Experimental Installations

Appendix A Experimental Installations

A.1 EAS Arrays and Cosmic Ray Ground Facilities

A.1.1 Lists of Array and Facility Sites

In the following we present a list of air shower arrays of the past and present (Table A.1). The altitudes of the arrays are listed together with the corresponding atmospheric depths. The latter are in most cases the vertical atmospheric depths, i.e., the average vertical overburden [g cm−2]. In some cases, however, authors may specify different values for the overburden in different publications for the same array. The reason for these discrepancies is that in some cases authors consider the slant depth for the average near vertical shower, e.g., ∼15◦, as compared to the depth for perfectly vertical showers, that are rather rare exceptions in practice. Some table entries with similar altitudes suggest contradicting altitude-overburden relations, but these are explained by differing average atmospheric and meteorological conditions (see Sect. B.3). Figure A.1, which is a reproduction from a web page of the Yakutsk group, shows the aperture in units of square kilometer-steradian [km2 sr] of the largest air shower arrays of the past and present, and of arrays and detector systems currently under construction or in the planing phase. In Table A.2 we list emulsion chamber sites, and in Table A.3 the threshold energies of the muon detectors of some of the arrays listed in Table A.1. Note that for some arrays different threshold energies were used simultaneously, in others different thresholds at different times. Table A.4 is a partial list of major gamma ray air Cherenkov detectors of past and present.

P.K.F. Grieder, Extensive Air Showers, DOI 10.1007/978-3-540-76941-5 22, 1035 C Springer-Verlag Berlin Heidelberg 2010 1036 A Experimental Installations

Table A.1 EAS array sites and experiments of past and present Name, place, country (nearest major city, region) Approximate Altitude a.s.l. Atmospheric depth [m] [g cm−2] AGASA, Akeno (Kofu) Japana 900 935 Agassiz, (Boston) USAa 183 1,020 ANI/MAKET Mt. Aragats, (Yerevan), Armenia 3,200 700 ARGO, Yangbajing, (Lhasa), Tibet, Chinab 4,370 606 Auger South, (Malargue),¬ Argentina 1,300Ð1,400 875 Auger North, (Lamar) Colorado, USAd ∼1,500 ∼865 Bagneres` de Bigorre, Francea 456 965 Baksan, Kabardian-Balkarian Rep., Russiac 2,060 805 Buckland Park, (Adelide), SA, Australia s.l. 1,033 CASA/MIA, (Dugway), Utah, USAa 1,435 870 Chacaltaya, (La Paz), Bolivia 5,230 530 Cornell, (Ithaca), NY, USAa 260 998 Cygnus, (Los Alamos), New Mexico, USAa 2,220 800 Darjeeling, India (Exp. at Siliguri, s.l.) 2,200 802 Dugway, Utah, USA (Durham (GB) Exp.)a 1,450 865 Durham, Englanda 60 1,025 EAS-Top, Gran Sasso, Italya 2,005 810 Echo Lake, Colorado, USAa 3,260 715 El Alto, (La Paz), Boliviaa 4,200 630 Elbrus Laboratory 1,850 820 Evans, Mt., (Denver) Colorado, USAa 4,300 615 Fly’s Eye 1, (Dugway), Utah, USAa 1,585 860 Fly’s Eye 2, (Dugway), Utah, USAa 1,435 870 GAMMA, (Yerevan), Armenia 3,200 700 GRAND, (Notre Dame), Indiana, USA 220 1,018 GRAPES, Ootacamund (Mysor), India 2,200 800 GREX, Haverah Park, (Leeds), Englanda 220 1,018 Gulmarg, (Srinagar), Kashmir, Indiaa 2,743 740 Haverah Park, (Leeds), Englanda 212 1,018 HEGRA, La Palma, Canary Islandsa 2,250 800 Homestake, South Dakota, USAa 1,615 843 Issyk-Kul Lake, (Almaty), Kazakhstanb 1,600 845 JANZOS, New Zealanda 1,640 840 KASCADE-Grande, Karlsruhe, Germanya 110 1,022 Kiel, Germanya s.l. 1,033 Kobe, Japan s.l. 1,033 KGF, Kolar Gold Fields, (Karnataka), Indiaa 920 920 L3+C (CERN, Geneva) Switzerlanda 374 1,000 Liang Wang, Mt., Yun-Nan, Chinab 2,720 735 Lodz, Polanda 230 1,000 MILAGRO, (Los Alamos), N.M., USA 2,630 750 Moscow, Russia 192 1,020 Musala Mountain, Bulgariaa 2,925 713 NASCA, see Akeno Ð Ð Norikura, Mt., (Matsumoto), Japana 2,770 750 Ohya, (Nikko), Japana 149 1,020 Ootacamund, (Mysore), India 2,200 800 Pamir (old), Tadzhikistana 3,860 650 Pamir (new), Tadzhikistan 4,380 590 A.1 EAS Arrays and Cosmic Ray Ground Facilities 1037

Table A.1 (continued) Name, place, country (nearest major city, region) Approximate Altitude a.s.l. Atmospheric depth [m] [g cm−2] Pic du Midi, Pyrenees, Francea 2,860 729 Samarkand, Uzbekistan 750 958 SPASEa, SPASE-II, South Pole 3,300 695 SPICA, see Akeno Ð Ð SUGAR, (Narrabri), Australiaa 260 998 Sulphur Mountain, Alberta, Canadaa 2,285 800 Sydney, Australiaa 30 1,016 Telescope Array, Dugway, Utah, USA 1,400 865 Tibet, Yangbajing, (Lhasa) 4,370 606 Tien Shan, (Almaty), Kazakhstan 3,340 690 Tokyo, INS, Japana 59 1,020 TUNKA-133, (Baikal), Russiab 675 960 UMC array, see CASA/MIA/Fly’s Eyea ÐÐ Verrieres` (Paris), Francea 100 1,020 Volcano Ranch, (Albuquerque), N.M., USAa 1,768 834 Yakutsk, Siberia, Russia 105 1,020 a Shut-down. b Under construction or partial operation. c 1,700 m a.s.l. for underground laboratory. d In planning phase or proposed. Note: Some of the atmospheric depths listed above do not correspond exactly to the vertical air column at the speciﬁed altitude, but to the effective air column of an incident trajectory subtend- ing a mean zenith angle of about 10Ð15◦. This zenith angular cut is frequently used to select a reasonable number of quasi vertical events for analysis.

107

6 JEM-EUSO 10 OWL

105

sr] Auger 2 104 HiRes

Telescope Array 103 Fly's Eye

Aperture [km SUGAR 102 AGASA Yakutsk Haverah Park 101 Volcano Ranch 100 1950 1960 1970 1980 1990 2000 2010 2020 Array Operation [y] Fig. A.1 Apertures of the large arrays of the past and present, of arrays under construction or expansion, and of the proposed JEM-EUSO and OWL satellite based detector systems (curtesy of the Yakutsk Group) 1038 A Experimental Installations

Table A.2 Emulsion chamber sites Name, place, country Approximate (nearest major city, region) Altitude a.s.l. [m] Atmospheric depth [g cm−2] Chacaltaya, (La Paz), Boliviaa 5,230 530 Fuji, Mt., Japan 3,776 650 Kanbala, Mt., Tibet, Chinab 5,500 520 Pamir Mountains, Tadzhikistan (Old Station)b 3,860 625 Pamir Mountains, Tadzhikistan (New Station) 4,237 600 a coupled with dedicated electronic detector array. b shut-down.

Table A.3 Threshold energies of Muon detectors at various EAS sites Site Threshold energy [GeV] comments Agassiz ≥0.4, ≥0.5, ≥1.0 Akeno/AGASA ≥0.5, ≥1.0 AMANDA ≥1,000 ANI/Aragaz ≥5.0 Auger ∼1.0 Baksan ≥230 Chacaltaya ≥0.6 Cornell ≥2.0 Cygnus ≥1.0, ≥2.0 EAS-Top ≥1.5, ≥2.0 EAS-1000 ≥1.0 GAMMA ≥5.0 GRAPES-3 ≥1.0 Haverah Park ≥0.3, ≥0.41, ≥0.6, ≥0.7, ≥1.0 Haverah Park/Durham 1 ≤ p ≤ 1, 000 GeV/c magn. spectrometera HEGRA ≥0.3 Ice Cube ≈1TeV KASCADE ≥ 0.23, ≥ 0.49, ≥ 0.8, ≥ 2.4 KGF ≥1.0, ≥220, ≥640,≥1,700, ≥12 TeV Kiel ≥2.0, magn. spectrometera Lodz ≥0.6, ≥5.0 LVD ≥1,300 MACRO ≥1,300 MIA ≥0.85 Milagro ≥2, >500, >1,200 Moscow ≥0.5, ≥10.0, magn. spectrometerb Norikura, Mt. ≥0.3, ≥0.7 North Bengal (NBU) ≥2.5, 2 magn. spectrometersa Nottingham ≥0.41 Ohya ≥14.0 SUGAR ≥0.75 Tien Shan ≥5.0 Tokyo (Fukui) ≥2.0 Volcano Ranch ≥0.22 Yakutsk ≥0.3, ≥0.7, ≥1.0c a solid iron magnet spectrometer (Earnshaw et al., 1968). b maximum detectable momentum 600 GeV/c (Vernov et al., 1979). c since 1979 (Diminstein et al., 1979). A.1 EAS Arrays and Cosmic Ray Ground Facilities 1039

Table A.4 TeVa gamma ray air Cherenkov detector sites and experiments of past and present (Arrays and Telescopes, partial List only) Name, place, country (nearest major city, region) Approximate Altitude [m] Atmospheric depth [g cm−2] AIROBIC (see HEGRA) Ð Ð ANI, Aragats Mt., (Erevan), Armenia 3,200 690 ASGAT, (Targasonne) France 1,650 840 BLANCA, (Dugway, Utah) USA 1,435 865 CACTUS, (Daggett), CA, USA 610 965 Cangaroo, (Woomera), South Australia 160 1,020 Crimean AP Obs., (Nauchny), Ukraina 2,100 800 Cygnus, (Los Alamos), NM, USA 2,200 800 GAMMA, Mt. Aragats (Erevan), Armenia 3,200 700 GASP 1, South Pole 3,300 695 DICE, (Dugway, Utah) USA 1,450 865 Haleakala, (Maui, HI) USA 3,297 695 HEGRA, (La Palma), Canary Islands 2,200 800 H.E.S.S., (Windhoek), Namibia 1,800 830 JANZOS, (Wellington), New Zealand 1,640 840 MACE, (Hanle), India 4,240 600 MAGIC, (see HEGRA) Ð Ð Pachmarhi, (Madhya Pradesh),India 1,100 920 Plateau Rosa, Italy 3,500 675 Potchefstrom, South Africa 1,429 880 SHALON, (Tien Shan), Kazakhstan 3,340 690 Srinagar, (Kashmir), India 1,730 835 STACEE, (Albuquerque), NM, USA 1,740 830 TACTIC,(Mt. Abu, Rajasthan) India 1,219 905 TACT, Tien Shan, Kazakhstan 3,340 690 Themistocle, (Targasonne), France 1,650 840 VERITAS (see Whipple) Ð Ð Whipple Obs., Mt. Hopkins, Arizona, USA 2,380 730 Woomera, South Australia 320 1,000 a Some systems claim to have thresholds as low as 0.1 TeV. For a summary of early gamma ray air Cherenkov detectors, see Baillon (1991)orLorenz (1993).

Table A.5 Locations of some old cosmic ray experimental sites Name, location Altitude [m a.s.l.] Albuquerque, New Mexico (USA) 1,575 Echo Lake, CO (USA) 3,260 Ithaca, NY (USA) 260 Jungfrau-Joch (Switzerland) 3,454 Mt. Evans, CO (USA) 4,300 Sulfur Mountain Alberta (Canada) 2,285 1040 A Experimental Installations

A.1.2 Layouts of Selected Air Shower Arrays of Past and Present

On the following pages we show a selection of layouts of air shower arrays of the past and present. Some of the older arrays are historically relevant as they represent landmarks of air shower research efforts and discoveries. It should be kept in mind that layouts and configurations of most arrays are being changed in the course of time to suit new and particular scientific aims. Thus, the layouts shown here apply to particular periods. On the other hand, some array layouts had not been changed for many years. In a few cases different array configurations are shown that existed at the same site but at different times. For accurate current array configurations the reader should consult the particular research group or the proceedings of recent Cosmic Ray conferences.

AGASA Array

TB Nagasaka Center Takane Center

Fig. A.2 Layout of the AGASA array at Akeno (Japan), located at 900 m a.s.l. (920 g cm−2). The symbols ◦ represent scintillation detectors of area 2.2 m2, muon detector of · 2 AB different area, are 1 m large SB Sudama Center scintillation detectors belonging to the 1 km2 Akeno Akeno array, four of them shown as Laboratory • belong to AGASA.The Akeno Center dashed lines identify the boundaries between the four sections, labeled as NB, TB, SB and AB,andthesymbols indicate the location of the branch centers (Chiba et al., 1992) 0 1 2 3 km A.1 EAS Arrays and Cosmic Ray Ground Facilities 1041

Fig. A.3 Layout of the M.I.T. Agassiz, Sea Level detector array used by Clark et al. (1961) at Agassiz. The four detectors in the C-ring were used to record showers D-Ring as small as 5 · 104 particles

M-Ring

C-Ring

100 m

34 m Antonov

Fig. A.4 Air shower array installed on board of an air plane, used by Antonov et al. (1971, 1973) to study air showers in the stratosphere. The spark chambers ()were used to determine the direction of incidence of the shower, the scintillation detectors (◦) to determine the lateral distribution, the shower size, and to locate the position of the shower axis 1042 A Experimental Installations

0 200 m N

Central Lab.

1 m2 Scint. 2 m2 Scint. Air Cherenkov 25 m2 μ Det. Station 1.7 km 100 m2 μ Det. Substation Dome

Fig. A.5 Layout of the Akeno array of the 1980s for which the detection efficiency is plotted in Fig. 2.7. This configuration covers an area of approximately 1 km2, has a slope of 11◦ to the southÐwest and is located at 900 m a.s.l. (920 g cm−2). The different detector types and dimensions are identified in the insert at the lower left. A 90 m2 hadron calorimeter is located at the central laboratory (+). The thresholds for of the muon detectors are 1 and 0.5 GeV for the 25 and 100 m2 detectors, respectively (for further details see Hara et al., 1979) A.1 EAS Arrays and Cosmic Ray Ground Facilities 1043

Loma Amarilla

Coihueco

Los Morados

Malargüe

Los Leones 10 km

Fig. A.6 Layout of the giant Auger (South) Observatory installations in Argentina. Shown are the 1,600 deep water Cherenkov surface detectors and the four ﬂuorescence detector telescopes that overlooking the surface array (courtesy of A. Haungs, FZ Karlsruhe, Germany and the Auger Collaboration)

Baksan Array 2060 m a.s.l.

Fig. A.7 The Baksan “Andyrchy” air shower array is located above the large Baksan underground 4-level scintillation telescope. The array is located at an average height of 2,060 m a.s.l. and is 40 m inclined. It consists of 37 plastic scintillators of 5 cm thickness and 1 m2 area. The detector separation as given in the ﬁgure is the 40 m approximate separation in the horizontal projection. A cutaway view of the entire installation at Baksan is drawn in Fig. A.38 of the Appendix A.2 (Alexeyev et al., 1993; Chudakov et al., 1999) 1044 A Experimental Installations

8 C A 12 12 D

6 3 H F G E

9 5 4 11

5 m B 10 Fig. A.8 Balloon mounted air shower array layout, used by Antonov et al. (1977), to explore the altitude dependence of air shower observables up to 12 km. The symbols labeled A, B and C are scintillation detectors of area 0.25 m2 each; D, E and F are small scintillators, each of area 0.07 m2. The central unit labeled G represents an arrangement of 30 large Geiger-Mueller (GM) counters, each of area 86 cm2, and 30 small counters, each of area 5.4 cm2. The open squares 1Ð6 show the location of GM trays containing 20 large and 20 small counters, the open circles 7Ð12 are similar trays holding 20 large and 10 small GM counters of dimensions as speciﬁed above. The square on the right labeled H represents a cluster of counters consisting of 24 sub-assemblies of area 688 cm2 each and 12 units of large GM counters (86 cm2), mounted below the main array. Each of the sub-assemblies holds a set of 8 large GM counters A.1 EAS Arrays and Cosmic Ray Ground Facilities 1045

Fig. A.9 Plan of the extended Buckland Park Array Buckland Park EAS array (sea level), status 1977. The J various boxes represent detector locations. Sites A to H have particle detectors; A, D, I , J and K were used 150 m for particle density measurements, A to E served also for fast timing. In K I addition sites A, F, G, H, L A and M were equipped with Antenna Cherenkov detectors. At C1 location C1 was a caravan E B holding a Cherenkov detector C for pulse proﬁle D measurements (rise time F 31 m H ∼2 ns) (Kuhlmann et al., 1977). At times the Antenna array was also equipped with 90 m antennae for EAS radio burst G studies (Clay et al., 1975)

90 m N

L 100 m

M 1046 A Experimental Installations

Fig. A.10 Layouts of the CASA - MIA - BLANCA Arrays, DICE, 1435 m a.s.l. CASA (Chicago Air Shower Array), MIA (MIchigan muon Array), and BLANCA (Broad Lateral Non-imaging Cherenkov Array) arrays, and of the two DICE (Double Imaging Cherenkov Experiment) detectors at Dugway, Utah (USA). Also indicated are the Utah air Cherenkov telescopes (Cassidy et al., 1997; Ong et al., 2007)

CASA Detectors 15 m Michigan Muon Detectors Utah Cherenkov Telescopes BLANCA Cherenkov Detectors DICE Detectors A.1 EAS Arrays and Cosmic Ray Ground Facilities 1047

N, (y)

n Chacaltaya 5230 m a.s.l.

