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1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2%%% magic-tdas.tex -- template to write MAGIC-TDAS documents
3%%%-----------------------------------------------------------------
4%%% Kopyleft (K) 2000 J C Gonzalez
5%%% Max-Planck-Institut fuer Physik,
6%%% Foehringer Ring 6, 80805 Muenchen, Germany
7%%% E-mail: gonzalez@mppmu.mpg.de
8%%%-----------------------------------------------------------------
9%%% This program is free software; you can redistribute, copy,
10%%% modify, use it and its documentation for any purpose,
11%%% provided that the above copyright notice appear in all
12%%% copies and that both that copyright notice and this
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14%%%
15%%% This piece of code is distributed in the hope that it will
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17%%% implied warranty of FITNESS FOR A PARTICULAR PURPOSE.
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19%%% Although you can actually do whatever you want with this
20%%% file (following the copyright notice above), your are
21%%% strongly encouraged NOT to edit directly this file.
22%%% Instead, make a copy and edit the copy for your purposes.
23%%%
24%%% Modifying thie original file means that you actually have
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27%%% support :-)
28%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
29%%% Last update: Time-stamp: <Thu Mar 2 09:31:41 CET 2000>
30%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
31%
32\documentclass[12pt]{article}
33
34\usepackage{magic-tdas}
35
36%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
37%% BEGIN DOCUMENT
38%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
39\begin{document}
40
41%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
42%% Please, for the formatting just include here the standard
43%% elements: title, author, date, plus TDAScode
44%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
45\title{ The Reflector simulation program v.0.5 }
46\author{A.Moralejo\\
47 \texttt{<moralejo@pd.infn.it>}}
48\date{June 04, 2002\\}
49\TDAScode{MAGIC-TDAS 02-05\\ 020604/AMoralejo}
50%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
51
52%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
53\maketitle
54
55%% abstract %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
56\begin{abstract}
57In this document we provide a brief description of Reflector program
58(version 0.5) and a guide to install and run it.
59\end{abstract}
60
61%% contents %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
62\thetableofcontents
63
64\newpage
65
66%% body %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
67
68%------------------------------------------------------------
69\section{Introduction}
70
71The Reflector program was originally written by Jose Carlos Gonz\'alez
72and then improved by Harald Kornmayer. In September 2001 D. Bastieri
73and C. Bigongiari released a new version (v.0.4) to adapt it to a
74format change in the MMCS output. The Reflector program reads in MMCS
75output files (cerxxxxxx files from corsika) and writes an output file
76with the information about all the photons which reach the telescope
77focal plane (taking into account atmospheric and mirror absorption)
78and which are within the camera radius defined in the file
79{\bf magic.def}.
80
81%------------------------------------------------------------
82\section{Description of simulation}
83
84The main steps of the simulation are:
85
86\begin{enumerate}
87
88\item Atmospheric absorption.
89
90\item Checking if the photon hits the dish.
91
92\item Aluminum absorption.
93
94\item Determination of the mirror hitted.
95
96\item Mirror reflection.
97
98\item Checking if the photon is inside the camera borders.
99
100\item Calculation of photon arrival time on camera.
101
102\end{enumerate}
103
104The reflection of each mirror element is simulated in a realistic way
105by introducing a gaussian spread of the reflected photons positions on
106the camera plane. The sigma of this PSF is defined via the
107{\bf point\_spread} parameter in the telescope description file {\bf
108magic.def}, and has a value of 0.5 cm, which corresponds approximately
109to the quality of the MAGIC mirrors produced up to date. Also the
110possible misalignment of mirror elements is simulated (see section
111\ref{neededfiles}).
112
113\section{Notes on version 0.5}
114
115\begin{enumerate}
116
117\item An error was found by T. Hengstebeck in step 2 (see above) in version
1180.4. This was the main reason for the release of this corrected
119version 0.5. The error was in {\bf ph2cph.c}, and was a confusion between
120{\it CORSIKA}'s coordinate system and the coordinate system of the
121telescope. The error had no effect when the telescope was pointing at
122zenith, but resulted on a loss of photons (which should have been
123reflected), which became larger with increasing $\theta$. The
124fractions of lost photons were negligible up to $\theta \simeq
12510^\circ$ and then 0.006, 0.012, 0.019, 0.070, 0.286, 0.433
126respectively for $\theta = $ 15, 20, 25, 40, 60 and $70^\circ$.
