DELPHI
4.5 Cosmic-Ray Detectors
4.5.1 Interaction of Cosmic Rays with the Atmosphere
Extensive Air Showers
The physics of electromagnetic and hadronic showers has been described before; here we particularize the results obtained to the development of the showers due to the interaction of high-energy particles with the atmosphere. These are called extensive air showers (EAS).
High-energy hadrons, photons, and electrons interact in the high atmosphere. As we have seen, the process characterizing hadronic and electromagnetic showers is conceptually similar (Fig.4.34).
For photons and electrons above a few hundred MeV, the cascade process is dominated by the pair production and the bremsstrahlung mechanisms: an energetic photon scatters on an atmospheric nucleus and produces ane+e−pair, which emits
e+
e+
e- primary γ
e–
e+
e+ e+ e–
e–
e–
e– e– e+ e+
+
π+ π–
+- K , etc.
nucleons,
+- K , etc.
nucleons,
π0
π+ π0
μ– _ γ
γ
μ
γ γ νμ
νμ cosmic ray (p, α, Fe ...)
γ γ
γ γ
atmospheric nucleus
EM shower EM shower
EM shower
atmospheric nucleus
Fig. 4.34 Schematic representation of two atmospheric showers initiated by a photon (left) and by a proton (right). From R.M. Wagner, dissertation, MPI Munich 2007
0 2 4 6 8 10
5 10 15 20 25 30 35
Atmospheric depth (r.l.)
log (Shower Size)
0.5
0.6 0.7 0.8 0.9 1 1.1 1.2
1.3
s = 0.4
300 GeV
120 TeV
370 PeV
20 15 12 10 9 8 7 6 5 4 3 2 1 0
Height a.s.l. (km)
30 GeV
1.8 TeV 13 TeV
0
Fig. 4.35 Longitudinal shower development from a photon-initiated cascade. The parameters describes the shower age. From R.M. Wagner, dissertation, MPI Munich 2007; adapted from reference [F4.1] in the “Further reading”
secondary photons via bremsstrahlung; such photons produce in turn a pair, and so on, giving rise to a shower of charged particles and photons, degrading the energy down to the critical energyEcwhere the ionization energy loss of charged particles starts dominating over bremsstrahlung.
The longitudinal development of typical photon-induced extensive air showers is shown in Fig.4.35for different values of the primary energies. The maximum shower size occurs approximately after ln(E/Ec)radiation lengths, the radiation length for air being about 37 g/cm2(approximately 300 m at sea level and NTP). The critical energyEcis about 80 MeV in air.16
The hadronic interaction length in air is about 90 g/cm2for protons (750 m for air at NTP), being shorter for heavier nuclei—the dependence of the cross section on the mass numberAis approximatelyA2/3. The transverse profile of hadronic showers is in general wider than for electromagnetic showers, and fluctuations are larger.
Particles release energy in the atmosphere, which acts like a calorimeter, through different mechanisms—which give rise to a measurable signal. We have discussed these mechanisms in Sect.4.1.1; now we reexamine them in relation to their use in detectors.
16In the isothermal approximation, the depthxof the atmosphere at a heighth(i.e., the amount of atmosphere aboveh) can be approximated as
xXe−h/7 km, withX1030 g/cm2.
166 4 Particle Detection 4.5.1.1 Fluorescence
As the charged particles in an extensive air shower go through the atmosphere, they ionize and excite the gas molecules (mostly nitrogen). In the de-excitation processes that follow, visible and ultraviolet (UV) radiations are emitted. This is the so-called fluorescence light associated to the shower.
The number of emitted fluorescence photons is small—of the order of a few photons per electron per meter in air. This implies that the fluorescence technique can be used only at high energies. However, it is not directional as in the case of Cherenkov photons (see below), and thus it can be used in serendipitous observations.
4.5.1.2 Cherenkov Emission
Many secondary particles in the EAS are superluminal, and they thus emit Cherenkov light that can be detected. The properties of the Cherenkov emission have been discussed in Sects.4.1.1and4.2.
At sea level, the value of the Cherenkov angleθCin air for a speedβ=1 is about 1.3◦, while at 8 km a.s.l. it is about 1◦. The energy threshold for Cherenkov emission at sea level is 21 MeV for a primary electron and 44 GeV for a primary muon.
Half of the emission occurs within 20 m of the shower axis (about 70 m for a proton shower). Since the intrinsic angular spread of the charged particles in an electromagnetic shower is about 0.5◦, the opening of the light cone is dominated by the Cherenkov angle. As a consequence, the ground area illuminated by Cherenkov photons from a shower of 1 TeV (the so-called light pool of the shower) has a radius of about 120 m, with an approximately constant density of photons per unit area. The height of maximal emission for a primary photon of energy of 1 TeV is approximately 8 km a.s.l., and about 150 photons per m2 arrive at 2000 m a.s.l. (where typically Cherenkov telescopes are located, see later) in the visible and near UV frequencies.
This dependence is not linear, being the yield of about 10 photons per square meter at 100 GeV.
The atmospheric extinction of light drastically changes the Cherenkov light spec- trum (originally proportional to 1/λ2) arriving at the detectors, in particular sup- pressing the UV component (Fig.4.36) which is still dominant. There are several sources of extinction: absorption bands of several molecules, molecular (Rayleigh) and aerosol (Mie) scattering.
Radio Emission. Cosmic-ray air showers also emit radio waves in the frequency range from a few to a few hundred MHz, an effect that opens many interesting possibilities in the study of UHE and EHE extensive air showers. At present, however, open questions still remain concerning both the emission mechanism and its strength.
Fig. 4.36 Spectrum of the Cherenkov radiation emitted by gamma-ray showers at different energies initiated at 10 km a.s.l. (solid curves) and the corresponding spectra detected at 2200 meters a.s.l. (lower curve).
From R.M. Wagner, dissertation, MPI Munich 2007
[nm]
Cherenkov
300 400 500 600
dN/d
0 50 100 150
200 500 GeV photon
200 GeV photon 100 GeV photon 50 GeV photon