6 3 1 p c 12 10 a 15 4 2 W E, (x) 7 M g e b 17 16 d 5 11 8 k i hf

9 l j 13

m o 300 m S Fig. A.11 Layout of the Chacaltaya air shower array, status 1977 (Aguirre et al., 1977). The covered area measures approximately 700 m by 700 m at an altitude of 5,230 m (550 g cm−2). It holds sixteen unshielded fast-timing scintillation detectors, twelve of area 0.87 m2,9.6cmthick,(a to l) and four of area 1 m2,10cmthick(m to p). The latter are also used to measure particle densities together with twenty 0.83 m2 scintillators, 7.5 cm thick, indicated by open circles (1Ð20) and eight 2 cm thick scintillators of area 1/16 m2 (full circles). In addition a shielded scintillator of 60 m2 (15 · 4m2) and thickness 5 cm, labeled m and located at the origin of the reference frame is used as muon detector with a threshold of 600 MeV 1048 A Experimental Installations

150 a)

100 F N

50 G

0 Distance [m] –50

–100 Chacaltaya MAS Array

–150 –150 –100 –50 0 50 100 150 Distance [m]

30 m

–30 m 30 m

S NT

–30 m G Chacaltaya MAS Array Central Part

Fig. A.12 Chacaltaya (5,230 m a.s.l.) Minimum Air Shower (MAS) array, (a), and central part of array, (b). L, G, S, N, F and NT detectors are unshielded. The L detectors are 4 m2 plastic scintillators with an additional 1 m2 scintillator. The L, G, S and NT detectors are used as timing detectors and to measure particle density. A 60 m2 muon detector with a threshold of 600 MeV is located at the array center (Shirasaki et al., 1997; Ogio et al., 2004) A.1 EAS Arrays and Cosmic Ray Ground Facilities 1049

Fig. A.13 Layout of the BASJE air shower array at Chacaltaya Chacaltaya (5,230 m a.s.l.) in BASJE 1965 (Toyoda et al., 1965)

60 m2 SD

100 m

Fig. A.14 Cornell air shower 250 m array (Linsley, 1963b) Cornell, Ithaca 260 m a.s.l.

100 m Fig. A.15 The CYGNUS II CACTI array was located near the Los Alamos National Laboratory at an altitude of 2,310 m a.s.l. (780 g cm−2) and consisted of 96 scintillation detectors (◦)and a70m2 muon detector with a threshold of ∼2GeV(Allen et al., 1992). The CACTI experiment consisted of 6 wide angle Cherenkov detectors (•)(Paling CYGNUS II Muon et al., 1997) Detector 1050 A Experimental Installations

Durham (GB)

25 m

Fig. A.16 The Durham (GB) array consisted of scintillation detectors measuring 2 m2 ( ), 1.6 m2 (), 1 m2 ( ) and 0.75 m2 (). It had a solid iron magnet spectrometer (MARS) (Ayre et al., 1972a, b)() and a hadron chamber ()(Rada et al., 1977)

100 HM 0

–100

a –200 b y [m]

–300

–400

EAS-TOP –500

–500 –400 –300 –200 –100 0 100 200 300 x [m] Fig. A.17 EAS-TOP air shower array (2,005 m a.s.l.) status of 1998. The symbols which indicate the location of different detector units represent the following kind of detectors: scintillator module, wide acceptance Cherenkov telescope, × radio antennae for the detection of radio bursts associated with air showers, and the combined hadron calorimeter-muon detector, labeled HM (twin units). The two rectangular areas that are outlined with dashed and the solid lines, labeled a and b, identify the ﬁducial regions, i.e., the core location regions, for two sets of spectral measurements (Aglietta et al., 1989, 1999) A.1 EAS Arrays and Cosmic Ray Ground Facilities 1051

150

100

0 Y [m]

–50

–100

–150 –150 –100 –50 0 50 100 150 X [m] Fig. A.18 GAMMA air shower experiment at Mt. Aragats in Armenia located at an altitude of 3,200 m a.s.l. (700 g cm−2). The 33 black squares represent scintillation detectors consisting of 3 units, each measuring 1 m2.Thedashed contour indicates the underground part with 150 m2 of scintillation detectors having a muon threshold energy of ≥5GeV.Theinner rectangle is the contour of the calorimeter of the ANI project, currently under construction (Shaulov, 2007; Garyaka et al., 2007)

150 GRAPES Ootacamund 2200 m a.s.l. 100

0 Y [m]

–50

–100

Electron Detectors Muon Detectors –150 –150 –100 –50 0 50 100 150 X [m] Fig. A.19 Layout of the GRAPES experiment at Ootacamund, India (2,200 m a.s.l., 800 g cm−2). The muon tracking detector combination which is at present the largest of its kind has an effective area of 560 m2 (Gupta et al., 2005). The shower detectors plotted as • are those that were used at that epoch. The muon detector which has a threshold of 1 GeV consists of 16 modules measuring 35 m2 each (). The modules consist of large proportional counters (Hayashi, 2005; Hayashi et al., 2005) 1052 A Experimental Installations

Fig. A.20 Haverah Park air Haverah Park, 210 m a.s.l. shower array status of 1968 (Earnshaw et al., 1968). The D 50 m crosses indicate the location C 150 m N of radio antennae for the detection of radio bursts associated with air showers (Allan, 1971) 2.15 km

1.80 km A2 1.85 km A4 1.80 km E 150 m A1 B 50 m

A3 1.95 km 1.80 km

G 150 m F 50 m

HEGRA

Fig. A.21 Original proposal of ﬁrst HEGRA array at Roque de los Muchachos (2,250 m a.s.l.), La Palma (Canary Islands), by Allkofer (1985) who founded the project in the early 1980s, showing two kinds of 1 m2 scintillation detectors. Up to date, the site has seen a wide variety of particle and air Cherenkov detectors and 10 m Cherenkov telescopes (for details see the HEGRA web site) A.1 EAS Arrays and Cosmic Ray Ground Facilities 1053

KASCADE Muon Tracker 100

0 Calorimeter KASCADE -Grande –100

–200 Piccolo [m]

Y –300

–400

–500

–600

–700 –700 –600 –500 –400 –300 –200 –100 0 100 X [m] Fig. A.22 Layout of the elaborate KASCADE-Grande air shower array at the Forschungszen- trum Karlsruhe (Germany) (110 m a.s.l.) (Kampert et al., 2003; Haungs et al., 2003; Navarra et al., 2004). The resolutions of the Grande array are 13 m for core location, 0.3◦ for arrival direction, and 15% for the shower size at a primary energy of 100 PeV (1017 eV). The KASCADE array has 252 stations that are distributed over an area of 200 × 200 m2 (Antoni et al., 2003). Each station consists of liquid scintillators to measure the shower particle density (EEM ≥ 5MeV) and shielded (10 cm Pb + 4 cm Fe) plastic scintillators underneath to measure the muon density (Eμ > 0.23 GeV). The central detector consists of a 9-layer hadron calorimeter with 40,000 chan- nels of liquid ionization chambers; it has a threshold energy of 50 GeV. Additional muon facilities are located in and under the calorimeter with threshold energies of 0.49 and 2.4 GeV, and a muon tracker in a tunnel with a threshold of 0.8 GeV. The Picolo cluster sub-array serves as a trigger. The array has a 100% trigger efﬁciency for events with primary energy of 10 PeV over the entire Grande collecting area (dashed circle). A low frequency radio antenna array (40Ð80 MHz) called LOPES (not shown above), a prototype of LOFAR, is also integrated in the KASCADE-Grande array to detect air shower radio pulses (Horneffer et al., 2003) 1054 A Experimental Installations

Fig. A.23 Air shower array Kolar Gold Fields Surface Array, 1000 m a.s.l. at the Kolar Gold Fields, status 1977 (Acharya et al., 1977). The squares and circles are 2.25 and 1 m2 plastic scintillation detectors, respectively, the full circles 1.15 m2 liquid scintillation detectors used for fast timing. The symbol marks the intersection of a perpendicular from the center 100 m 60 m 40 m of the 2 × 1 × 2m3 neon ﬂash tube telescope, located at a depth of 266 m underground 20 m (muon threshold 220 GeV). A cross-sectional view of the abandoned underground installations is shown in Fig. A.40

Moscow, 192 m a.s.l.

100 m

Fig. A.24 Air shower array at the Moscow State University M (Vernov et al., 1979). The open squares are charged particle detectors, the central system (C) contains 3,000 C hodoscope counters. A total of 8,160 Geiger counters are used. At each detector location which is 60 m or more from the center of the array a 0.5 m2 scintillation detector is installed. Muon detectors of area 18 m2 and threshold 10 GeV are located at 180, 250 and 280 m from the center. In addition a 32 m2 muon detector and a solid iron magnetic muon spectrometer are located at the center, at a depth of 40 m.w.e A.1 EAS Arrays and Cosmic Ray Ground Facilities 1055

Mount Norikura, 2770 m a.s.l.

1 3

2 Lab Bldg. 20 m L Fig. A.25 One of many air shower array configurations used at Mt. Norikura in Japan (Miyake et al., 1979). The figure shows a total of 152 scintillation detectors of area 0.25 m2 (•) each, arranged in a lattice as shown, and 6 additional detectors of area 1 m2 () in the outer area. × identifies fast timing detectors. A 25 m2 proportional counter array shielded with 2 cm of Pb located under a 6 m by 5.5 m water tank of height 2 m (1) was used to observe high energy gamma rays. During a certain period the proportional counters were replaced by 48 plastic scintillators above and 48 below the tank. This arrangement served as core detector. In addition a cloud chamber (2) was used occasionally. Two neon hodoscopes of 6 and 4 m2 (3 and 4) shielded by 35 cm of lead were also incorporated. For details of special apparatuses see Sasaki et al. (1979); for earlier array layouts see Miyake et al. (1968, 1973)andKino et al. (1975) 1056 A Experimental Installations

Ootacamund, 2200 m a.s.l.

TASS

10 m

Fig. A.26 One of several arrangements used for the air shower array at Ootacamund, India (Chatterjee et al., 1965b). The different symbols identify the following detectors: , and represent 0.36, 1.0 and 1.44 m2 scintillators, respectively; 1.0 m2 muon detectors consisting of Pb-shielded Geiger-Mueller hodoscope arrays, × fast timing scintillators, ◦ BF3 neutron detectors, and the 1 m2 total absorption scintillation spectrometer (TASS) to record nuclear interacting particles of energy >100 GeV, with a muon detector underneath. In addition there was a 4 m2 combination of energy ﬂow detectors for the soft and hadronic components A.1 EAS Arrays and Cosmic Ray Ground Facilities 1057

Pic du Midi 3 2862 m a.s.l. 7 12 6 2 4 8 Observatory 5

1 9 11 10

NM Terrace

0 10 20 m

Fig. A.27 Air shower array of the University of Kiel at the terrace of Pic du Midi, France, located at an altitude of 2,862 m. (Van Staa et al., 1973, 1974). The full symbols 1Ð13 represent 0.25 m2 scintillation detectors. Detectors 1Ð4 were equipped for fast timing, and NM indicated a neutron monitor. The square containing the four scintillators 5Ð8 that serve as trigger detectors represents the hadron detector and the hatched area within it is the 14 m2 neon hodoscope with approximately 80,000 neon tubes that serves as burst detector. The hadron target consists of a layer of 100 cm of sand and 25 cm of concrete, topped with a 10 cm thick layer of lead to absorb the photon-electron component

Potchefstroom

Fig. A.28 The Potchefstroom array was very small and consisted of 10 scintillation detectors and 2 muon detectors (De Villiers 20 m et al., 1979) 1058 A Experimental Installations

10 Sydney Array, Sea Level

0 64 Scint. Array

–10 meters –20 –10 0 10 20 30

SUGAR, Narrabri, 260 m a.s.l.

–5 –4 –3 –2 –1 0 1 2 3 km

6 Time Signal Transmitter 5

4 South Lat. 30°30' N East Long. 149°35' 3

–1

–2

–3

–4

–5

Fig. A.29 Upper figure: Sydney air shower array, status 1965 (Bray et al., 1965). Circles represent trays with 3 Geiger counters, the four boxes at the corners hold 48 Geiger counters each. In the upper right corner is the 64 scintillator array. Lower figure: Layout of early status of the Sydney University Giant air shower Array (SUGAR) at Narrabri (Brownlee et al., 1970). Except for the central section the counters are underground and record chiefly muons A.1 EAS Arrays and Cosmic Ray Ground Facilities 1059

Fig. A.30 Layout of the giant Telescope Array located at Dugway, Utah (USA), 1,400 m a.s.l., 39.3◦ N, long. 112.9◦ W(Kasahara et al., 2007). It consists of 3 ﬂuorescence stations, each having 12 identical telescopes, and 512 plastic scintillation detectors. The aperture of the surface detectors is 1,900 km2sr and the ﬂuorescence detectors have a stereoscopic aperture of 860 km2sr at 1020 eV with a duty factor of ∼10%. Participating in this joint venture project are mainly Japanese universities and institutions, some American and a few Korean universities, and a German institution. The approximate linear dimensions of the array are 17 km by 20 km (courtesy of Ken Honda and the Telescope Array Collaboration) 1060 A Experimental Installations

–2 Tibet Array, Yangbajing, 606 g cm , 4300 m a.s.l.

EXC EC

15 m Fig. A.31 Layout of Tibet II Array located at Yangbajing (606 g cm−2, 4,300 m a.s.l.). The array consists of 221 scintillation detectors that are placed 15 m apart and has a threshold for particles and gamma rays of 10 TeV. Its angular resolution is about 1◦ (Amenomori et al., 1997a,b).Forthe layout of the Tibet III array see Amenomori et al. (2003, 2006) A.1 EAS Arrays and Cosmic Ray Ground Facilities 1061

18 9

17 8 15 19 130 m 180 m 70 m 70 m 13 14 11 4 5 34 m 7 55 m 12 20 m 73 m 1 6 16 Tien Shan 3 3340 m a.s.l.

2 10

Fig. A.32 Layout of the complex air shower array at Tien Shan (Kazakhstan) (690 g cm−2, 3,340 m a.s.l.) (Abdrashitov et al., 1981). This array was for many years the worldwide best equipped air shower installation. It consisted of a 6 m by 6 m (36 m2) central ionization chamber calorimeter (1) that was interlaced with 15 rows of ionization chambers, each measuring 10 × 15 × 300 cm3, that were separated by layers of 2.5 cm and 5 cm of Pb, totaling 850 g cm−2 of Pb. The accuracy of the hadron spatial resolution was 25Ð30 cm, that of the energy measurement 15%. The chamber was covered with an carpet of 64 scintillation detectors of 0.25 m2 area each that were uniformly distributed about the chamber center over an area measuring 11 m by 11 m (121 m2). The shower detection array comprised 115 scintillation detectors, partly arranged in clusters (4, 5, 7, 8,and9) with a total effective area of 53 m2, distributed out to 130 m from the center of the ionization chamber. The four detectors of type (5)of1m2 area were used to determine the shower axis location and direction. The circular symbols (19) represent air Cherenkov detectors. A total of 9 Geiger-Muller¬ hodoscope detector trays (6, 11, 12, 13, 14, 15, 16, 17,and18) with an effective area of 38.4 m2, located at distances of 5, 10, 20, 34, 55, 70, 73, 130 and 180 m from the center (see labels attached to the thin dotted lines) permitted reliable muon measurements. In addition, a 45 m2 muon detector hodoscope was operated in a tunnel (10) at a depth of 20 m w.e., having a muon energy threshold of ≥5 GeV. An underground calorimeter of 9 m2 effective area (2, 3) below the larger surface unit with 15 trays of ionization chambers, separated by 5 cm of Pb, served to analyze the high energy muon component in the shower core. (For earlier layout versions see Erlykin et al., 1965; Aseikin et al., 1971; Betev et al., 1977.) Note that the new Tien Shan installation is at a slightly different location and consists mainly of air Cherenkov detectors for gamma ray astronomy purposes. For a recent layout see Slavatinsky (2001) 1062 A Experimental Installations

Station 2 Tokyo INS, 59 m a.s.l.