127
128\item NEW VARIABLES: some variables which were unused in the event
129header of the output have changed meaning to incorporate
130some relevant items. The header size is the same as before, so this
131output files will be readable by all {\bf camera} versions at least up
132to 0.5. The twelve new variables (see header structure in section
133\ref{out}) are the following:
134%
135\begin{itemize}
136\item {\bf TelescopePhi, TelescopeTheta:} telescope orientation chosen in
137the input card (in degrees).
138\item {\bf ViewConeRadius:} if ViewConeRadius $> 0$, indicates the outer radius
139of the viewing cone chosen in {\it CORSIKA} via the \texttt{VIEWCONE}
140option for the random generation of the of the primaries' incidence
141directions. The inner radius is assumed 0, and the direction around
142which the cone is defined is given by the header variables {\bf ThetaMin},
143{\bf PhiMin} (which equal in that case {\bf ThetaMax}, {\bf PhiMax}). The
144\texttt{VIEWCONE} option should be the standard for MAGIC MC
145generation in the case of hadronic primaries. However, if ViewConeRadius
146is 0, it will mean that the \texttt{VIEWCONE} option has not been used and
147the generation of directions has been done in a ``square'' sky window
148{\bf (PhiMin, PhiMax), (ThetaMin, ThetaMax)}, as in older versions of
149{\it CORSIKA}.
150\item {\bf num\_mirrors:} total number of mirrors in the dish. For
151{\it historical} reasons we are using as default a dish with 920
152mirrors. This should perhaps be updated in the future to the final
153design with (may be) 956 mirrors. It is not a very critical detail,
154since the only difference will be a global change in the amount of
155light reaching the camera, and this amount depends also on other
156factors like mirror reflectivity (which in the real telescope will
157change with time).
158\item {\bf mean\_reflectivity:} mean value of the mirror reflectivity values
159in the range 270 - 610 nm, as read from the input file
160{\bf reflectivity.dat}. No spectral weighting is done on this mean, since at
161the time of the calculation the Cherenkov spectrum is not known by the
162program. In principle, we will still use a constant reflectivity value of 0.9,
163independent of wavelength, but this may change in the future to render
164the simulation more realistic.
165\item {\bf longi\_Nmax, logi\_t0, longi\_tmax, longi\_a, longi\_b, longi\_c,
166longi\_chi2:} longitudinal charged particle distribution
167parameters and $\chi^2$ of the fit. See {\it CORSIKA} manual for
168precise meaning of these (which changed slightly from version
1695.61 onwards). The most important of them is {\bf longi\_tmax}, the
170atmospheric depth (in g/cm$^2$) of the shower maximum.
171\end{itemize}
172%
173\item We added an option to tell the Reflector program where (in
174{\it CORSIKA}'s
175coordinates) the telescope should be placed (see section
176\ref{opt}). This is important because the cerxxxxxx files contain only
177the photons which reach the ground
178near the telescope (in the standard mode of production for MAGIC,
179those hitting a sphere of 20 m diameter centered on the telescope),
180and the previous versions of Reflector only worked if the
181telescope was placed at its default position (0,0). For certain
182studies it is sometimes necessary to shift the telescope to a
183different position (for instance, to generate showers with impact
184point fixed with respect to the telescope).
185
186\item In the magic.def file which comes with Reflector\_0.5 the value of the
187parameter {\bf camera\_width} (radius around the center of the camera
188beyond which the photons are not written to the Reflector output file)
189has been changed from 100 to 70 cm, which allows to reduce the size of
190the output files, while it is a value safe enough to keep all the
191photons needed by the camera program.
192
193\item Removed some useless bits of code: in previous versions a
194binary file, {\bf magic.def.mirr}, containing the mirror data was
195created once the ASCII file {\bf magic.def} was read. Later, everytime the
196Reflector was run, it read the mirror data from magi.def.mirr. Now
197magic.def.mirr has been suppressed and the data are always read from
198magic.def. Another obsolete file, {\bf focals.dat} has been removed
199from the {\bf Data/} directory.
