MAGIC
442telescope. The first level trigger rate for the background is for a
443discriminator threshold of 4~mV well below the maximal trigger rate
444(1000 Hz) that the MAGIC daq system will be able to handle.
445For these standard settings the energy threshold is around 45 GeV.
446There is a potential in optimizing the trigger system and studies in
447this direction are ongoing. Also the development of the
448second-level-trigger is in progress. This should allow to lower the
449threshold and achieve the aim of 30 GeV for the energy threshold.
450The MAGIC collaboration is presently simulating air showers with
451higher zenith angles.
452The newest results will be presented on
453the conference.
454
455
456\begin{acknowledgements}
457The authors thank all the "simulators" of the MAGIC collaboration
458for their support in the production of the big amount of Monte Carlo
459data. We thank also M. Dosil and D. Petry for writing the Star field
460adder program. The support of MAGIC by the BMBF (Germany), the INFN
461and MURST (both italy) and the CYCIT
462(Spain) is acknowledged.
463
464
465\end{acknowledgements}
466
467%\appendix
468%
469%\section{Appendix section 1}
470%
471%Text in appendix.
472%
473
474\begin{thebibliography}{99}
475
476\bibitem[(MAGIC 1998)]{mc98}
477MAGIC Collaboration, "The MAGIC Telescope, Design Study for
478the Construction of a 17m Cherenkov Telescope for Gamma
479Astronomy Above 10 GeV", Preprint MPI-PhE 18-5, March 1998.
480
481\bibitem[Heck and Knapp(1995)]{hk95}
482Heck, D. and Knapp J., CORSIKA Manual, 1995.
483
484\bibitem[Mirzoyan and Lorenz(1997)]{ml97}
485Mirzoyan R. and E. Lorenz, Proc. 25th ICRC, Durban, 7, p.356, 1997
486
487\bibitem[Mirzoyan and Lorenz(1994)]{ml94}
488Mirzoyan R. and E. Lorenz, Measurement of the night sky light background
489at La Palma, Max-Planck-Institut report MPI-PhE/94-35
490
491\end{thebibliography}
492
493\end{document}
494
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