2740 1 a) 3 m 5 0 m

INS Station 1 1 8 Array INS Station 4 9 1530 m 0

8 m 00 19

Station 3

Tokyo INS Array M2 59 m a.s.l. 40 m b)

–40 m 40 m

–40 m

Fig. A.33 (a) Air shower array at the Institute for Nuclear Studies (INS) of the University of Tokyo, status 1973 (Kawaguchi et al., 1973). Stations 1Ð4 have a pair of scintillation detectors of area 2 m2 each that are 50 m apart. (See also Suga et al., 1971). (b) Details of local INS array. M1 and M2 are muon detectors having a threshold of 5 and 15 GeV, respectively. The open squares represent 1 m2 scintillation detectors, the full squares are a later addition. For further details see Matano et al. (1971). For earlier arrangements see Hara et al. (1970) A.1 EAS Arrays and Cosmic Ray Ground Facilities 1063

TUNKA 133 340 m 340 m

340 m Fig. A.34 Layout of the TUNKA-133 optical Cherenkov array, located in the Tunka valley (675 m a.s.l.) in Russia, near lake Baikal (Budnev et al., 2005, 2007). The array was operated at earlier stages with much fewer detector units while it was under construction and systematically enlarged

0 1 2 3 km

Volcano Ranch 1768 m a.s.l. Array 1963

Fig. A.35 Layout of Volcano Ranch air shower array, status 1963 (Linsley, 1963a, b) 1064 A Experimental Installations

Fig. A.36 Layout of Volcano 0 1 km Ranch array 1973 Volcano Ranch (Linsley, 1973) 1768 m a.s.l. Array 1973

Fig. A.37 Layout of Yakutsk Yakutsk, 105 m a.s.l. air shower array, status 1973 (Diminstein et al., 1973). For an earlier layout see Egorov 1 km et al. (1971); further details are also given by Kozlov et al. (1979), Diminstein et al. (1979)andArtamonov et al. (1983, 1991)

A.2 Cosmic Ray Underground Installations of Past and Present

A.2.1 Underground Muon and Neutrino Detectors

Table A.6 is a list of muon and neutrino detectors of the past and present. Most of these detectors are being operated or had been operated autonomously, but some could be used jointly with nearby air shower arrays. Those underground installations that are or were located underneath of an air shower array or in its immediate vicin- ity, so that components of the same shower event could be recorded simultaneous, that had been operated jointly, are marked. A.2 Cosmic Ray Underground Installations of Past and Present 1065

Table A.6 List of major underground muon and neutrino detectors of past and present Detector (Location) Mass tons Depth m.w.e. Size m Eμ TeV Status AMANDA (Antarctica) ∼106 m3 ICˇ 1,000 evolving 0.4 operating Antares (France) WCˇ constr. Baikal (Russia) 3·107 WCˆ 1,300 200·300 0.5 operating 0.400 Baksan (Russia) a 85 Sc 850 16·16 0.23 operating C.W.I. (SA) 20 ScFt 8,200 90·0.13·1.5 10 shut-dn. DUMAND 1 (USA) 3·105 WCˇ 4,500 70¿·70 3.5 shut-dn. DUMAND 2 (USA) 2·106 WCˇ 4,500 106¿·230 3.5 discont. Frejus (F/I) 912 Fe 4,400 6·12 3 shut-dn. 3 Gallex (Italy) 110 GaCl3 ∼3,300 54 m 3 shut-dn. 3 Homestake (USA) 615 C2 Cl4 4,200 390 m 3 shut-dn. Homestake (USA) a 300 WCˇ 4,200 8·24 3 shut-dn. HPW/(USA) 1,000 WCˇ 1,700 10¿ 0.6 discont. Icarus (Italy) 104 LA 3,100 Ð 3 discont. ICECUBE (Antarctica) a ∼109 ICˇ 1,200 1 km3 0.5 operating IMB (USA) 8,000 WCˇ 1,570 17·23 0.6 shut-dn. Issyk-Kul (Kyrgyzstan) 106 m3 WCˇ 500 ∼1km2 ≥0.15 discont. Kamiokande (J) 2,900 WCˇ 2,700 16¿·16 >1 shut-dn. KGF (India) a - Sc 730 6 m2 0.22 shut-dn. KGF (India) a -WCˇ 1,590 10 m2 0.64 shut-dn. KGF (India) - ScFt 2,895 6·6 1.7 shut-dn. KGF (India) 375 Fe Pc 7,500 6·6 12 shut-dn. LSD (Italy) 200 Sc 5,200 7·8 4 shut-dn. LVD (Italy) a 3,600 Sc 3,100 31·13·12 1.3 operating MACRO (Italy) a - ScStTe 3,100 72·12·10 1.3 shut-dn. NEMO (Italy) WCˇ planning NESTOR (Greece) b 2.8·105 WCˇ 3,800 34¿·400 3.0 discont. NUSEX (Italy) 150 Fe Ft 5,000 3.5·3.5 4 shut-dn. Ohya (Japan) a - Fe 31 400 m2 0.015 shut-dn. SAGE (Russia) - Ga operating Soudan 1 (USA) 30 FeCon 2,100 3·3 0.6 shut-dn. Soudan 2 (USA) a 1,000 FeCon 2,100 8·16 0.6 operating SNO Sudburry (CND) - D2 operating Super Kamiokande (J) 32,000 WCˇ 2,700 38¿·40 >1 operating Utah 1,800 WCSpMag.ˇ >150 12 · 10 · 6 0.5 shut-dn. a EAS array at surface. b per tower. Eμ Ð muon threshold; ¿ Ð diameter; ICˇ Ð ice Cherenkov; WCˇ Ð water Cherenkov; Sc Ð scintillation counters; Ft Ð Flash tubes; Con Ð concrete; LA - liquid argon; St Ð Streamer tubes; Te Ð Track etching; Sp - Spark chambers; D2 - deuterium; Mag. Ð magnetized iron plates. 1066 A Experimental Installations

A.2.2 Layouts of Major Underground Detectors Associated with Air Shower Arrays

(a) Comments to Layouts The underground detector experiments shown here had been operated autonomously but also in coincidence with an air shower array at the surface above or near the underground installation. The simultaneous acquisition of data from a surface and underground installation enriches the data and improves their interpretation signiﬁ- cantly. Underground detectors supply complementary data that are otherwise inac- cessible to surface measurements, such as data on single and multiple high energy muons in showers, on delayed penetrating particles, and other phenomena. They also offer an alternative method to determine the arrival direction of showers.

Fig. A.38 Cutaway view of Baksan the Baksan installation Underground Station showing the surface array and Surface Detector Array the underground scintillation telescope BUST (16 × 16 × 11 m3) under an overburden of ∼850 g cm−2. The layout of the surface array is given in Fig. A.7.

(Alexeyev et al., 360 m 1979a, b, 1993; Chudakov 1700 m a.s.l. et al., 1999) BUST Access Tunnel

550 m

Mt. Aquila 2370 m a.s.l.

Fig. A.39 Cutaway view showing the locations of the EAS-TOP EAS-TOP, LVD and MACRO Array detectors at Gran Sasso (Aglietta et al., 2004). Details 2005 m a.s.l. of the EAS-TOP installation are shown in Fig. A.17.The minimum rock overburden in the direction of the EAS-TOP array is 3,100 m w.e. The ° MACRO detector measured 35 76.6 × 12 × 4.8m3 (Ahlen et al., 1992, 1993; Ambrosio et al., 2002), the LVD detector (still operating) LVD . × . × 3 measures 22 7 13 2 10 m MACRO Tunnels (Bari et al., 1989; Aglietta 963 m a.s.l. et al., 1992) References 1067

EAS Array

Surface 266 m

U1 Level (>220 GeV) 6 m2Scint. Counter 590 m

U2 Level (>640 GeV) Water Cherenkov Det.

Kolar Gold Fields Underground Installations (Depth Profile) 1070 m

U3 Level (>1700 GeV) Horiz. Neutrino Telescope Fig. A.40 Muon and neutrino telescopes underneath the Kolar Gold Fields (KGF) air shower array, now shut-down (Chatterjee et al., 1965a). Illustrated are the experimental sites at the three different depth levels. The surface is at an altitude of 920 m a.s.l. (920 g cm−2), the lowest level is 1,070 m below the surface which corresponds to a depth of approximately 7,500 m w.e. (water equivalent)

References

Abdrashitov, S.F., et al.: PICRC, 6, p. 156 (1981). Acharya, B.S., et al.: PICRC, 8, p. 36 (1977). Aglietta, M., et al.: Nucl. Instr. Meth., A277, p. 23 (1989). Aglietta, M., et al.: Nuovo Cim. A, 12, p. 1793 (1992). Aglietta, M., et al.: Astropart. Phys., 10, p. 1 (1999). Aglietta, M., et al.: Astropart. Phys., 21, pp. 223Ð240 (2004). Aguirre, C., et al.: PICRC, 8, p. 208 (1977). Ahlen, S., et al., MACRO Collaboration: Phys. Rev. D, 46, p. 4836 (1992). Ahlen, S., et al., MACRO Collaboration: Nucl. Instr. Meth. A, 324, p. 337 (1993). Alexeyev, E.N., et al.: PICRC, 10, p. 276 (1979a). Alexeyev, E.N., et al.: PICRC, 10, p. 282 (1979b). Alexeyev, E.N., et al.: PICRC, 2, p. 474 (1993). 1068 A Experimental Installations

Allan, H.R.: Progress in Elementary Particle and Cosmic Ray Physics, North-Holland, Amsterdam, Vol. X, pp. 169Ð302 (1971). Allen, R.C., et al.: Nucl. Instr. Meth. A, 311, p. 350 (1992). Allkofer, O.C.: PICRC, 3, p. 418 (1985). Ambrosio, M., et al.: Nucl. Instr. Meth. A, 486, p. 663 (2002). Amenomori, M., et al.: PICRC, 5, p. 245 (1997a). Amenomori, M., et al.: PICRC, 5, p. 249 (1997b). Amenomori, M., et al.: Proceedings of the International Science Symposium “The Universe Viewed in Gamma Rays”, University of Tokyo, Sept. 25Ð28, 2002, R. Enomoto, M. Mori, S. Yanagita, ed., Universal Academy Press, Inc., Japan (2003). Amenomori, M., et al.: Adv. Space Res., 37, p. 1932 (2006). Antoni, T., et al.: Nucl. Instr. Meth. A, 513, p. 490 (2003). Antonov, R.A., et al.: PICRC, 6, p. 2194 (1971). Antonov, R.A., et al.: Yadernaya Fiz. 18, p. 554 (1973) (in Russian). Antonov, R.A., et al.: PICRC, 8, p. 137 (1977). Artamonov, V.P., et al.: PICRC, 8, p. 196 (1983). Artamonov, V.P., et al.: PICRC, 4, p. 375 (1991). Aseikin, V.S., et al.: PICRC, 6, p. 2152 (1971). Ayre, C.A., et al.: Nucl. Instr. Meth., 102, pp. 19Ð28 (1972a). Ayre, C.A., et al.: Nucl. Instr. Meth., 102, pp. 29Ð34 (1972b). Baillon, P.: CERN/PPE 91-12 (1991). Bari, G., et al.: Nucl. Instr. Meth., A277, p. 11 (1989). Betev, B., et al.: PICRC, 8, p. 123 (1977). Bray, A.D., et al.: PICRC, 2, p. 685 (1965). Brownlee, R.G., et al.: Acta Phys. Acad. Sci. Hung., 29, S3, p. 651 (1970). Budnev, N.M., et al.: PICRC, 8, p. 255 (2005). Budnev, N.M., et al.: PICRC, pre-conference edition, paper 0629, Merida, Mexico (2007). Cassidy, M., et al.: PICRC, 5, p. 189 (1997). Chatterjee, B.K., et al.: PICRC, 2, p. 627 (1965a). Chatterjee, B.K., et al.: PICRC, 2, p. 734 (1965b). Chiba, N., et al.: Nucl. Instr. Meth., A311, pp. 338Ð349 (1992). Chudakov, A.E., et al.: arXiv:astro-ph/9912192v1 Dec. (1999). Clark, G.W., et al.: Phys. Rev., 122, p. 637 (1961). Clay, R.W., et al.: PICRC, 8, p. 3093 (1975). De Villiers, E.J., and D.J. van der Walt: PICRC, 13, p. 277 (1979). Diminstein, A.S., et al.: PICRC, 5, p. 3232 (1973). Diminstein, O.S., et al.: PICRC, 8, p. 122 (1979). Earnshaw, R.A., et al.: Can. J. Phys., 46, p. S5 (1968). Egorov, T.A., et al.: PICRC, 6, p. 2059 (1971). Erlykin, A.D., et al.: PICRC, 2, p. 731 (1965). Garyaka, A.P., et al.: Astropart. Phys., 26, p. 169 (2007). Gupta, S., et al.: Nucl. Instr. Meth. A, 540, p. 311 (2005). Hara, T., et al.: Acta Phys. Acad. Sci. Hung., 29, S3, p. 361 (1970). Hara, T., et al.: PICRC, 8, p. 135 (1979). Haungs, A., et al.: PICRC, 2, p. 985 (2003). Hayashi, Y., GRAPES Collaboration: PICRC, 10, p. 243 (2005). Hayashi, Y., et al.: Nucl. Instr. Meth. A, 545, p. 643 (2005). Horneffer, A., et al.: PICRC, 2, p. 696 (2003). Kampert, K.H., et al.: Nucl. Phys. B (Proc. Suppl.), 122, p. 422 (2003). Kasahara, K., et al.: PICRC, pre-conference edition, paper 0955, Merida, Mexico (2007). Kawaguchi, S., et al.: PICRC, 4, p. 2562 (1973). Kino, S., et al.: PICRC, 8, p. 2837 (1975). Kozlov, V.G., et al.: PICRC, 8, p. 356 (1979). References 1069

Kuhlmann, J.D., et al.: PICRC, 8, p. 239 (1977). Linsley, J.: Phys. Rev. Lett., 10, p. 146 (1963a). Linsley, J.: PICRC, 4, p. 77 (1963b). Linsley, J.: PICRC, 5, p. 3212 (1973). Lorenz, E.: Nucl. Phys. B (Proc. Suppl.), 33A,B, p. 93 (1993). Matano, T., et al.: PICRC, 7, p. 2724 (1971). Miyake, S., et al.: Can. J. Phys., 46, p. S17 (1968). Miyake, S., et al.: PICRC, 5, p. 3220 (1973). Miyake, S., et al.: PICRC, 13, p. 171 (1979). Navarra, G., et al.: Nucl. Instr. Meth. A, 518, pp. 207Ð209 (2004). Ogio, S., et al.: Astrophys. J., 612, pp. 268Ð275 (2004). Ong, R.A., et al., CASA-MIA Collaboration: PICRC, pre-conference edition, paper 814, Merida, Mexico (2007). Paling, S., et al.: PICRC, 5, p. 253 (1997). Rada, W.S., et al.: PICRC, 8, p. 13 (1977). Sasaki, H., et al.: PICRC, 8, p. 190 (1979). Shaulov, S., et al.: PICRC, pre-conference edition, paper 483, Merida, Mexico (2007). Shirasaki, Y., et al.: PICRC, 4, p. 53 (1997). Slavatinsky, S.A., Tien Shan Collaboration: Nucl. Phys. B (Proc. Suppl.), 97, p. 109 (2001). Suga, K., et al.: PICRC, 7, p. 2742 (1971). Toyoda, Y., et al.: PICRC, 2, p. 708 (1965). Van Staa, R., et al.: PICRC, 4, p. 2676 (1973). Van Staa, R., et al.: J. Phys. A, 7, p. 135 (1974). Vernov, S.N., et al.: PICRC, 8, p. 129 (1979).

Appendix B Miscellaneous Relations, Tables, Lists and Constants

B.1 Electromagnetic Interaction Related Constants and Parameters

Table B.1 Radiation length χ◦, critical energy Ecrit and density ρ of frequently used elements −2 −3 Element Z A χ◦ gcm χ◦ cm Ecrit MeV ρ gcm Aluminum 13 26.98 24.1 8.9 40 2.70a Carbon 6 12.01 42.7 18.8 79 2.25b Copper 29 63.54 12.9 1.43 18.8 8.89c Hydrogen 1 1.008 62.8 7,500 (m) 350 0.07d Helium 2 4.003 93.1 5,600 (m) 250 0.15d Iron 26 55.85 13.8 1.76 20.7 7.85e Lead 82 207.21 6.4 0.56 7.40 11.34 Nitrogen 7 14.008 38.6 331 (m) 85 0.81d Oxygen 8 16.00 34.6 258 (m) 75 1.14d Silicon 14 28.09 21.8 9.36 37.5 2.35f a drawn. b graphite. c hard drawn. d liquid. e wrought. f amorphous.

Table B.2 Radiation length χ◦ and critical energy Ecrit of mixtures and compounds −2 Compound Z A χ◦ gcm χ◦ cm Ecrit MeV Air 7.4 14.8 37.15 304 (m) 84.4 Water 7.2 14.3 36.1 36.1 73.0 Emulsion-G5 11.4 2.98 16.4

1071 1072 B Miscellaneous Relations, Tables, Lists and Constants

Table B.3 Data on Ilford G-5 emulsion Property Composition g cm−3 Z Density 3.907 g cm−3 Silver 1.85 47 Atoms cm−3 8.12 · 1022 Bromine 1.36 35 Mean A 28.98 Iodine 0.024 53 Mean Z 13.17 Carbon 0.27 6 Mean Z 2 456 Hydrogen 0.056 1 Radiation Length, χ 2.93 cm Oxygen 0.27 8 λp,Emul ∼ . int 37 cm Sulfur 0 010 16 Nitrogen 0.067 7

B.2 Bethe-Bloch Ionization Loss Formula

The Bethe-Bloch equation given below includes the density correction term of Sternheimer et al. (1984) to account for the density effect of ionization, δ.The equation is written in the form derived by Petrukhin and Shestakov (1968) (see also Sternheimer, 1952, 1953, 1954a, b, 1956, 1959, 1961, 1971, 1984; Eidelman et al., 2004). dE Zm 2m γ 2β2 E E2 − = 2π N α2λ2 e ln e m − 2β2 + m − δ . (B.1) dx A e Aβ2 I 2(Z) 4E2

The symbols stand for the following quantities: α = 1/137.036 ﬁne structure constant 23 NA = 6.023 · 10 Avogadro’s number Z atomic number of absorber A atomic weight of absorber me rest masses of electron mμ rest masses of muon β = p/E ppmuon momentum EEmuon energy γ = E/mμ Lorentz factor of muon −11 λe = 3.8616 · 10 cm Compton wavelength of electron I (Z) mean ionization potential of absorber and Em maximum energy transferable to electron For Em we write

2 = 2me p , Em (B.2) 2 + 2 + 2 + 2 me mμ 2me p mμ and δ is the density correction term, B.3 The Atmosphere 1073

m δ(X) = 4.6052 X + a(X1 − X) + C , for X0 < X < X1 (B.3) and

δ(X) = 4.6052 X + C , for X > X1 . (B.4)

The quantity X as used by Sternheimer et al. (1984) is expressed as p X = lg , (B.5) mc where p is the momentum and m the rest mass of the particle, and c is the velocity of light.