200
201\end{enumerate}
202
203%------------------------------------------------------------
204\section{How to Install Reflector Program \label{installation}}
205
206You can get the current version of the Reflector Program from the
207MAGIC web page: \\
208{\bf http://hegra1.mppmu.mpg.de/MAGICWeb/ }\\
209You can find
210the latest public version of this program as tarred gzipped file in
211the Monte Carlo Download area (you need the usual password). You have to
212download the file reflector\_0.5.tar.gz and then follow the
213instructions below:
214
215\begin{description}
216\item[Decompress the file using:]
217 gunzip reflector*.tar.gz
218\item[Unpack the tar file with:]
219 tar xvf reflector*.tar
220\item[Make symbolic links running the script:]
221 refl-install
222\item[Go to the directory where the source files are:]
223 cd MagicProgs/Simulation/Detector/Reflector\_0.5/
224\item[Check if all dependencies are fulfilled:]
225 make depend
226\item[Compile the program:]
227 make
228\end{description}
229
230If everything goes right you should have an executable file called
231{\bf reflector}.
232
233%------------------------------------------------------------
234\section{How to Run Reflector Program \label{running}}
235
236You need a steering card to run the Reflector program. You can find an
237example in the {\bf MagicProgs/Simulation/Detector/Reflector\_0.5/input.card}
238file. You have to modify this file according to your needs (see below
239for instructions about steering card) and then run the program with the
240following statement:\\
241
242\hspace{1cm}{\bf reflector $<$ input.card}
243
244%------------------------------------------------------------
245\section{Needed Files \label{neededfiles}}
246
247The Reflector program needs some other files to run. These files are
248the following:
249\begin{itemize}
250\item {\bf magic.def}: contains the description of MAGIC telescope
251geometry, together with some other parameters needed by the Reflector
252program.
253\item {\bf axisdev.dat}: contains data to simulate the possible
254deviation of the spot of each single mirror on the camera plane due
255to its non perfect alignment. The values are x, y coordinates
256distributed at random (according to a gaussian with $\sigma \simeq
2570.5$ cm).
258\item {\bf reflectivity.dat}: contains the mirror reflectivity index as
259a function of the wavelength.
260\end{itemize}
261
262All these files are usually in the {\bf
263MagicProgs/Simulation/Detector/Data/} directory and in principle you
264should {\bf not} make any change in them.
265
266%------------------------------------------------------------
267\section{Steering Card}
268
269The steering card sets all the parameters and options
270to steer the reflection simulation. Each line of the steering card is
271a statement with its parameters, if it is the case. Lines beginning
272with \# are considered comments. The Reflector program parses all the
273lines sequentially. Then if you repeat a statement with different
274options only the last one will be considered.
275
276\subsection{Mandatory Commands}
277
278\begin{description}
279
280\item[reflector 0.5]
281
282 This statement must be the first line of the steering card
283 file. The Reflector program checks it to verify if it is reading
284 a steering card.
285
286\item[output\_file /disk99/reflex/Gamma\_0\_7\_1001to1010\_w0.rfl]
287
288 The output\_file command specifies the name and the
289 path of the output file. The path can be absolute, like in the
290 example above, or relative. Although any name can be used,
291 conventionally the Reflector program
292 output file name has the .rfl extension, and starts with
293 the primary particle name. The first number indicates the
294 zenith angle of the incident primaries, the second one
295 indicates the production site (7 is for Padua) and is related
296 to the random number generator seed used by CORSIKA. Then the run
297 number range is shown (10 runs in this case, from 1001 to
298 1010). Each run corresponds to 10000 showers. Finally, the
299 label "w0" means no wobble mode was used (telescope pointing
300 at the source). Alternatively, the "w+" or "w-" labels (only
301 in gamma files) refer to the two pointings in the
302 Wobble-observation mode (see TDAS 01-05 by W. Wittek).
303
304\item[ct\_file ../Data/magic.def]
305
306 The ct\_file statement defines where the program can find the
307 telescope characteristics. The path in the example above is
308 correct to run reflector in
309 MagicProgs/Simu\-la\-tion/De\-tector/Reflector\_0.5/ directory.
310 If you want to run it in a different directory you have to modify the
311 path accordingly.