Additional Physical Constants 23 −1 Avogadro constant NA 6.023 · 10 mol Boltzman constant k 1.380 · 10−23 JK−1 −13 Classical electron radius re 2.817 · 10 cm

B.3 The Atmosphere

B.3.1 Characteristic Data and Relations

To provide a better understanding of the secondary processes which take place in the atmosphere, some of its basic features are outlined. The Earth’s atmosphere is a large volume of gas with a density of almost 1019 particles per cm3 at sea level. With increasing altitude the density of air decreases and with it the number of molecules and nuclei per unit volume, too. Since the real atmosphere is a complex system we frequently use an approximate representation, a simpliﬁed model, called the standard isothermal exponential atmosphere, where accuracy permits it. The atmosphere consists mainly of nitrogen and oxygen, although small amounts of other constituents are present. In the homosphere which is the region where thermal diffusion prevails the atmospheric composition remains fairly constant. This region extends from sea level to altitudes between 85 and 115 km, depending on thermal conditions. Beyond this boundary molecular diffusion is dominating. 3 Table B.5 gives the number of molecules, ni , per cm of each constituent, i,at standard temperature and pressure (ST P), i.e., at 273.16 K and 760 mmHg, and the relative percentage, qi , of the constituents. 1074 B Miscellaneous Relations, Tables, Lists and Constants

Table B.4 Parameters for Eq. (4.9) and unit radiation length of atoms, χ0 (after Tsai, 1974) ZÐAtomic Number, AÐAtomic Weight, f ÐCoulomb Corrections

ZA f χ0 ZA f χ0 [g cm−2][gcm−2] 1 1.0080 6.4005 · 10−5 63.0470 47 107.8700 1.2850 · 10−1 8.9701 2 4.0026 2.5599 · 10−4 94.3221 48 122.4000 1.3351 · 10−1 8.9945 3 6.9390 5.7583 · 10−4 82.7559 49 114.8200 1.3859 · 10−1 8.8491 4 9.0122 1.0234 · 10−3 65.1899 50 118.6900 1.4373 · 10−1 8.8170 5 10.8110 1.5984 · 10−3 52.6868 51 121.7500 1.4893 · 10−1 8.7244 6 12.0111 2.3005 · 10−3 42.6983 52 127.6000 1.5419 · 10−1 8.8267 7 14.0067 3.1294 · 10−3 37.9879 53 126.9040 1.5951 · 10−1 8.4803 8 15.9994 4.0845 · 10−3 34.2381 54 131.3000 1.6489 · 10−1 8.4819 9 18.9984 5.1654 · 10−3 32.9303 55 132.9050 1.7032 · 10−1 8.3052 10 20.1830 6.3715 · 10−3 28.9367 56 137.3400 1.7581 · 10−1 8.3073 11 22.9898 7.7022 · 10−3 27.7362 57 138.9100 1.8134 · 10−1 8.1381 12 24.3120 9.1566 · 10−3 25.0387 58 140.1200 1.8693 · 10−1 7.9357 13 26.9815 1.0734 · 10−2 24.0111 59 140.9070 1.9256 · 10−1 7.7379 14 28.0860 1.2434 · 10−2 21.8234 60 144.2400 1.9824 · 10−1 1.7051 15 30.9738 1.4255 · 10−2 21.2053 61 145.0000 2.0396 · 10−1 7.5193 16 32.0640 1.6196 · 10−2 19.4953 62 150.3500 2.0972 · 10−1 7.5727 17 35.4530 1.8236 · 10−2 19.2783 63 151.9600 2.1553 · 10−1 7.4377 18 39.9480 2.0435 · 10−2 19.5489 64 157.2500 2.2137 · 10−1 7.4830 19 39.1020 2.2731 · 10−2 17.3167 65 158.9240 2.2725 · 10−1 7.3563 20 40.0800 2.5142 · 10−2 16.1442 66 162.5000 2.3317 · 10−1 7.3199 21 44.9560 2.7668 · 10−2 16.5455 67 164.9300 2.3911 · 10−1 7.2332 22 47.9000 3.0308 · 10−2 16.1745 68 167.2600 2.4509 · 10−1 7.1448 23 50.9420 3.3059 · 10−2 15.8425 69 168.9340 2.5110 · 10−1 7.0318 24 51.9960 3.5921 · 10−2 14.9444 70 173.0400 2.5714 · 10−1 7.0214 25 54.9380 3.8892 · 10−2 14.6398 71 174.9700 2.6321 · 10−1 6.9237 26 55.8470 4.1971 · 10−2 13.8389 72 178.4900 2.6930 · 10−1 6.8907 27 58.9332 4.5156 · 10−2 13.6174 73 180.9480 2.7541 · 10−1 6.8177 28 58.7100 4.8445 · 10−2 12.6820 74 183.8500 2.8155 · 10−1 6.7630 29 63.5400 5.1837 · 10−2 12.8616 75 186.2000 2.8771 · 10−1 6.6897 30 65.3700 5.5331 · 10−2 12.4269 76 190.2000 2.9389 · 10−1 6.6763 31 69.7200 5.8924 · 10−2 12.4734 77 192.2000 3.0008 · 10−1 6.5936 32 72.5900 6.2615 · 10−2 12.2459 78 195.0900 3.0629 · 10−1 6.5433 33 74.9216 6.6402 · 10−2 11.9401 79 196.9670 3.1252 · 10−1 6.4608 34 78.9600 7.0284 · 10−2 11.9082 80 200.5900 3.1876 · 10−1 6.4368 35 79.9090 7.4258 · 10−2 11.4230 81 204.3700 3.2502 · 10−1 6.4176 36 83.8000 7.8323 · 10−2 11.3722 82 207.1900 3.3128 · 10−1 6.3688 37 85.4700 8.2478 · 10−2 11.0272 83 208.9800 3.3756 · 10−1 6.2899 38 87.6200 8.6719 · 10−2 10.7623 84 210.0000 3.4384 · 10−1 6.1907 39 88.9050 9.1046 · 10−2 10.4101 85 210.0000 3.5013 · 10−1 6.0651 40 91.2200 9.5456 · 10−2 10.1949 86 222.0000 3.5643 · 10−1 6.2833 41 92.9060 9.9948 · 10−2 9.9225 87 223.0000 3.6273 · 10−1 6.1868 42 95.9400 1.0452 · 10−1 9.8029 88 226.0000 3.6904 · 10−1 6.1477 43 99.0000 1.0917 · 10−1 9.6881 89 227.0000 3.7535 · 10−1 6.0560 44 101.0700 1.1389 · 10−1 9.4825 90 232.0380 3.8166 · 10−1 6.0726 45 102.9050 1.1869 · 10−1 9.2654 91 231.0000 3.8797 · 10−1 5.9319 46 106.4000 1.2356 · 10−1 9.2025 92 238.0300 3.9429 · 10−1 5.9990 B.3 The Atmosphere 1075

Table B.5 Composition of the atmosphere (STP) −3 Molecule ni [cm ] qi = ni /nair[%] air 2.687 · 1019 100 19 N2 2.098 · 10 78.1 18 O2 5.629 · 10 20.9 Ar 2.510 · 1017 0.9 15 CO2 8.87 · 10 0.03 He 1.41 · 1014 5.0 · 10−4 Ne 4.89 · 1014 1.8 · 10−3 Kr 3.06 · 1013 1.0 · 10−4 Xe 2.34 · 1012 9.0 · 10−6

Specific regions within the atmosphere are defined according to their temperature variations. These include the troposphere where the processes which constitute the weather take place, the stratosphere which generally is without clouds, where ozone is concentrated, the mesosphere which lies between 50 and 80 km, where the temperature decreases with increasing altitude, and the thermosphere where the temperature increases with altitude up to about 130 km. The temperature profile of the atmosphere versus altitude is shown in Fig. B.1. The layers between the different regions are called pauses, i.e., tropopause, stratopause, mesopause and thermopause. The variation of density with altitude in the atmosphere is a function of the barometric parameters. The variation of each component can be represented by the barometric law, h T (h0) dh ni (X) = ni (X0) exp − , (B.6) T (h) h0 hs,i where

−3 ni (X) number of molecules of i-th component at X [molecules cm ] −3 ni (X0) number of molecules of i-th component at X0 [molecules cm ] hs,i = RT/Mi g(h) scale height of i-th component [cm] R universal gas constant (8.313 · 107 [erg mole−1 K−1]) Mi atomic or molecular mass of the i-th component [g/mole] h altitude (height) at X [cm] X atmospheric depth at h [g cm−2] −2 X0 atmospheric depth at h0 [g cm ] (usually sea level) h0 altitude (height) at X0 [cm] T (h) temperature at h [K] T (h0) temperature at h0 [K] g(h) gravitational acceleration [cm s−2]

In a static isothermal atmosphere, for which complete mixing equilibrium of all constituents is assumed, Eq. (B.6) reduces to 1076 B Miscellaneous Relations, Tables, Lists and Constants

200 Night

Day

100 Thermosphere Mesopause

Altitude, h [km] Altitude, Mesosphere Stratopause Stratosphere Tropopause 0 Troposphere 0 200 400 600 800 1000 1200 Temperature, T [K] Fig. B.1 Schematic representation of the atmosphere showing its temperature proﬁle h n(h) = n(h0)exp − , (B.7) hs where hs [cm] is the mean scale height of the mixture (see Table B.6).

Table B.6 Scale heights at different depths in the atmosphere X [g cm−2] 10 100 300 500 900 5 hs [10 cm] 6.94 6.37 6.70 7.37 8.21

For the real atmosphere, the same relation applies, but the scale height varies slightly with altitude. Table B.6 gives some values of hs for different atmospheric depths. A similar relation applies to the variation of pressure with altitude. Figure B.2 shows the relation between density and altitude in an isothermal atmosphere, in the region which is important for cosmic ray propagation and transformation processes. In an inclined direction, i.e., for non-zero zenith angles, the change of density per unit path length is less than in the vertical direction. Furthermore, for an incident particle the total thickness of atmosphere that must be traversed to reach a certain ﬁxed altitude increases with increasing zenith angle. For small zenith angles the “ﬂat Earth” approximation can be used to compute the inclined column density (or slant depth) that follows a sec(θ) dependence as given below,

X(h,θ) = X(h,θ = 0) · sec(θ)[gcm−2] . (B.8)

However, for large zenith angles (θ → 90◦) this approximation diverges and the curvature of the Earth must be considered, requiring the Chapman function (Chap- man, 1931), discussed in Sect. B.4, to compute the column density of a given path in the atmosphere correctly. B.3 The Atmosphere 1077

1000 ] –2 cm

100 Atmospheric Depth [g

10 0102030 Altitude [km] Fig. B.2 Relation between vertical depth and altitude in an isothermal atmosphere. The dashed line is an exponential ﬁt to the overall data

B.3.2 Standard and Real Atmospheres

As briefly discussed before, for many applications and calculations the simple Stan- dard, Isothermal, Exponential Atmosphere is adequate. However, several organiza- tions have developed formulas to describe the density profile of the atmosphere more accurately and offer density profiles in tabulated form. One must also be aware of the fact that besides seasonal changes the atmospheric density and temperature profiles exhibit also a latitude dependence, and for special applications in-situ measurements may be required. The relation between altitude and depth in the real atmosphere is illustrated in Fig. B.3. Frequently used tabulated density profiles are those available from COSPAR or the Standard US Air Force Atmosphere. In Table B.7 we present the basic data of the COSPAR International Reference Atmosphere (Barnett and Chandra,1990).

B.3.3 Special Atmospheres and Their Variations

The real average atmospheric profile manifests significant variations across the entire globe. Some of these are related to local climatic conditions, the structure of the Earth, to gravitational anomalies, and to the Earth’s rotation. There is a well pronounced latitude dependence. In addition, the atmospheric profile is influenced by the ambient temperature and pressure, and is therefore subject to seasonal as 1078 B Miscellaneous Relations, Tables, Lists and Constants

Table B.7 COSPAR international reference atmosphere: 30◦N annual mean (after Barnett and Chandra, 1990) Pressure scale Pressure [mb] Geometric Geopotential Temperature [K] heighta heightb [m] heightc [m] 17.50 2.544·10−5 119,656 11,7361 370.1 17.25 3.266·10−5 116,732 11,4545 324.8 17.00 4.194·10−5 114,192 11,2096 287.2 16.75 5.385·10−5 111,965 109,948 256.9 16.50 6.914·10−5 109,982 108,034 233.7 16.25 8.878·10−5 108,161 106,275 218.1 16.00 1.140·10−4 106,471 104,642 207.5 15.75 1.464·10−4 104,861 103,085 199.6 15.50 1.880·10−4 103,319 101,594 194.1 15.25 2.413·10−4 101,823 100,146 189.9 15.00 3.099·10−4 100,364 98,734 187.0 14.75 3.979·10−4 98,931 97,345 185.0 14.50 5.109·10−4 97,518 95,976 183.7 14.25 6.560·10−4 96,118 94,619 182.8 14.00 8.423·10−4 94,727 93,269 182.5 13.75 1.082·10−3 93,340 91,924 182.5 13.50 1.389·10−3 91,953 90,577 183.3 13.25 1.783·10−3 90,562 89,226 185.2 13.00 2.290·10−3 89,158 87,862 187.9 12.75 2.940·10−3 87,733 86,477 191.2 12.50 3.775·10−3 86,284 85,068 194.8 12.25 4.847·10−3 84,804 83,628 198.6 12.00 6.224·10−3 83,298 8,216 201.9 11.75 7.992·10−3 81,766 80,670 204.4 11.50 1.026·10−2 80,217 79,161 206.3 11.25 1.318·10−2 78,662 77,646 207.8 11.00 1.692·10−2 77,097 76,120 209.2 10.75 2.172·10−2 75,521 74,581 210.8 10.50 2.789·10−2 73,932 73,031 212.5 10.25 3.582·10−2 72,333 71,469 214.3 10.00 4.599·10−2 70,720 69,893 216.4 9.75 5.905·10−2 69,087 68,296 219.2 9.50 7.582·10−2 67,433 66,678 222.6 9.25 9.736·10−2 65,754 65,035 226.4 9.00 0.1250 64,048 63,364 230.4 8.75 0.1605 62,308 61,660 234.5 8.50 0.2061 60,539 59,926 238.9 8.25 0.2647 58,739 58,160 243.6 8.00 0.3398 56,905 56,361 248.5 7.75 0.4363 55,029 54,519 253.9 7.50 0.5603 53,116 52,639 259.1 7.25 0.7194 51,170 50,726 263.5 7.00 0.9237 49,198 48,786 266.5 6.75 1.1861 47,213 46,832 267.1 6.50 1.5230 45,231 44,880 266.0 6.25 1.9556 43,265 42,942 263.0 6.00 2.5110 41,325 41,030 258.8 B.3 The Atmosphere 1079

Table B.7 (continued) Pressure scale Pressure [mb] Geometric Geopotential Temperature [K] heighta heightb [m] heightc [m] 5.75 3.2242 39,425 39,155 253.8 5.50 4.1399 37,563 37,316 248.7 5.25 5.3157 35,737 35,513 243.7 5.00 6.8255 33,948 33,744 238.9 4.75 8.7642 32,198 32,013 234.4 4.50 11.25 30,479 30,313 230.3 4.25 14.45 28,788 28,638 226.9 4.00 18.55 27,120 26,986 223.9 3.75 23.82 25,478 25,359 221.0 3.50 30.59 23,860 23,754 218.3 3.25 39.28 22,267 22,174 215.6 3.00 50.43 20,697 20,616 212.8 2.75 64.76 19,151 19,080 210.0 2.50 83.15 17,625 17,564 207.1 2.25 106.77 16,116 16,065 205.8 2.00 137.09 14,604 14,561 208.5 1.75 176.03 13,055 13,019 214.8 1.50 226.03 11,450 11,421 223.6 1.25 290.23 9,771 9,750 234.6 1.00 372.66 8,011 7,995 247.0 0.75 478.51 6,148 6,138 259.9 0.50 614.42 4,197 4,192 272.1 0.25 788.93 2,166 2,164 283.1 0.00 1013.00 57 57 295.1 a The pressure scale height is minus the natural logarithm of pressure relative to the surface pressure; it is dimensionless. b The geometric height or altitude of an element is its distance above the reference sea level terrestrial ellipsoid, given in meters. c The geopotential height above the reference sea level ellipsoid is given in meters. It can be considered to be its geometric height plus (or minus) a correction which depends upon latitude and height. The difference between geometric and geopotential height is zero at the surface at 30◦N and increases with height; the difference varies with latitude. well as daily variations. Moreover, the profile of the polar atmospheres deviates strongly from mid-latitude or equatorial profiles and there are also remarkable dif- ferences between the arctic and Antarctic atmospheric profiles for corresponding seasons. As an example of the seasonal variations of local atmospheres we present in Figs. B.4 and B.5 the seasonal deviation of the average atmospheric profiles measured at Stuttgart, Germany, and at Pampa Amarilla, Mendoza, Argentina, respectively (Keilhauer et al., 2004; Blumer¬ et al., 2005), from the US Standard Atmo- sphere (NASA, 1976). Similar studies were carried out for the Fly’s Eye site at Dugway, Utah (Wilczynska« et al., 2005) and at other locations. The conse- quences of these variations are discussed in Sect. 7.7 and in Chap. 17 in connec- tion with air fluorescence measurements and longitudinal shower development (see Fig. 7.24). 1080 B Miscellaneous Relations, Tables, Lists and Constants

Fig. B.3 Relation between 103 vertical depth or column density and altitude in the real atmosphere, after Cole 102 and Kantor (1978) ] –2

101

100

10–1 Atmospheric Depth [g cm

10–2

10–3 0 102030405060708090 Altitude [km]

Fig. B.4 Deviation of the 30 average seasonal atmospheric ] Stuttgart –2 20 depth proﬁles measured at Summer (Germany) Stuttgart, Germany, from the 10 US Standard Atmosphere US Standard (NASA, 1976; Keilhauer 0 Atmosphere et al., 2004) –10 Winter –20 Depth Deviation [g cm Depth Deviation

–30 0 5 10 15 20 25 30 35 40 Height a.s.l. [km]

] Summer Argentina Fig. B.5 Deviation of the –2 20 average seasonal atmospheric Winter 1 depth proﬁles measured at 15 Winter 2 Pampa Amarilla, Argentina, 10 from the US Standard Atmosphere (NASA, 1976). 5 Spring Autumn Winter 1 and winter 2 refer to US Standard 0 two different atmospheric [g cm Depth Deviation Atmosphere models, depending on the –5 pressure condition (for details 0 5 10 15 20 25 see Keilhauer et al., 2004) Height a.s.l. [km] B.4 Chapman Function 1081

B.4 Chapman Function

In a standard isothermal exponential atmosphere that is characterized by a constant scale height hs = (kT/Mg) [cm], where k is Boltzman’s constant, T [K] the temperature in Kelvin, M [g/mole] the molecular weight and g [cm−1s−2] the gravitational acceleration, the vertical column density X [g cm−2] of air overlaying a point P at altitude h [cm] is given by the common barometer formula

− / − X(h) = X(h = 0)e (h hs ) [g cm 2] . (B.9)

For inclined trajectories the Chapman function permits to compute the thickness or column density of inclined trajectories in the atmosphere accurately, taking into account the curvature of the Earth (Chapman, 1931). Depending on the accuracy required it should be used for trajectories whose zenith angle, θ, exceeds about 70◦. Various approximate forms of the Chapman function are available (see Fitzmau- rice, 1964; Swider and Gardner, 1967; Brasseur and Solomon, 1986). We give here the expression of Swider and Gardner (1967) for zenith angles ≤ (π/2) which gives the ratio of the total amount of atmosphere in the inclined direction, θ, with respect to the vertical (cf Fig. B.6). π πx 1/2 θ θ Ch x,θ ≤ = 1 − erf x1/2 cos exp x cos2 , (B.10) 2 2 2 2 where R + h x = E . (B.11) hs

RE is the radius of the Earth, h the altitude of observation in the atmosphere, and hs is the appropriate scale height of the atmosphere.

Fig. B.6 Atmospheric column density X1 in curved atmosphere encountered by a cosmic ray incident under zenith angle θ1 ≤ π/2to reach point P1 at altitude h. Also shown is the situation for point P2 at θ>π/2and column density X2,a situation that may arise when h is large 1082 B Miscellaneous Relations, Tables, Lists and Constants

Fig. B.7 Relation between ] zenith angle and atmospheric 2 thickness or column density at sea level for the “curved” Earth, as described by the 4 Chapman function 10 Atmospheric Thickness [g/cm 103 010 20406080 30 50 70 90 Zenith Angle, θ [Degrees]

For θ = π/2, i.e., for horizontal direction we get π Ch(x, ) = (πx/2)1/2 , (B.12) 2 which is about equal to 40. In other words, the column density or atmospheric thickness is approximately 40 times larger than for vertical incidence (θ = 0◦). Figure B.7 displays the atmospheric column density as a function of zenith angle as is obtained with the Chapman function.

B.5 Gross Transformation

The Gross transformation allows to transform the altitude dependence of the rate of air showers to the zenith angle distribution (Gross, 1933). Moreover, it permits to calculate the vertical intensity RV (X,θ = 0) of air showers per unit solid angle at an atmospheric depth X in terms of the measured rate of all showers R(X)atthis depth. The Gross transformation can be written in different forms; it is frequently expressed as (Galbraith, 1958; Allkofer, 1975) 1 ∂ R(X) R (X,θ = 0) = (n + 1)R(X) − X [m−2s−1] (B.13) V 2π ∂ X where

n = 2(γ − 1) + (kγ ) − κ.

γ is the exponent of the density spectrum, κ is the exponent of the decoherence rate, R, i.e., R ∝ d−κ , determined empirically, k is related to the counter geome- try and response, and d is the counter separation (Galbraith, 1958; Allkofer, 1975, Khristiansen, 1980). B.6 Energy, Particle, Photon and Magnetic Field Densities in Space 1083

B.6 Energy, Particle, Photon and Magnetic Field Densities in Space

Energy and field densities in space are of great importance for the propagation of cosmic rays, irrespective whether they are of galactic or extragalactic origin. Mag- netic fields in space deflect the charged particles and thus mask their origin for the observer on Earth. On the other hand radiation in space provokes interactions that degrade the original primary energy of all particles, charged and neutral. In Table B.8 we have listed the energy and/or number densities of particles and photons in the different regions of space, i.e., in the heliosphere, the Galaxy, extragalactic (metagalactic) space and the Universe. Some of the data are rather speculative. The anisotropy of the cosmic microwave background radiation CMBR is discussed in the article of Smoot (2000). The spectral distributions of the CMBR and of the radiation from other contributing sources are plotted in Fig. B.8. The plot shows the distribution of the power per unit frequency bandwidth per unit area and solid angle.

Table B.8 Energy and number density of particles and photons Type of particle or photon Energy density Number density [eV cm−3][cm−3] Cosmic rays in Galaxy, alla,b 0.9 Ð Cosmic rays in Galaxy, p onlya 0.65 Ð Cosmic rays near Earth, solar min.d 0.60 Ð Cosmic rays at 1 pc from Sune 0.80Ð1.0 Ð 2.7 K CMBR < E >= 6.4 · 10−4 eV f,g 0.24 410 Starlight, < E >= 1eVh 0.6 0.25 EG Starlight, < E >= 2eVf 10−2 5 · 10−3 Neutrinos, E 0.03 eVb,c Ð 108 Galactic magnetic fieldh 0.2 Ð Local Galactic magnetic field strength B 4 − 9μGi Galactic magnetic field strength at few pc B 1.6μGi Extragalactic magnetic field strength B 1nGj,k a Ginzburg (1958). b Khristiansen (1980). c Fermi energy. d Ginzburg and Syrovatskii (1969). e Bloemen (1987). f Ramana Murthy and Wolfendale (1993). g Bergstrom and Goober (2004). h Longair (1981). i Beck (2009a, b). j Kotera and Lemoine (2008). k Kronberg (1994). 1084 B Miscellaneous Relations, Tables, Lists and Constants

Fig. B.8 Intensity of the 10–10 microwave sky from 3 to Dust 10–11 3,000 GHz near a Galactic ] ◦ latitude of b = 20 .The –1 –12 CMB

sr 10 ordinate is the brightness of –2 –13 the sky, S(ν), multiplied by 10 cm the frequency, ν 10–14 Dipole

(Smoot, 2000) ) [W –15 ν 10

.S( –16 ν 10 Synchrotron 10–17 free - free 10–18 101 102 103 Frequency [GHz]

B.7 Data on Cherenkov Radiation

B.7.1 Cherenkov Radiation in the Atmosphere

Figure B.9 is a quick reference diagram for practical applications to extract the relevant parameters of Cherenkov radiation in the atmosphere, and in Table B.9 we list the Cherenkov threshold energies in water and air (at NTP) for electrons, muons, pions and protons.

3 3 3

2 2 2

Threshold Yield 100 1.0 0.10

5 5 5

3 3 3 Angle Cherenkov Angle [deg.] 2 2 2 Cherenkov Yield [ph/cm]

Cherenkov Threshold, Electrons [MeV] 10 0.1 0.01 10 100 1000 Atmospheric Depth [g cm–2] Fig. B.9 Characteristic properties of the Cherenkov radiation of electrons in the Earth’s atmosphere. Shown is the threshold energy for the production of Cherenkov photons, the opening angle of the Cherenkov cone of emission with respect to the velocity vector of the electrons and the photon yield per centimeter as a function of atmospheric depth References 1085

Table B.9 Cherenkov threshold energies of particles in water and air Particle Kinetic energy in Water Air (NTP) Electron 257 keV 21 MeV Muon 53 MeV 4.4 GeV Pion 70 MeV 5.8 GeV Proton 475 MeV 39 GeV

References

Allkofer, O.C.: Introduction to Cosmic Radiation, Verlag Karl Thiemig, Munchen (1975). Barnett, J.J., and S. Chandra: COSPAR International Reference Atmosphere. Adv. Space Res., 10, 12, p. 7 (1990). Beck, R.: arXiv:0810.2923v4 [astro-ph] 12 Jan (2009a). Beck, R.: Astrophys. Space Sci. Trans., 5, p. 43 (2009b) Bergstrom,¬ L., and A. Goobar: Cosmology and Particle Astrophysics, Springer, Berlin, 2nd ed. (2004). Bloemen, H.: Proc. Symp. Interstellar Processes, Hollenbach, D.J., and H.A. Thronson, Jr., eds., Astrophysics and Space Science Library, D. Reidel Publ. Co. Dordrecht (1987). Blumer,¬ J., et al., Pierre Auger Collaboration: PICRC, 7, p. 123 (2005). Brasseur, G., and S. Solomon: Aeronomy of the Moddle Atmosphere, D. Reidel Publishing Com- pany, Dordrecht/Boston/Lancaster (1986). Chapman, S.: Proc. Phys. Soc. (Lond.), 43, p. 483 (1931). Cole, A.E., and A.J. Kantor: Air Force Reference Atmosphere, AFGL-TR-78-0051 (1978). Eidelman, S., et al.: Particle Physics Booklet, Particle Data Group, Springer, Berlin (available from LBNL and CERN) (2004), and Phys. Lett. B, 592, p. 1 (2004). Fitzmaurice, J.A.: Appl. Opt., 3, p. 640 (1964). Galbraith, W.: Extensive Air Showers, Butterworths Scientiﬁc Publishers, London (1958). Ginzburg, V.L.: Progress in Elementary and Cosmic Ray Physics, North Holland Publishing Co., Amsterdam, Vol. 4 (1958). Ginzburg, V.L., and S.I. Syrovatskii: The Origin of Cosmic Rays, Gordon and Breach, New York (1969). Gross, B: Zeitschr. f. Physik, 83, p. 214 (1933). Keilhauer, B., et al.: Astropart. Phys., 22, p. 249 (2004). Khristiansen, G.B.: Cosmic Rays of Superhigh Energies, Verlag Karl Thiemig, Munchen (1980). Kotera, K., and M. Lemoine: arXiv:0706.1891v2 [astro-ph] 4 Jan (2008). Kronberg, P.P.: Rep. Prog. Phys., 57, p. 325 (1994). Longair, M.S.: High Energy Astrophysics, Cambridge University Press, Cambridge, MA (1981). NASA, National Aeronautics and Space Administration, US Standard Atmosphere 1976, NASA- TM-X-74335 (1976). Petrukhin, A.A., and V.V. Shestakov: Can. J. Phys., 46, part 1, p. S377 (1968). Ramana-Murthy, P., V., and A. W. Wolfendale: Gamma Ray Astronomy, Cambridge University Press, Cambridge, MA, 2nd ed. (1993). Smoot, G.F.: Phys. Rep., 333Ð334, pp. 269Ð308 (2000). Sternheimer, R.M.: Phys. Rev., 88, p. 851 (1952). Sternheimer, R.M.: Phys. Rev., 89, p. 1309 (1953), Erratum. Sternheimer, R.M.: Phys. Rev., 93, p. 351 (1954a). 1086 B Miscellaneous Relations, Tables, Lists and Constants

Sternheimer, R.: Phys. Rev., 93, p. 1434 (1954b), Erratum. Sternheimer, R.: Phys. Rev., 103, p. 511 (1956). Sternheimer, R.: Phys. Rev., 115, p. 137 (1959). Sternheimer, R.: Phys. Rev., 124, p. 2051 (1961). Sternheimer, R.M., and R.F. Peierls: Phys. Rev. B, 3, p. 3681 (1971). Sternheimer, R.M., et al.: “The Density Effect for the Ionization Loss of Charged Particles in Various Substances”, Atomic and Nuclear Data Tables, 30, p. 261 (1984). See also Groom, D.E., et al., ibid 78, pp. 183Ð356 (2001) and Ivanov, D.Yu., et al.,: Phys. Lett. B, 442, p. 453 (1998) for corrections. Swider, W., and M.E. Gardner: Environmental Research Papers No 272, Air Force Cambridge Research, Bedford, MA (1967). Tsai, Y.S.: Rev. Mod. Phys., 46, p. 815 (1974). Wilczynska,« B., et al.: PICRC, 7, p. 203 (2005). Appendix C List of Symbols

Table C.1 Roman symbols used in this book a Length, distance Parameter A Area Atomic weight or mass Mass number Parameter b Length, distance Parameter B Magnetic induction Parameter, general constant, background c Velocity of light in vacuum C Constant, parameter D Distance, separation e Electric charge of the electron e− Electron E0 Initial or primary energy of a particle Es Scattering energy ER Elongation rate f (dN) Differential shower size spectrum F(N) Integral number or size spectrum FWHM Full width at half maximum of pulse G(ρ) Shower density spectrum h Height (vertical) or altitude in atmosphere hs Scale height of atmosphere H Magnetic ﬁeld strength H Humidity I Intensity I (N) Differential spectrum I (> N) Integral spectrum J Flux, integral spectrum, k Constant, scale factor K Inelasticity Azimuthal asymmetry ratio (geomagnetic) Constant, normalizing -, scale factor l Length, element of L Distance, scattering length

1087 1088 C List of Symbols

Table C.1 (continued)

me Rest mass of electron M Coincidence fold M0 Azimuthal asymmetry factor Primary mass n Index of refraction Exponent, secondary particle multiplicity N All-particle shower size NA Avogadro’s number Nch Charged particle shower size Ne Electron shower size Nμ Muon shower size p Momentum pl Longitudinal momentum pt Transverse momentum P Pressure Q Cherenkov photon density (visible) r Radius, radial distance re Classical electron radius R Rate of events Radius, radius of nucleon, radial distance Radial distribution function (of Cherenkov photons) s Age parameter of air showers Center of mass energy squared S Magnetic rigidity Path length Sensitivity t Time Thickness (of target, air, etc.) in radiation units td Delay time t f Fall time of a pulse tr Rise time of a pulse tt Top time of a pulse T Temperature of atmosphere, etc. veμ/m2 Vertical equivalent muons per square meter (for deﬁnition see Blake et al., ICRC 8, p. 189, 1977) x Distance, path length X Column density, atmospheric, underground, etc. Xs Slant depth, atmospheric, underground Xmax Depth of shower maximum in atmosphere X0 Vertical atmosperic column density at sea level y Rapidity Y Yield Z Atomic number, atomic charge C List of Symbols 1089

Table C.2 Greek symbols used in this book α Fine structure constant Barometric coefficient of air showers Decoherence exponent β Temperature coefficient of air showers Velocity divided by velocity of light, v/c χ0 Radiation length, cascade unit χa Radiation length in air δ Angle Δ Increment c Critical energy (of electrons) η Elasticity φ Azimuthal angle γ Exponent of spectra (size, number, density, etc.) Γ Exponent of integral primary spectrum κ Ratio, signal-to-noise λ Geomagnetic latitude Optical wavelength λabs Absorption length of shower particles λμ abs Absorption length of muons in showers λint Interaction mean free path (i.m.f.p.) λN int Interaction mean free path of nucleons λπ int Interaction mean free path of pions Λatt Attenuation length of air shower rate μN Attenuation coefficient of air shower rate μp Absorption coefficient of shower particles ρ Particle or photon density Radius of curvature of charged particle In magnetic field σ Cross section Standard deviation ± σ0 Total e pair production probability σinel Inelastic cross section σ p,air inel Inelastic proton-air cross section σint Interaction cross section θ Zenith angle Angle of emission ξ Angle Function ζ Constant related to the cascade unit

Appendix D Abbreviations and Acronyms

The following table contains a partial list of frequently used abbreviations and acronyms of experimental sites, installations, experiments and instruments.