312
313\item[atm\_model ATM\_CORSIKA]
314 The atm\_model statement says to the program what kind of
315 atmospheric absorption model to use. Possible choices are:
316 ATM\_CORSIKA, ATM\_ISO\-THERMAL, ATM\_90\-PER\-CENT and
317 ATM\_NO\-ATMO\-SPHE\-RE.
318
319\item[fixed\_target 0. 90.]
320
321 This statement fixes the telescope axis position. The first
322 number is the zenith angle $\theta$ (deg) while the second is
323 the azimuthal angle $\phi$ (deg). This corresponds to {\it
324 CORSIKA}'s definition of primary particle incident direction
325 (see {\it CORSIKA} manual). $\phi = 90^\circ$ means that the
326 telescope is pointing towards East (bear in mind that in {\it
327 CORSIKA} $(\phi, \theta)$ indicates the direction of the {\it
328 momentum} of the incident particle).
329
330
331\item[cer\_files]
332
333 All the lines following this statement are considered files to
334 be processed by the Reflector program, one for each line,
335 eventually with their paths (see the example below). Therefore this
336 command must be the last one.\\
337 \\
338 cer\_files\\
339 /disk99/cer001001\\
340 /disk99/cer001002\\
341 /disk99/cer001003\\
342 ........ \\
343 /disk99/cer001009\\
344 /disk99/cer001010\\
345 \\
346 The cer file name can be followed by two numbers, for example:
347 \\
348 /disk99/cer001001 376 5723\\
349 \\
350 In this case the program processes only the events between and
351 including the numbers given.
352
353\end{description}
354
355\subsection{Optional Commands \label{opt}}
356
357\begin{description}
358
359\item[verbose\_level 1]
360
361 Sets the quantity of information printed out by Reflector
362 when running. Possible values are 0 to 4
363
364\item[max\_events 50000]
365
366 Fixes the maximum number of events to process.
367
368\item[energy\_cuts 100 1000]
369
370 This statement forces the Reflector to process only showers
371 with primary energy between the given values (GeV).
372
373\item[seeds n1 n2]
374
375 Seeds for the random number generators to used by the program
376 for the simulation of the absorption (both in the atmosphere
377 and on the mirror). Default values are 3141592 and
378 2718182.
379
380\item[telescope\_position x y]
381
382 Option included in version 0.5 of Reflector. Usually it is
383 not needed, since for normal MC production for MAGIC the
384 telescope is placed at the origin of coordinates (0,0). But,
385 if for some reason, we produce cerxxxxxx files with the
386 telescope in a different position, we must inform the
387 Reflector program in the input card using this option
388 (otherwise Reflector will fail to {\it find} the photons
389 in the cer file).
390
391\item[reflectivity\_file /path/reflectivity.dat]
392
393 File containing mirror reflectivity as a function of
394 wavelength (see section \ref{neededfiles}). If this option is
395 not supplied, the program will look for
396 ``../Data/reflectivity.dat'' as previous versions of
397 Reflector did.
398
399\item[axisdev\_file /path/axisdev.dat]
400
401 File containing single mirror spot deviation in {\bf x} and
402 {\bf y} on the camera in cm (see section
403 \ref{neededfiles}) for each mirror. If this option is not
404 supplied, the program will look for ``../Data/axisdev.dat''
405 as previous versions of Reflector did.