Table D.1 List of abbreviations and acronyms AGASA Akeno Giant Air Shower Array (Japan) AIRES AIR shower Extended Simulation AMANDA Antarctic Muon and Neutrino Detector Array ANITA Antarctic Impulsive Transient Antenna experiment ASICO Air shower SImulation and COrrelation BLANCA Broad Lateral Non-imaging Cherenkov Array CASA Chicago Air Shower Array (Dugway, Utah, USA) CERN European Center for Particle Physics (Geneva, CH) CMBR Cosmic Microwave Background Radiation CORSIKA COsmic Ray SImulation for KAscade CREAM Cosmic Ray Energy And Mass experiment DICE Dual Imaging Cherenkov Experiment (Dugawy, USA) DPM Dual Parton Model EM Electro-Magnetic EPOS Energy Parton Off-shell Splitting (MC simulation) FNAL Fermi National Accelerator Laboratory (Chicago, USA) FORTE Fast On-orbit Recording of Transient Events FWHM Full Width at Half Maximum GLUE Goldstone Lunar Ultrahigh energy neutrino Experiment GRAPES Gamma Ray Astronomy at PeV EnergieS (Ooty, India) GZK Greisen-Zatsepin-Kuzmin cutoff HAS Horizontal Air Shower HEGRA High Energy Gamma Ray Astronomy (Canary Islands) HESS High Energy Stereoscopic System (Namibia) HSA Hillas Splitting Algorithm IC Inverse Compton scattering ISR Intersecting Storage Ring (CERN, Geneva, Switzerland) KASCADE KArlsruhe Shower Core and Array DEtector (Germany) KNO Koba-Nielsen-Olesen scaling LAAS Large Area Air Shower experiment (Japan) LANL Los Alamos National Laboratory (NM, USA) LAP Local Age Parameter, Lateral Age Parameter LDF Lateral Distribution Function

1091 1092 D Abbreviations and Acronyms

Table D.1 (continued) LEP Large Electron Positron collider (CERN, Geneva, CH) LHC Large Hadron Collider (CERN, Geneva, Switzerland) LPM Landau Ð Pomeranchuk Ð Migdal effect LVD Large Volume Detector (Gran Sasso, Italy) MACRO Monopole Astrophysics Cosmic Ray Observatory (Italy) MC Monte Carlo method MIA MIchigan Array (Dugway, Utah, USA) MOCCA MOnte Carlo CAscade simulation program NKG Nishimura Ð Kamata Ð Greisen Ð function NTP Normal Temperature and Pressure OWL Orbiting Wide-angle Light collector QGS Quark Gluon String RHIC Relativistic Heavy Ion Collider (Brookhaven, USA) RICE Radio Ice Cherenkov Experiment (Antarctica) SHALON Russian abbr. for “EAS from Neutrinos” (Tien Shan) SIBYLL MC event generator SPS 300 GeV Super Proton Synchrotron (CERN, Switzerland) TACTIC TeV Atmospheric Cherenkov Telescope with Imaging Camera TRACER Transition Radiation Array for Cosmic Energetic Radiation TTC Time-Track-Complementarity VERITAS Very Energetic Radiation Imaging Telescope Array System (Whipple Observatory, Arizona, USA) Appendix E List of Cosmic Ray Conferences

1. Cracow, Poland 1947 17. Paris, France 1981 2. Como, Italy 1949 18. Bangalore, India 1983 3. Bagneres de Bigorre, F 1953 19. La Jolla, Ca., USA 1985 4. Guanjuato, Mexico 1955 20. Moscow, U.S.S.R. 1987 5. Varenna, Italy 1957 21. Adelaide, Australia 1990 6. Moscow, U.S.S.R. 1959 22. Dublin, Ireland 1991 7. Kyoto, Japan 1961 23. Calgary, Canada 1993 8. Jaipur, India 1963 24. Rome, Italy 1995 9. London, England 1965 25. Durban, South Africa 1997 10. Calgary, Canada 1967 26. Salt Lake City, USA 1999 11. Budapest, Hungary 1969 27. Hamburg, Germany 2001 12. Hobart, Tasmania, Aus. 1971 28. Tsukuba, Japan 2003 13. Denver, Co., USA 1973 29. Pune, India 2005 14. Munich, Germany 1975 30. Merida, Mexico 2007 15. Plovdiv, Bulgaria 1977 31. Lodz, Poland 2009 16. Kyoto, Japan 1979 32. Beijing, China 2011

1093

Index

A detection of showers, 14 Absorption radiation of showers, 4, 176 atmospheric optical, 862, 892 Air density effect, 281 of Cherenkov light, 862 on shower of fluorescence light, 892 development, 255, 1031 of photons, total, 149 Air fluorescence, 165, 195 of shower particles, 249 absorption, 892 Absorption coefficient detection of showers, 14, 39 and energy loss spectra, 666 scattering, 892 of shower particles, 247, 249, 1010 of showers, 4, 39, 176 and water tank spectra, 666 Air scintillation, 14, 879 Absorption length see fluorescence 879 of shower particles, 178, 247, 249, 1010 Air shower parameters accessibility, Acceleration of cosmic rays, 570 determination, 51 Accelerators, 81 Air shower simulation, 419, 422, 441, 459, Accuracy of 470, 988 arrival direction, 55 program architecture, 996 celestial coordinates, 555 AIRES simulation code, 131 core location, 56 Akeno experiment, 375, 387, 431, 627 Acoustic detection of Aligned events, 982 air showers, 46 All-particle primary spectrum, 12, 504 cascades in water, solids, 46 Altitude dependence of neutrinos in water, ice, 46 shower development, 252 Active galactic nuclei shower rate, 252, 255, 266 AGN, 497, 499, 568, 570, 571 shower size, 252 Aerosols in atmosphere, 864 Analytic treatment of cascade theory, 179 AGASA experiment, 371, 387, 431, 627, 909 Angular accuracy of zenith angle, 403 plastic scintillation detectors, 70 Anisotropy, 551, 562 Age dependence of cosmic radiation, 552 azimuthal, 381 data, 557 of density spectrum, 647, 653 ANITA experiment, 925 of lateral distr. fct., 374 Ankle in Age parameter, 9, 197, 251, 464, 1010 primary spectrum, 11, 12, 615 lateral, 461, 468 size spectrum, 615 longitudinal, 460 Ankle spectral indices, 504 Air Annomalous nuclear enhancement, 732 composition, 153 Anti-sidereal time, 563 radiation length, 153 Antihyperons, 96 Air Cherenkov Antimatter, 488

1095 1096 Index

Antinucleons, 404, 721 seasonal variations, 336 predicted in air showers, 995 mixing equilibrium, 1075 production neutrinos, 24, 497 at accelerators, 995 overburden, 1012 in showers, 8, 96, 119, 711, 721, 995 scale height, 1029, 1076, 1081 Approximation slant depth, 1012 A, 179, 181, 183, 1011 temperature profile, 1075, 1076 B, 180, 181, 190, 1011 thickness, 254, 1012, 1076 C, 1011 v/s zenith angle, 1081 ARGO experiment, 37 transmission, optical, 883, 896 Array acceptance, efficiency, 58 Atmospheric fluorescence, 879Ð910 Array layout, 35 primary mass estimation, 905 Arrival direction Atomic excitation, 159 of cosmic rays, 552 Attenuation of showers atmospheric optical, 862 determination, 54, 403, 424 of Cherenkov light, 862 errors, 55 of fluorescence light, 895 Arrival time profile of cosmic rays of showers, 15, 402 in atmosphere, 84 ASICO program system, 127, 993 unaccompanied, 85 Astronomical unit, AU, 1012 of photons, total, 149 Astrophysical neutrinos, 496 of shower rate, 249 Asymmetry of shower arrival Attenuation coefficient, 253 azimuthal, 1013 of shower rate, 247, 249, 1012 Atmosphere, 1073 Attenuation length in atmosphere characteristic of hadron rate, 108 data, 1073 of nucleon rate, 248 relations, 1073 of protons, 261 COSPAR, 1077 of shower rate, 247, 249, 1013 reference, 1078 Auger experiment, 16, 41, 49, 56, 387, 631, tabulated, 1078 664, 668 of curved Earth, 1081 Avogadro’s number, 1013 Chapman function, 1081 Azimuthal angle, 7 depth v/s altitude, 1077 Azimuthal asymmetry effect, 7, 1013 elemental composition, 1073 Azimuthal asymmetry of particle distribution, exponential 35, 378, 380 isothermal, 1077, 1080 Azimuthal dependence of real, 1076 absorption length, 434 standard, 1073 age parameter, 460 U.S., 1077 Azwidth, 860 static, isothermal, 1075 Atmospheric B absorption, optical, 895 Background attenuation, optical, 895 optical, of night sky, 892 Cherenkov radiation, 836 radiation, 162 detection of showers, 38 2.7 K CMBR, 167 emission by showers, 38 radio emission, data, 928 column density, 254, 1012, 1076 Balloon experiments, 83 for curved Earth, 1082 Bandwidth of recording system, 319 v/s zenith angle, 1082 Barometer formula, 6, 1081 depth, 1012 Barometric effects, 336 coefficient, 256, 1014 geographic dependence, 336 effect, 10, 255, 256 Index 1097

data, 277 electronic component, 828 on muons, 279 muons, 779 on shower development, 238 Charged particle multiplicity, 95 on shower rate, 238, 256 Charm, discovery, 13 law, 1075 Charmed particles, 136 Bethe-Bloch formula, 1072 production, 131 Bethe-Heitler in showers, 723 diagram, 208 Cherenkov formula, 169 angle, 838, 1015 BLANCA experiment, 627 aperture, 23 Blazars, 568 calorimetry, 836, 854 Blazer-like source, 572 density spectra, 660, 667, 874 Boltzmann andenergyloss,667 distribution, 80, 120 at fixed core dist., 667 law, 103, 116 detection Bottom-up models, 570 at ground level, 23 Bremsstrahlung, 174 min. primary γ energy, 23 Coulomb, 148, 151, 155 event reconstruction, 321 magnetic, 148 gamma ray astronomy, 837 medium, 836, 839 C index of refraction, 839 Calorimeters, 108 relation, 837 Calorimetric method, 115 ring effect, 844 CASA-MIA experiment, 627 wavelength, 1015 Cascade Cherenkov imaging, 22 phenomenology, 176 Azwidth, 860 structure function, 180 Miss parameter, 860 unit, 151, 1014 parameters, 861 Cascade theory of showers, 844 analytic treatment, 179 stereo technique, 862 approximation A, 175, 179 system, 837 approximation B, 175, 180 technique, 858, 859 one-dimensional, 176 Cherenkov light three-dimensional, 180 detectability, 864 Celestial coordinates accuracy of determina- minimum flux, 865 tion, 555 emission angle, 837, 844 Centauro events, 115, 981 maximum angle, 838 Central processes, hadronic, 98 fluctuations, 22, 325 CERN front ISR, 80 arrival time, 321 LHC, 81 curvature, 321, 852, 871 pp collider, 82 photon density, 667 Chacaltaya experiment, 618, 640, 836, 846 pulse Chapman function, 254, 1012, 1014, 1076, arrival profile, 316, 836, 849 1081 shape, 322, 849, 850, 871 Characteristic scale radii, 380 substructures, 850 Characteristics of gamma ray showers, 20 Cherenkov radiation, 148, 165, 835 Charge in air showers, 842 asymmetry in showers, 383 angular distribution, 846, 865 exchange, 107 atmospheric, 195 separation, 35 absorption, 862 symmetry, 80, 916 attenuation, 862 Charge ratio of coherence condition, 839 1098 Index

coherent radiation, 835Ð837 CKP correlations between formula, 1015 observables, 857 model, 118, 119 discovery, 835 emission angle, 121 energy Classification of nuclei, 88, 482 fraction of shower, 420 Cloud chambers, 62, 684, 690, 699, 711, 718 loss of shower, 840 CMBR, 167 radiated by shower, 840 CODALEMA, 925, 937 environmental aspects, 864 Coherence effects in radio emission, 927 fundamental process, 837 Colliders, 81 historic, 835 Collision de-excitation of air molecules, 882 lateral Column density, 6 distribution, 846, 865 atmospheric structure function, 836, 867 inclined, 254 longitudinal development vertical, 1080 in showers, 844 Competition interaction/decay, 135 in nuclear emulsion, 874 Composition of optical emission, 839 atmosphere, chemical, 1073 phenomenology, 837 primary radiation, 528 photon number shower particles, 9 radiated, 840 Compton total in shower, 854 absorption, 149, 160 polarization, 837, 839, 852 cross section, 161 primary energy effect, 147, 160 estimation, 853 inverse scattering, 167 properties scattering, 19, 78, 149, 160, 161, 174 in atmosphere, 1084 of electrons, 78 radio Compton-Getting effect, anisotropy, 558, 562, emission, 836 565 frequency, 839 CONEX hybrid simulation progr., 1005 relative contribution to Constant intensity cuts, 238 fluorescence, 885, 897 Constants of materials, 1069 shower profile, 847 Conventional acceleration, 568 signal/noise ratio, 864 Conversion factors size-primary energy, 438 single particle, 837 Coplanar events, 982 yield, 862 Core angle measurements, 783 spectral Core angle of muons, 783, 787 distribution, 840, 841, 852 Core location temporal determination, 424 properties, 836, 849, 871 errors, 56 theory, 836, 837 method, 56 visible, 839 Core structure, 723, 725 X-ray emission, 839 multi-core, 8, 725 yield, 840 single-core, 8, 723 Cherenkov telescope, 860 Correlated showers, 28, 971 Cherenkov threshold Correlations, 949 energy long distance (LAAS) for μ± in air at NTP, 23 angular correlated events, 971 for e± in air at NTP, 23 time correlated events, 971 for p p in air at NTP, 23 miscellaneous, 966 in water, air, 368, 1085 Ne − Nμ, 950 velocity Ne − Nh , 957 of charged particles, 838 Correlations between Index 1099

interaction observables, 113, 419 Declination, 552, 564 shower observables, 419, 949 definition, 1016 CORSIKA program system, 127 Decoherence, 650, 979, 1016 Cosmic microwave background radiation measurements, data, 979 (CMBR), 167 rate, 257 Cosmic rays experimental sites, 1039 spectrum, 650 Coulomb scattering, 148, 384 Deep water Cherenkov detectors, 36, 57, 67, multiple 368, 425 of electrons, 158 Deficit of muons, 79 of hadronic energy, 720 Crab Nebula, 496 in showers, 720 gamma ray source, 495 Delayed particles Critical altitude of pions, kaons effect on density meas., 392 in atmosphere, 137 effect on primary Critical energy, 154, 177 energy estimation, 438 of electrons, 154, 1015 Delta-rays, 159, 1016 of elements, 1069 Density effect of gamma rays, 154 atmospheric, 1014 of gaseous media, 154 on showers, 255, 256, 1031 table of media, 1071 of ionization, 160 Critical field strength for Density fluctuations of particles, 58 magnetic bremsstrahlung, 171 Density measurements, 367 magnetic pair production, 171 lateral, accuracy, 372 Cross sections optimization, 431 A − A, 85 Density measurements using K − A, 85 ionization chambers, 367 N − A, 85 proportional counters, 367 N − Air, 83 scintillation detectors, 367 N − N, 82 Density of media table, 1071 p − p, 82 Density spectrum, 646, 1016 p − p, 82 at fixed core dist., 662 π − A, 85 change of slope, 648 π − Air, 83 of charged particles, 650 π − N, 82 Depth of geometric nuclear, 1016 shower maximum, 284, 303, 311, 325, 328, hadronic 346, 457, 847, 1017 energy dependence, 81 fluctuations, 354 inclusive, invariant, 123 in atmosphere, 4 Cryptons, 547 under approx. A, 196 Curvature under approx. B, 197 of muon front, 777 Derived observables, parameters, 419 of shower front, 400, 403 Detector age dependence, 468 response, 61, 367, 370 Curvature radiation, 148, 171 to charged particles, 389 Curved Earth atmosphere, 254, 1012, 1076 saturation, 366, 373 Cutoff energy of cascades, 197 transition effects, 61 Cygnus X-3, 550 DICE experiment, 627 distance, 550 Diffraction dissociation, 125 D hadronic, 98 Dark matter, 481 Diffractive interactions, 101 cold dark matter, 547 Diffuse gamma radiation, 22, 492 Decay length of unstable particles, 136 Diffusion equations 1100 Index

electromagnetic pair production, 19, 149 in atmosphere, 180 Coulomb, 157 nucleonic, 136 magnetic, 171 in atmosphere, 108 shower size spectrum, 614 of cascade theory, 180 Electron number solutions, 183 at shower maximum, 197 Diffusive shock acceleration, 523 approx. A, 197 Direct pair production Electron-hadron correlation, 957 of electrons Electron-muon correlation, 950 by muons, 214 Electron-photon component, 803 of muons charge ratio, e−/e+, 828 by muons, 219 density ratio e±/γ , 828 Dissociation nuclear, in space, 162 energy flow density, 825 Distribution functions array specific, 387 e± − γ energy ratio, 828 Diurnal variation, 1017, 1031 energy spectra Double-bang ντ signature, 27 measured, 824 DPMJET simulated, 822 event generator, 131 lateral distribution, 806 model, 131 Greisen, 806 Duller-Walker plot, 116 Lagutin, Uchaikin, 808 DUMAND project, 47 measured, 810 Dust grain hypothesis, 27 simulated, 809 of showers, 27 theoretical, 806 number ratio, e±/γ , 828 E temporal properties, 831 Earth’s atmosphere Elementary particles curved Earth, 254, 1012, 1081 discoveries, 13 flat Earth, 255, 1014, 1076 in cosmic rays, 13 EAS-TOP experiment, 700, 1066 Elongation, 243 East-west effect, 563 Elongation rate, 6, 243, 284, 303, 407, 457, Effective radiation length 1017 for magnetic data summary, 340 bremsstrahlung, 172 definition, 304 pair production, 172 Emission angle EGRET data, 493, 546 Cherenkov, 837 Elasticity, 106 in CKP model, 121 definition, 106 emission angle determination, 106 Cherenkov, 844 energy dependence, 109 Emission radio in showers, 913 of hadronic collisions, 106, 240, 723 Emulsion indirect determination, 108 chambers, 98, 685, 711 mass dependence, 110 experiments, 115 of π N-collisions, 108 nuclear, 85 of NN-collisions, 107 composition, 1072 of nucleons, 248 stacks, 98 Electromagnetic Energy dependence of cascades, 4 pt , hadronic, 80 theory, 174 cross sections, 80 component, 683 multiplicity, 97 interactions, 147 Energy deposit of sub-cascades, 174 shower particles in Electron atmosphere, 245, 246, 366 initiated showers, 17, 23 detectors, 386 Index 1101

scintillators, 71 Equal intensity water detectors, 69, 390 all-particle data, 288 Energy estimation recent measurements, 292 primary, using curves, 238 Cherenkov rad., 440, 853 cuts, 252, 305 energy loss density, 367 distributions, 284, 305 fluorescence, 905 method, 285 muon size, 438 muon data, 294 shower size, 371, 431 Equilibrium of truncated muon number, 438 electrons and hadrons, 735 Energy estimator, primary, 370, 425 Eμ · rμ product, 784 Energy flow, 385 EUSO, JEM-EUSO distribution, 191 experiment, 16, 26 in EM cascades, 190 Event generators hadronic, 118, 127, 129 of particle types Event-source correlations astrophysical, 571 in showers, 363 Excitation, atomic of fluorescence, 148 in showers, 370, 385 Exclusive lateral distrib., 385 cross section, 1018 of EM-component, 385 reaction, 1018 Energy fraction of Extra-terrestrial neutrinos, 481 Cherenkov rad. of shower, 420 Extragalactic fluorescence of shower, 420 cosmic rays, 13, 506, 521, 524, 572 Energy loss gamma rays, 19, 496, 546 by bremsstrahlung, 156 magnetic fields, 554 density, 369, 663, 665 origin calibration, units, 664 of cosmic rays, 480 definition, 665 sources, 572 of muons, 208 in dense media, 208 F in standard rock, 213 Feynman parameter, 665 graphs, 208 of showers, 665 scaling, 99, 103, 1004 spectra, 662, 665, 666, 1018 hypothesis, 1030 spectra of model, 123 particles ρ(xxx) data, 667 variable x, 123, 1018 photons Q(xxx) data, 667 Fireballs, 117 surface density, 663 First arriving particles, 403, 408 via synchrotron rad., 17 First interaction in atmosphere Energy of electrons height, depth, 4, 239, 457, 470, 844 in showers, average, 387 Fluctuations, 39, 242, 663 Energy partition among secondaries, 96 energy dependence, 240 Energy release of shower particles in in detection of atmosphere, 366 Cherenkov photons, 39 Energy spectrum in showers particles, 39 of electrons, 185, 822 in E.A.S., 1018 of hadrons, 699 non-Poissonian in of muons, 767 Cherenkov light, 39 of photons, 185, 822 of Cherenkov light, 325 Energy splitting method in simulations, 131, of Cherenkov photon flux, 22 1004 of first interaction, 471 Energy-size relationship, 239 of longitudinal dev., 239 Environmental effects on showers, 255 of multiplicity, 100 EPOS event generator, model, 131 of muon component, 793 1102 Index

of observables, 240 concept, 883 of particle density, 58, 370, 372 hemispherical, 879 of particle shower front, 331 optimization, 908 of Xmax distrib., 340, 346 trigger criteria, 906 energy dependence, 354 Fluorescence quenching, 889 FLUKA by collision, 889 event generator, 129 de-excitation, 882 model, 129 Fluorescence yield, 884, 886 Fluorescence accelerator data, 885 atmospheric, 879 electron beam data, 885 basic concept, 879 modern data, 885 basic data, 882, 885 old data, 882 calorimetry, 881 α particle beam data, 882 Cherenkov per MeV, 882 background, 896 photon yield, 882 relative contribution, 897 spectral distribution, 882 decay time, 882 Fly’s Eye experiment, 883 emission FNAL Tevatron collider, 82 isotropic, 879, 881 Fokker-Planck approximation, 180 energy fraction of shower, 420 Fractional energy, 156 energy loss in showers, 882 losses, electromagnetic, 160 fluctuations, 881 Fragmentation, 89 light transmission in formulas atmosphere, 883, 895, 896 semi-empirical, 89 light, emission, 879 of heavy primaries, 8 molecular collision total, 664 de-excitation, 882 limiting, 125 night sky background, 883 nuclear, 98 primary energy total, 664 estimation, 905 parameters, 90 primary mass region, 84, 307 estimation, 905 in space scattering of dust, 28 in atmosphere, 883 of nuclei, 28 shower Fragments of primary nuclei, 6, 106, 724, detection, 900 726Ð728 profile, 903 reconstruction, 900, 903 G signal level, 901 Gaisser-Hillas function, 904 signal to noise, 883, 884 Galactic spectrum, 882 clusters, 570 time structure, 901 cosmic rays track length, 883 lifetime, 89 trajectory, 902 leakage, 11 image, 883 magnetic fields, 553 Fluorescence detection, 882, 884 rigidity disadvantages, 881 confinement, 11 stereo, 881 Gamma ray threshold, 881 absorption Fluorescence detectors in space, 19, 165, 577 all-sky, 885 astronomy, 22, 480, 495, 575 aperture, 906 background, 858, 861 calibration, 908 Cherenkov technique, 837 Index 1103

early history, 859 H ground based, 858 H.E.S.S. telescopes, 569 bursters, GRB, 499 Hadron Cherenkov telescope, 861 astronomy, 553, 572 diffuse flux, 22, 492, 858 calorimeters, 687, 700, 711 galactic sources, 857 at EAS-TOP, 691 point sources, 22, 495, 858 at KASCADE, 691 primaries, 857 cascades, 133 showers, 17, 162, 326, 543, 857 analytical treatment, 137 characteristics, 20 Monte Carlo method, 991 Gamma ray/charged ratio, 80 charged/neutral (C/N) ratio, 711 Gamma ray/hadron ratio primary, 548 content in showers, 715 Gamma rays from Cygnus X-3, 550 high energy, 718 GEANT4 event generator, model, 130 low energy, 716 Geiger counter, 62 cross sections, 81 Genetic shower parameters, 794 energy spectra in showers, 699 Genetics of muons, 794 initiated showers Geo-synchrotron radiation, 925 characteristics, 3 Geoelectric lateral distribution, 688 charge separation, 922 temporal properties, 707 radio emission, 922 Hadron-N interactions, 108 Geomagnetic Hadron-muon cascade, 242 charge separation, 919 Hadron-Pb interactions, 108 deflection, 324, 326, 333 Hadronic effects, 35, 255, 319 collisions on lateral distribution, 383 elasticity, 106 on muons, 779 inelasticity, 106 field, 55 leading particle effect, 106 radio emission interactions, 77 by charge separation, 919 Hadrons, unaccompanied, 711 Geometric effect temperature related, 257, 282 Hagedorn model, 119, 726 Geometric relations of cross sections, 86 Half law of multiplicity, 99 GHEISHA, 1005 Halo events, 982 event generator, model, 130 Hard component, 9, 237, 683, 1018 Glauber theory, 84, 107, 109 Harmonic analysis Global time reference in shower disc, 401 of anisotropy Gluons, 127 of cosmic radiation, 555 Gran Sasso underground exp., 50 Haverah Park Greisen type detectors, 367 electron-photon component properties, 67, 368 lateral distribution, 806 water Cherenkov detectors, 67 Greisen formula for muons, 744 Haverah Park experiment, 367, 387, 631, 640, Greisen-Zatsepin-Kuzmin (GZK) cutoff, 11, 663, 667 162, 504, 573 layout, 1052 Gribov-Regge concept, theory, 127 HDPM event generator, model, 130 Gross transformation, 268, 1018, 1082 Heavy primaries, 8, 242 Ground parameter fragmentation, 8 ρ(600), 429 HEGRA experiment, 48 ρ(xxx), 666 layout, 1052 Grouping of primaries, 88, 482 Height of first interaction, 457, 470 Growth rate of cascades in atmosphere, 4, 239, 240, 844 EM, 174, 180, 185 Height of origin, production of hadronic, 240 hadrons, 727, 734 1104 Index

muons, 403, 412, 783, 787 of NN-interactions showers, 463 in CKP model, 120 Height of shower max., 4, 240, 284, 303, 457 of pp interactions, 109 Heitler model, 132 of p-air interactions, 109 High energy Integral operators, 181 interaction models Interaction early models, 115 length of unstable particles, 136 modern models, 127 mean free path, 6, 80, 88, 108, 1019 HiRes Fly’s Eye, 885 models, 129 Historical overview of cascade theory, 175 Intergalactic medium, 570 Homosphere, 1073 International Reference Atmosphere COSPAR, Horizontal 1078 air showers, 10, 26, 213, 742, 976 Interstellar muon intensity, 978 dust, 28 neutrino intensity, 978 medium, 89 HSA model, algorithm, 131 Invariant Humidity effect, 257, 281 cross section, 1020 on shower development, 255 of HE interactions, 80 Hybrid inclusive cross section, 123 data, 518, 519 Inverse Compton experiments, 342, 351, 527 energy boost, 167 reconstruction, 41 scattering, 17, 24, 148, 167, 487 Hybrid method Ionization, 148 calorimeter, 83 of Xmax determination, 333 of EAS simulation, 176, 179, 195, 1004 detection by RADAR, 42 of shower detection, 48, 548 loss in air, 1021 Hyperons in showers, 96 losses logarithmic rise, 159 of atmosphere I by micro meteorites, 43 IceCube experiment, 51 potential, 160 Imaging technique Cherenkov, 22, 858 Isobar-fireball model, 119, 122 Inclined showers, 976 Isobars, 98 Inclusive cross section, 103, 1019 J reaction, 1019 JEM-EUSO experiment, 26 Index of refraction, 1019 Johnson noise, 928 in atmosphere versus altitude, 841 K of air, 841 Kahn and Lerche theory, 914, 917, 919, 921 of water, 841 Kaon-nucleus cross sections, 85 Inelastic cross sections, 81 Kaon/pion ratio, 116 Inelasticity, 80, 95, 106, 116 Kaons in showers, 723 average, 107 KASCADE experiment, 631, 700, 942 definition, 106 KASCADE-Grande experiment, 642 determination, 106 KGF experiment, 748, 1067 distribution, 107 Kinematic regions, 102 energy dependence, 80, 107, 109 Kinematics of secondaries, 102 fluctuations, 107 Klein-Nishina of hadronic collisions, 106, 240, 723 cross section, 161 indirect determination, 108 formula, 167 mass dependence, 110 Knee of π N interactions in density spectrum, 647, 648, 654 in CKP model, 121 in muon size Index 1105

spectrum, 504, 639 Rayleigh, 894 in primary Light transmission spectrum, 11, 504, 615, 634 in atmosphere, 895 in shower size spectrum, 615 Light year, definition, 1023 second spectral knee, 504, 615 Limiting fragmentation, 125 KNO scaling, 101 hypothesis, 1023 Knock-on electrons, 159 model, 119 Local time reference in shower disc, 401 L LOFAR, 925, 937 LAAS type experiment, 973 Logarithmic law of multiplicity, 99 LAAS/ARPEGIO experiment, 28 Logarithmic rise of ionization loss, 159 Lagutin distribution, 808 Long baseline experiments, 28, 971 Landau approximation, 180, 182, 1021 Long distance (LAAS) Landau-Pomeranchuk-Migdal angular correlated events, 971 effectsee LPM-effect 148 time correlated events, 971 Large pt and multi-core showers, 242 Long-flying component, 275, 982 Lateral Longitudinal age parameter, 461, 468 development, 4, 177, 196, 237, 238 distribution function direct observation, 40 array specific, 387 LPM effect, 195 LDF, 191, 359, 1021 pre-showering, 195 shower shower age, 460 development, 4 LOPES, 925, 937, 942 structure function, 359 LPM effect, 148, 168, 169, 242, 343, 1021 spread of criterion, 170 EM-cascades, 158 Lund model, 131 all shower particles, 360 LVD experiment, 748, 1066 electrons, photons, 158 Lateral distribution of M all shower particles, 198, 373 MACRO experiment, 748, 1066 Cherenkov photons, 392 Magnet spectrometers, 49, 50, 685, 723 electrons and photons, 192 Magnetic energy flow, 385 bremsstrahlung, 148, 168, 171 hadrons, 688 cloud chambers, 702, 714 muons, 743 deflection, 1023, 1028 Leading of charged particles, 553 nucleon, 106 of protons from Cygnus, 553 particle, 96, 106, 723 of shower particles, 384 effect, 102, 106, 240, 723 pair production, 19, 148, 168, 171 pion, 107 rigidity, definition, 1029 LHC, 14, 81, 243 Markarian 421 LIDAR system, 909 gamma ray point source, 496 Lifetime MARS spectrometer, 752 of cosmic rays, 89 Mass absorption in Galaxy, 89 coefficient, 1023 Light absorption length, 1023 in atmosphere, 895 of showers, 256 of fluorescence, 895 Mass attenuation Light scattering coefficient, 1023 in atmosphere, 894 of photons, 149 Mie, 894 length, 1023 on aerosols, 894 Mass classification of primary nuclei, 88, 482 on air molecules, 894 Mass composition of primary radiation, 528 1106 Index

Mass estimation superposition, 664 primary using thermodynamic, 119 atmos. Cherenkov rad., 849 UrQMD, 130 atmos. fluorescence, 905 VENUS, 131 Mass related temporal features, 453 Molecular Maximum development of collision de-excitation, 882 γ initiated shower, 189 effect on radiation length, 153 e± initiated showers, 189 Moliere` hadron initiated showers angle, 193 (see also Xmax), 346 distribution, 1024 showers in atmosphere radius, 191, 192, 199, 253, 807, 1024 atmos. depth, 4 scattering theory, 180, 182, 192 height a.s.l., 4 unit, 191, 1024 Mesopause, 1075 Moliere` radius for Mesosphere, 1075 electrons and photons, 380 Micro meteorites atmospheric ionization, 43 hadrons, 380 Mie scattering in atmosphere, 862, 894 muons, 380 Milagro experiment, 37 Momentum spectra of Mini-jet muons, 767 model, 127, 131 Monte Carlo production, 131 method, 176, 194 Minimum detectable simulation air Cherenkov flux, 865 of air showers, 991 air fluorescence flux, 884 Most energetic events, 559 Minimum ionization, 159 Multi-core showers, 8, 104, 242, 725, 727 Miss parameter Multi-dimensional cascade simulations, 194 in Cherenkov imaging, 860 Multi-muons, 790 Missing energy in showers, 983 Multi-particle production, 119 MOCCA code, 132 Multi-peripheral model, 104, 119, 727 Models Multiple Coulomb scattering, 158, 191, 1025 CKP, 118 Multiplicity, 116 DPMJET, 131 average v/s energy, 97 EPOS, 131 dependence on Feynman scaling, 123 energy, 97, 98 fireball, 118 projectile mass, 100 first generation (old), 118 target mass, 100 FLUKA, 129 distribution, 100 GEANT4, 130 negative binomial, 101 GHEISHA, 130 hadronic Hagedorn, 119, 726 energy dependence, 98 HDPM, 130 in isobar-fireball model, 122 of high energy in scaling model, 124 interactions, 115, 127 laws, 99 isobar-fireball, 119, 122 of secondary particles, 95 limiting fragmentation, 119 Multivariate distributions, 454 multi-peripheral, 119, 727 Muon NEXUS, 131 absorption of particle production, 129 data, 265 catalog of, 129 in atmosphere, 265 QGSJEST, 131 in showers, 265 scaling, Feynman, 119 bremsstrahlung, 26, 79, 211 SIBYLL, 131 bundles, 790 statistical, 119 charge ratio, 779 Index 1107

core angle, 327, 783, 787 Negative binomial distribution of multiplicity, density spectrum, 659 101 equilibrium in showers, 79 Negative charge excess, 917 families, 790 Cherenkov radio emission, 917 flux in showers, 79 Neon hodoscope, 684, 810 genetics, 794 Neutral particles in primary radiation, 551 pair production, 19, 148, 164, 207 Neutrino population in showers, 79 astrophysical, 496 size spectrum, 639 diffuse flux, 499 timing, 783 from supernova, 496 tracking, 752, 783, 789 initiated showers, 24, 500, 976 triangulation, 742, 783 opaque Earth, 233 tridents, 219 oscillations, 27 Muon Eμ · rμ product, 784 point sources, 25, 497, 499 Muon energy production, cosmic, 18 determination via reactions energy loss, 774 in air, 24, 227 spectrometric methods, 767 in ice, 24 losses, 208 in rock, 24 by atomic excitation, 208 in water, 24, 227 by bremsstrahlung, 208 in showers, 9 by direct pair prod., 208 solar, 496 by ionization, 208 sources by photonuclear proc., 209 model predictions, 499 in atmosphere, 742 Neutron Muon front curvature, 777 monitors, 78, 685, 716 Muon induced background multiplicity underground, 213 in detectors, 716 Muon-hadron correlation, 966 stars, 570 Muon-poor showers, 23, 26, 163, 275, 276, Neutrons in showers, 8 857, 979 New particles, 551 Muon-rich showers, 979 NEXUS event generator, model, 131 Muons NEXUS model, 127 in dense media Night sky energy loss, 208 brightness survival probability, 208 fluctuations, 22 energy, momentum spectra, 767 luminosity, 862, 892, 893 experimental optical backgr., 836, 862, 883 lateral distributions, 747 airglow, 893 in gamma ray showers, 546, 547, 551 atmospheric Cherenkov, 896 general properties, 741 Nishimura-Kamata-Greisen (NKG) height of origin, 789 distribution, 179, 191, 198 height of production, 783, 789 function, 191, 198, 1022, 1025 lateral distribution, 743 theory, 179 mathematical lateral Non-parametric statistical techniques, 454 structure functions, 743 Non-Poissonian fluctuations of Cherenkov origin, 361, 783 light, 39 simulated Northern Auger Observatory, 16 lateral distributions, 746 Nova particle, 100 Nuclear N disintegration, 574 NAP, 9, 683 dissociation, in space, 162 NEEDS Workshop, 133, 243 emulsion, 80, 85 1108 Index