406
407\end{description}
408
409%------------------------------------------------------------
410\section{Output file \label{out}}
411
412The output file begins with some ascii lines:\\
413\\
414\verb"reflector 0.5" \\
415\verb"START---RUN" \\
416\verb"START-EVENT" \\
417After the \verb"START-EVENT" flag there is a blank line and then the
418binary event header, which contains the following informations (each
419variable is a 4-byte float number):
420\\
421
422\begin{tabular}{ll}
423
424Variable & Description \\
425\hline
426
427EvtNumber & Event Number \\
428PrimaryID & Primary particle identification code \\
429Etotal & Primary particle total energy (GeV) \\
430Thick0 & CORSIKA's starting altitude in g/cm2 \\
431FirstTarget & CORSIKA's number of first target if fixed \\
432zFirstInt & Height of first interaction in cm \\
433p[3] & Primary particle momentum in x,y,-z directions (GeV) \\
434Theta & Primary particle zenith angle (rad) \\
435Phi & Primary particle azimuth angle (rad) \\
436
437NumRndSeq & Number of different CORSIKA random sequences (max. 10) \\
438RndData[10][3] & RndData[i][0]: integer seed of sequence i \\
439 & RndData[i][1]: number of offset random calls (mod
440$10^6$) of sequence i. \\
441 & RndData[i][2]: number of offset random calls ($/
44210^6$) of sequence i. \\
443
444RunNumber & Run number \\
445DateRun & Date of run yymmdd \\
446Corsika\_version & Version of {\it CORSIKA} \\
447
448NumObsLev & Number of observation levels (should be always 1 for
449us) \\
450HeightLev & Height of observation level in cm \\
451num\_mirrors & Number of mirrors \\
452mean\_reflectivity & Mean reflectivity between 270 and 610 nm \\
453& \\
454& 6 next variables: CORSIKA longitudinal particle fit parameters \\
455& \hspace{0.5cm} (see CORSIKA manual for precise meaning and units)\\
456longi\_Nmax & Numer of charged particles at maximum \\
457longi\_t0 & Atmospheric depth of shower starting point (N=0) \\
458longi\_tmax & Atmospheric depth of shower maximum (g/cm$^2$) \\
459longi\_a & \\
460longi\_b & For {\bf longi\_a}, {\bf longi\_b}, {\bf longi\_c}, see CORSIKA manual \\
461longi\_c & \\
462longi\_chi2 & $\chi^2/dof$ of the fit\\
463& \\
464SlopeSpec & Energy spectrum slope \\
465ELowLim & Energy lower limit (GeV) \\
466EUppLim & Energy upper limit (GeV) \\
467
468ThetaMin & Minimum Theta of primaries (deg) \\
469ThetaMax & Maximum Theta of primaries (deg) \\
470PhiMin & Minimum Phi of primaries (deg) \\
471PhiMax & Maximum Phi of primaries (deg) \\
472
473CWaveLower & Wavelength lower limit (nm) \\
474CWaveUpper & Wavelength upper limit (nm) \\
475CorePos[2][20] & Core positions of randomized shower \\
476TimeFirst & Arrival time on camera of first photon (ns) \\
477TimeLast & Arrival time on camera of last photon (ns) \\
478
479 & Next three variables changed meaning in version 0.5: \\
480
481telescopePhi & Telescope azimuth (rad). Measured from South, counter-clockwise \\
482telescopeTheta & Telescope zenith angle (rad) \\
483
484ViewConeRadius & Outer radius (deg) in {\it CORSIKA}'s VIEWCONE
485option, if used. Inner r is assumed 0.\\
486
487
488\hline
489\end{tabular}
490%
491\newpage
492%
493\begin{tabular}{ll}
494
495Variable & Description \\
496\hline
497
498
499CORSIKAPhs & Original photons written by {\it CORSIKA} \\
500AtmAbsPhs & Photons absorbed by the atmosphere \\
501MirrAbsPhs & Photons absorbed by the mirror \\
502OutOfMirrPhs & Photons outside the mirror \\
503BlackSpotPhs & Photons lost in the "black spot" \\
504OutOfChamPhs & Photons outside the camera \\
505CPhotons & Photons reaching the camera \\
506
507\hline
508\end{tabular}
509
510\vspace*{1cm}
511The event header is followed by 8-word blocks, one for each photon
512that reaches the camera. A photon block contains the following
513variables:
514
515\begin{tabular}{ll}
516Variable & Description \\
517\hline
518w & Wavelength (nm) \\
519x, y & Impact point in camera coordinates (cm) \\
520u, v & Director cosines \\
521t & Arrival time on camera (ns) \\
522h & Production height (cm) \\
523phi & Incidence angle with respect to camera plane (rad) \\
524\hline
525\end{tabular}
526
527After the last event photon block there is a blank line, an \verb$END---EVENT$
528flag, another blank line and then the following event. After the last
529event in a run it appears the flag \verb$END-----RUN$, while after every
530processed runs, you can find a \verb$END----FILE$ flag.
531
532
533%------------------------------------------------------------
534
535\section{Future improvements}
536Possible improvements of the reflector simulation could be:
537\begin{enumerate}
538\item Introduce dependence of mirror reflectivity as a function of
539wavelength using recent measurements performed on real mirrors.
540\item Adittion of a Run header: some parameters which are the same for
541each run are still kept (again for historical reasons) in the event
542header. It would be better to move them to a Run header. This has not
543yet been implemented in this version in order to make it compatible with
544the corresponding version of the {\it camera} program. I would also
545allow to include more detailed information on the used telescope
546geometry (number and position of mirrors) and reflectivity (as a
547function of wavelength).
548\end{enumerate}
549\par
550Please contact \texttt{moralejo@pd.infn.it}. for suggestions on other
551features to be implemented in future versions.
552
553\section{Appendix}
554
555The list of all Reflector files follows.
556\begin{verbatim}
557
558refl-install
559
560MagicProgs/Simulation/Detector/Reflector_0.5/Makefile
561MagicProgs/Simulation/Detector/Reflector_0.5/atm.c
562MagicProgs/Simulation/Detector/Reflector_0.5/atm.h
563MagicProgs/Simulation/Detector/Reflector_0.5/attenu.f
564MagicProgs/Simulation/Detector/Reflector_0.5/config.mk.linux
565MagicProgs/Simulation/Detector/Reflector_0.5/config.mk.linux-gnu
566MagicProgs/Simulation/Detector/Reflector_0.5/config.mk.osf1
567MagicProgs/Simulation/Detector/Reflector_0.5/diag.c
568MagicProgs/Simulation/Detector/Reflector_0.5/diag.h
569MagicProgs/Simulation/Detector/Reflector_0.5/geometry.c
570MagicProgs/Simulation/Detector/Reflector_0.5/geometry.h
571MagicProgs/Simulation/Detector/Reflector_0.5/header.c
572MagicProgs/Simulation/Detector/Reflector_0.5/header.h
573MagicProgs/Simulation/Detector/Reflector_0.5/init.c
574MagicProgs/Simulation/Detector/Reflector_0.5/init.h
575MagicProgs/Simulation/Detector/Reflector_0.5/input.card
576MagicProgs/Simulation/Detector/Reflector_0.5/lagrange.h
577MagicProgs/Simulation/Detector/Reflector_0.5/parms.c
578MagicProgs/Simulation/Detector/Reflector_0.5/parms.h
579MagicProgs/Simulation/Detector/Reflector_0.5/ph2cph.c
580MagicProgs/Simulation/Detector/Reflector_0.5/reflector.c
581MagicProgs/Simulation/Detector/Reflector_0.5/version.h
582
583MagicProgs/Simulation/Detector/Reflector_0.5/doc/magic-tdas.sty
584MagicProgs/Simulation/Detector/Reflector_0.5/doc/magiclogo.eps
585MagicProgs/Simulation/Detector/Reflector_0.5/doc/Tdas0205.ps
586MagicProgs/Simulation/Detector/Reflector_0.5/doc/Tdas0205.tex
587
588MagicProgs/Simulation/Detector/Data/axisdev.dat
589MagicProgs/Simulation/Detector/Data/magic.def
590MagicProgs/Simulation/Detector/Data/reflectivity.dat
591
592
593\end{verbatim}
594
595%%% BIBLIOGRAPHY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
596
597%%>>>> Use the following if you are using BibTeX for bibliography
598%\theBibliography
599
600%%>>>> Or the following if you include here by hand your
601%%>>>> bibliographic entries
602
603\end{document}
604%
605%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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620%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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625%% time-stamp-line-limit:100
626%% End:
627%% EOF
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