fragmentation, 574 by muons, 214 fragments, 85 direct of muons photodisintegration, 574 by muons, 219 physics effects, 78 of muons, 164 spallation in space, 162 Pairproduction Nuclear active particles, NAP, 9, 683 Coulomb, 148 Nucleon magnetic, 148 elasticity, 106, 248 Parallax effects, 564 isobars, 116 Parametrized resonances, 116, 162 cross sections, 87 spectrum Parsec, deﬁnition, 1025 in atmosphere, 248 Particle Nucleon-air cross sections, 83 absorption length Nucleon-antinucleon in showers, 178 production, 106 detection arrays, 34 at accelerators, 995 generators cross section, 995 hadronic, 118 in air showers, 995 production, 95 Nucleon-nucleon models, 129 cross sections, 82 Particle detection in showers, 34 interactions, 82, 97, 120 Particle detectors, 165 Nucleon-nucleus cross sections, 85 Particle signatures of Xmax, 326 Number spectrum, 1025 Parton model, 127 Partons, 127 O Penetrating Ohya, underground exp., 748 component, 9, 683, 743, 1026 Old showers, 9 particles, 237 One-dimensional cascade theory, 176 showers, 238 Opaque Earth for neutrinos, 26, 233 Peyrou Plot, 102, 1026 Opaque Universe for gamma rays, 19, 577 Photo dissociation of nuclei, in space, 162, 574 Optical atmospheric Photo-pion production, 163 absorption, 862, 892 attenuation, 862, 895 Photoelectric background, 892 absorption, 149 airglow, 893 effect, 19, 78, 147, 162, 174 Cherenkov contrib., 896 Photon initiated showers, 17, 162 of night sky, 862, 892 Photon number scattering, 862, 892 at shower maximum, 197 Mie, 862 approx. A, 197 Rayleigh, 862 Photon production cosmic, 18 transmission, 883, 895 Photon to electron ratio, 804 Optical Cherenkov radiation, 835 Photon-electron Optimization of density measurements, 431 cascade theory, 174 Origin of cosmic radiation, 568 cascades, showers, 4 component Origin of muons, 361 ± Overburden atmospheric, 293, 1012, 1025 number ratio e /γ , 828 OWL-AIRWATCH, 16 Photon-nucleus Ozone, 862, 1075 cross section scaling, 163 P interactions, 163 Pair production, 174 Photon-photon Coulomb, 153, 164 cross section, 163 of electrons, 157 interactions, 19, 148, 164 direct of electrons Photonuclear Index 1109

cross section, 220, 221 neutrino showers, 24 interactions, 148 spectra of muons, 219 high energy, 502, 507 processes, 19 low energy, 483 reactions, 26, 79, 162, 246 Primary energy estimation Photoproduction, 246 errors due to of muon pairs, 207 delayed particles, 438 Physical constants, 1073 time dispersion, 438 Pion general, 57, 422 energy spectrum, 116 thumb rule, 58 of secondaries, 116 Primary energy estimation using interactions, gen., 99 atmos. Cherenkov Pion-air cross sections, 83 radiation, 440, 853, 855 Pion-nucleon atmos. fluorescence, 440, 905 interactions, 121 shower size, 371, 431 in isobar-fireball model, 122 truncated muon size, 438 Pion-nucleon cross sections, 82 water Cherenkov detectors, 425 Pion-nucleus cross sections, 85 Primary mass, 6, 11 Pionization, 98, 117, 122 composition, 294, 528 Pitch angle, definition, 1026 estimation methods, 441 Plastic scintillation detectors estimation using AGASA type, 70 atmos. fluorescence, 905 Point sources indicator, 309 of gamma rays, 22, 495 temporal sensitivity, 411 Poissonian Primary mass-dependent observables, 411 distribution, 248 Primary neutrinos, 496 statistics, 306 Primary particle groups, 88, 482 Polarization of radio emission, 927 Primary spectrum, 11 Polarized light from Crab, 18 all-particle spectrum, 502 Polarized photons, 161 composite, differential, 11 effect on high energy, 502, 507 Compton scattering, 161 low energy, 483 Poly-gonato model, 523, 524 Production height of muons, 783, Pomeron model, 109 787, 789 Positron annihilation, 148, 167 Projectile Pre-cascading, 148 fragmentation, 89 Pre-showering effect, 24, 148, 171, 343 mass dependence of Precession, terrestrial, 564 multiplicity, 100 effects, 565 Prompt muons, 977 Primary Propagation of composition, 465, 528 cosmic radiation, 89 electron showers, 17, 23 in space, 568 electrons, 484 photons in space, 575 energy estimator Proton astronomy, 570 atmos. Cherenkov, 854 Proton spectrum ρ(600), S(600), 370 secondary, 116 gamma radiation from collisions, 116 diffuse, 22, 491, 492 Proton-air discovery, 19 attenuation length, 261 origin, 17 cross section, 262 point sources, 22, 491, 495 Pseudo-rapidity, 103, 1026 gamma ray showers, 17 Punch-through, 213 gamma ray-hadron ratio, 548 in calorimeter, 1027 1110 Index

electromagnetic, 294, 747 pulse, burst characteristics, 936 particles, 36, 712 of showers, 4, 15, 41, 913 theories of production, 917 Q by transition radiation, 924 QCD, 84, 104, 109, 128 Radio galaxies, 570 QED, 150 Radiosondes, 336 QGS models, 127 Radius of curvature of shower front, 404 QGSJET event generator, model, 131 Rapidity, 103, 123, 1026, 1028 Quarks, 127 density distribution, 103 Quenching of air fluorescence, 882 distribution, 99, 123 Rate attenuation length, 108 R Rayleigh scattering, 147, 162 RADAR detection method of showers, 42 elastic, 149 Radial scaling, 1004 in atmosphere, 862, 894 Radiation length, 151, 181, 243, 1027 δ-rays, 159, 1016 effect Refractive index of molecular binding, 153, 243 of air, 841 on showers, 244 Reggeon model, 163 effective for magnetic Relativistic dust grains, 27 bremsstrahlung, 172 Resonances, nucleonic, 115 pair production, 172 RHIC collider, 85, 89 molecular effects, 1024 Right ascension, 552, 557, 564 of air, 153, 1071 definition, 1029 of compounds, 1071 Rigidity of elements, 1069, 1071 definition, 1029 of substances, mixtures, 153 dependent leakage, 523 table of media, 1071 Rigidity confinement, 11 Radiation unit, 151, 1027 Radio emission, 55, 148, 165, 195 background S sources, data, 928 S(r) particle density measurements, 390 calculations, 937 Sampling method by Cherenkov rad., 915, 917 for shower detection, 14 coherence effects, 927 in simulations, 176 coherent radiation, 916 Satellite based data, 929 EAS experiments, 26 detection of showers, 41, 913 Satellite based EAS experiments, 16 empirical relations, 929 Scale height atmospheric, 6, 1029 formula, 929 Scaling generation mechanisms, 914 Feynman, 99 by geo-synchrotron hypothesis, 1030 radiation, 925 KNO, 101 by geoelectric law, 99 charge separation, 922 model, 99, 119 by geomagnetic Scatter plot, Peyrou plot, 102 charge separation, 919 Scattered Cherenkov light, 885 in neutrino reactions, 26 contribution to by negative fluorescence, 894, 896, 903 charge excess, 914, 917 Scattered fluorescence light, 897 of showers, 168 Scattering polarization data, 933 angle polarization effects, 927 mean square, 158, 1023 predicted field strength, 921 of electrons, 1023 primary energy dependence, 929 energy, 155, 159, 807 Index 1111

length, 192, 1030 Shower density spectrum, 646 Scintillation detectors, 62 Shower detection Screening, 150, 156, 1030 using air fluorescence, 39 complete, 156, 157, 179, 1011 using atmos. Cherenkov rad., 38 cross section, 175 hybrid method, 48 energy, 150, 1030 methods, techniques, 33 ineffective, 156 by RADAR, 42 intermediate, 156 relevant observables, 35 of nuclear using shower particles, 34 Coulomb field, 155 special equipment, 49 Seagull effect, 118 Shower disc thickness, 402 Second spectral knee, 615 Shower energy estimation, 57, 422 Secondary ionization, 159, 1016, 1030 Shower front Secondary particles curvature, 8, 361, 399, 400, 403 multiplicity, 95 effect on density meas., 392 hadronic, 97 temporal structure production, 95 effect on energy determ., 438 Semi-empirical fragmentation formula, 89 Shower maximum, 178, 184, 196 Seyfert galaxies, 28 altitude in atmosphere, 303 Shock wave acceleration, 523, 569 atmospheric depth, 303 Shower height a.s.l., 284, 303 axis Shower parameters definition, 7, 33 derived, 419 location, 51 directly accessible, 52 core, 7 indirectly accessible, 419 location, 51 Shower particle absorption, data, 262 development Shower profile curves, 179, 189 longitudinal, 195, 238, 241, 243 lateral, 191 development, 237 longitudinal, 189, 196 fluorescence, 903 front, 7, 8 Shower rate time profile, 8 attenuation, data, 258 function, 189 Shower reconstruction lateral arrival direction, 54 structure function, 191 basic, direct, 52 size, 178, 196, 197 core location, 56 size at maximum indirect, 419 approx. A, 197 methods, 33 approx. B, 197 using simulations, 419 size-energy conversion, 58 Shower size size-energy relation, 57 determination, 57, 422 Shower age, 9, 184, 196, 262, 1030 spectrum, 614, 1031 determination, 57, 459, 464 underestimation, 619 effect on LDF, 619 Shower sub-cores, 726 exper., theor. aspects, 460 SIBYLL event generator, model, 131 experimental data, 464 Sidereal parameter s, 184 time, 563, 564, 1030 properties, 459 definition, 564 radial dependence, 199 variation, 1031 size dependence, 465, 619 Simulation of air showers, 988 transverse, longitudinal, 460 Simulations, general, 616 two age parameters, 199 Simultaneous observables, 15 Shower asymmetry, 55 Single core showers, 7 1112 Index

Size dependence of shower age, 465 remnants, 487, 523, 569 Size-primary energy SN-1054, Crab, 495, 496 conversion factors, 239, 438 SN-1987a, 496 thumb rule, 58 Superposition model, 664 relation, 57 Survival probability of muons in dense media, Slant depth, 315, 1031 208 atmospheric, 1012 Synchrotron Soft component, 9, 238, 683, 1031 energy losses, 18, 24 Solar radiation, 17, 148, 166 neutrinos, 496 critical frequency, 166 time, 563, 564, 1031 from Crab, 18 Southern Auger Observatory, 16 Space-time T energy window, 408 Tachyons, search, 404 profile, 402 Tangent plane, 401 structure, 403 Target treatment of cascades, 195 fragmentation, 89 Spallation, 89 mass dependence of nuclear, of cosmic rays multiplicity, 100 in space, 162 Tau neutrino, 27 Spectral initiated showers, 978 ankle, 12, 615 Tau neutrino flux, 978 knee, 11, 615 Telescope Array, 16, 41, 49, 1059 in density spectrum, 647 Temperature in muon size spectrum, 639 coefficient, 257, 1031 in size spectrum, 615 effect, 10, 255, 257, 281 second knee, 615 on shower rate, 238, 257 Spectrometer, magnet, 723 on showers, 238 S(r) particle density Temporal calibration, 390 distribution Standard of shower particles, 49 atmosphere, 1073 primary mass signatures, 453 pressure, 1073 properties temperature, 1073 of muons, 774 Statistical model of hadron prod., 104, 119 structure, 399 Strange phenomena, 981 of showers, 399 Stratopause, 1075 Thermo-acoustic Stratosphere, 1075 shock, 46 Strings, 127 shock wave in water, 46 Structure function Thermodynamic model, 119, 726 lateral, 179, 334, 1031 of hadronic interactions, 104 of shower, 311 Thermopause, 1075 Sub-cascades, 78 Thermosphere, 1075 hadronic Thinning method in simulations, 176, 1004 in showers, 727 Thomson cross section, 161, 167 Sub-cores, 8 Three-dimensional in showers, 726 cascade theory, 180, 181, 190 Sub-showers EM-cascade, 159 electromagnetic, 174 Threshold energy π ◦ production, 18 Super massive particles, 499 Tibet Array, 631, 1060 Supernova Time dispersion nonlinear diffusive shock of particles, 399 acceleration, 569 in shower disc, 399 Index 1113

Time profile of showers, 8 V Time variation of veμ m−2, definition, 368, 665 air shower rate, 562 VENUS cosmic radiation event generator, model, 131 diurnal, 1031 Vernal equinox, 564 sidereal, 1031 Vertical equivalent muons Time-track complementarity, 411, 789 definition, 368, 665 Timing energy deposit, 368, 389 fluctuations, 402 Vertical penetrating minimum, 390 observables ionizing particles definitions, 401 in scintillators, 390 Top-down models, 499, 546, 549, 571 Volcano Ranch experiment, 387 Topological defects, 546 Total absorption scintillation spectrometer W (TASS), 684 Water Cherenkov detectors, 367 Track length integral, 178 HaverahParktype,67 Transition Wilson cloud chamber, 684, 699 curve, 243 Winston Funnel, optical, 885 effects in detectors, 61, 366, 373 X radiation, 148, 165, 924 Xmax Transport equation nucleonic, 136 data summary, 340 Transverse determination, 304 mass, 123 determination using momentum, 80, 102, 360, 726 Cherenkov signatures, 305 distribution, 104, 116 hybrid method, 333 energy dependence, 105 particle signatures, 326 large, 8, 104 fluctuations, 346 of muon parents, 743 X and of muons, 784 max fluorescence tracking, 334 of secondaries, 783 muon core angle, 327 shower age, 460 particle Tropopause, 1075 arrival time profile, 328 Troposphere, 1075 front curvature, 330 Truncated muon size, 438, 694 lateral distribution, 327 Typical energies of photons, electrons, muons, X distributions 363 max of iron showers, 346 U of proton showers, 346 Ultrahigh energy (UHE) theoretical, predicted, 346 event-origin correlation, 572 astrophysical, 571 Y Unaccompanied cosmic rays, 85 Yakutsk experiment, 387, 621, 643, 660, 667, Under-ice experiment IceCube, 51 668, 846 Underground experiments, 50, 1064 Young showers, 9 Baksan, 50, 1066 Homestake, 50 Z Kolar Gold Fields, 50, 1067 Z-bursts, 499, 547 LVD, 50, 1066 Zenith angle, 7, 1032 MACRO, 50, 1066 dependence, 238, 367, 371 Ohya, 748 shower development, 254, 271 Universality of air showers, 677 shower rate, 254, 271, 282 Unseen energy in showers, 983 distribution, 1032 Upward directed showers, 26, 976 effect, 10, 255 UrQMD event generator, model, 130 PETER GRIEDER, born 1928 in Switzerland, obtained his MS degree in physics from the Illinois Institute of Technology in Chicago in 1957. He did the research for his thesis with the Argonne group of the U.S. Atomic Energy Commission at the University of Chicago. There he took part in cosmic ray physics seminars of Professors Simpson, Schein and Chandrasekhar. In 1961 he got his PhD from the University of Bern, Switzerland, where he did his research under Prof. F.G. Houter- mans in high energy cosmic ray physics. He then worked successively as a postdoctoral scientist at the Niels Bohr Institute in Copenhagen with Prof. Bernard Peters on quark-hunt experiments, at CERN in Geneva in the experimental and later on in the theoretical physics division with Drs. R. Hagedorn and M. Jacob on models of high energy hadronic interactions and multi-particle production, in conjunction with air showers. In 1968 he was appointed lecturer at the University of Bern, and in 1970 visiting professor for one year at the Institute for Nuclear Studies of the University of Tokyo, where he worked in the cosmic ray group of Prof. K. Suga. In 1978 he was appointed professor of physics at the University of Bern. From 1985 to 1987 he was secretary of the Swiss Physical Society. His research activities comprise high energy phenomena, extensive air showers and neutrino astronomy. He developed the ASICO air shower simulation program system which later on was renamed CORSIKA, that is widely used today with a variety of modern event generators, developed by many different authors. He was co-initiator together with Prof. Fred Reines, Nobel Laureate, and colleagues from other institutions of the pioneering DUMAND neutrino telescope project in Hawaii, that was the template for all presently existing and planned giant neutrino telescopes. He was guest professor for many years at the University of Hawaii and is the author of numerous scientific articles and several books.