COSMIC RADIATION

A. G. Gregory and R. W. Clay

The Nature of Cosmic Rays

Primary cosmic radiation, in the form of high-energy nuclear particles, electrons and photons from outside the solar system and from the Sun, continually bombards our atmosphere. Secondary radiation, resulting from the interaction of the primary cosmic rays with atmospheric gas, is present at sea level and throughout the atmosphere.

Secondary radiation is collimated by absorption and scattering in the atmosphere and consists of a number of components associated with different particle species. High-energy primary particles can produce large numbers of secondary particles forming an extensive air shower. Thus, a number of particles may then be detected simultaneously at sea level.

Primary particle energies accessible in the vicinity of the Earth range from ~10⁸ eV to ~10²⁰ eV. At the lower energies, the limit is determined by the inability of charged particles to traverse the heliosphere to us through the outward-moving solar wind. The upper energy limit is set by the practicality of building detectors to record particles with the extremely low fluxes found at those energies (Refs. 1, 23).

Primary Cosmic Rays

Primary Particle Energy Spectrum

Figure 1 shows the spectrum of primary particle energies. This includes all particle species. In differential form it is roughly a power law of intensity versus energy with an index of ~ –3. There appears to be a knee (a steepening) at a little above 10¹⁵ eV and an ankle (a flattening) above ~10¹⁸ eV. Figure 2 emphasizes the features in the spectrum at the highest energies through multiplying the flux with a strongly rising power law of energy. This figure should be used with caution as errors for the two axes are not now independent.

Data on the high-energy cosmic ray spectrum are uncertain largely because of limited event statistics due to the very low flux which might best be measured in particles per square kilometer per century. The highest energy event recorded to 1995 had an energy of 3 × 10²⁰ eV (Ref. 9).

It is expected that the highest energy cosmic rays will interact with the 2.7 K cosmic microwave background through photoproduction or photodisintegration. These interactions will appreciably reduce the observed flux of cosmic rays with energies above 5 × 10¹⁹ eV if they travel further than ~150 million light-years. This process is known as the Greisen-Zatsepin-Kuz’min (GZK) cutoff (Ref. 20).

At energies below ~10¹³ eV, solar system magnetic fields and plasma can modulate the primary component and Figure 3 shows the extent of this modulation between solar maximum and minimum (Refs. 16, 17).

Primary Particle Energy Density

If the above spectrum is corrected for solar effects, the energy density above a particle energy of 10⁹ eV outside the solar system is found to be ~5 × 10⁵ eV m^–3. As the threshold energy is increased, the energy density decreases rapidly, being 2 × 10⁴ eV m^–3 above 10¹² eV and 10² eV m^–3 above 10¹⁵ eV. The energy density at lower energies outside the heliosphere is unknown but may be substantially greater if the particle rest mass energy is included together with the kinetic energy (Ref. 24).

Primary Particle Isotropy

This is measured as an anisotropy (I_max – I_min)/(I_max + I_min) × 100%, where I, the intensity (m^–2s^–1sr ^–1), is usually measured with an angular resolution of a few degrees.

The measured anisotropy is small and energy dependent. It is roughly constant in amplitude at between 0.05 and 0.1% (with a phase of 0 to 6 hours in right ascension) for energies between 10¹¹ eV and 10¹⁴ eV and appears to increase at higher energies roughly as 0.4 × (Energy(eV)/10¹⁶)^0.5 % up to ~10¹⁸ eV. The latter rise may well be an artifact of the progressively more limited statistics as the flux drops rapidly with energy. It appears possible that a real anisotropy has been observed at the highest energies (above a few times 10¹⁹ eV) with a directional preference for the supergalactic plane (this plane reflects the directions of galaxies within about 100 million light-years) (Refs. 9, 21, 24).

Primary Particle Composition

The composition of low-energy cosmic rays is close to universal nuclear abundances except where propagation effects are present. For example, Li, Be, and B which are spallation products, are overabundant by about six orders of magnitude.

Composition at 10¹¹ eV per Nucleus

Measurements at higher energies indicate that there is an increase in the relative abundances of nuclei with charges greater than 6 at energies above 50 TeV/nucleus (Ref. 5) (1 TeV = 10¹² eV).

Cosmic ray composition at low energies is often quoted at a fixed energy per nucleon. When presented in this way, protons constitute roughly 90% of the flux, helium nuclei about 10%, and the remainder sum to a total of about 1%.

Certain radioactive isotopic ratios show lifetime effects. The ratio of Be¹⁰/B⁹ abundances is used to measure an “age” of cosmic rays since Be¹⁰ is unstable with a half-life of about 1.6 × 10⁶ years. A ratio of 0.6 is expected in the absence of Be¹⁰ decay and a ratio of about 0.2 is found experimentally (Refs. 16, 18).

At higher energies, composition determinations are indirect and are rather contradictory and controversial. Experiments aim to differentiate between broad composition models. The measurement technique is based on studies of cosmic ray shower development. A rather direct technique for such studies is to use fluorescence observations of the shower development to determine the atmospheric depth of maximum development of the shower. Such observations suggest a heavy composition (large atomic number) at energies ~10¹⁷ eV which changes with increasing energy to a light composition (perhaps protonic) above ~10¹⁹ eV (Ref. 12).

FIGURE 1. The energy spectrum of cosmic ray particles. This spectrum is of a differential form and can be converted to an integral spectrum by integration over all energies above a required threshold (E). Insofar as the spectrum approximates a power law of index –3, a simple conversion to the integral at an energy E/1.8 is obtained by multiplying the differential flux by the energy and dividing by 0.62.

FIGURE 2. Energy spectrum at the highest energies. This spectrum (after Yoshida et al., 1995) has the differential spectrum multiplied by energy cubed. It is from a compilation of a number of measurements and indicates the good general agreement at the lower energies and a spread due to inadequate statistics at the highest energies.

FIGURE 3. Energy spectrum of particles at lower energies. (a) Solar minimum proton energy spectrum. (b) Solar maximum proton energy spectrum. (c) Gamma ray energy spectrum. (d) Local interstellar electron spectrum.

Primary Electrons

Primary electrons constitute about 1% of the cosmic ray beam. The positron to negative electron ratio is about 10% (Ref. 11).

Antimatter in the Primary Beam

The ratio of antiprotons to protons in the primary cosmic ray beam (at about 400 MeV) is about 10^–5. At about 10 GeV the ratio is about 10^–3. At the highest measured energies (10 TeV), the upper limit to the ratio is about 20% (Refs. 4, 22).

Primary Gamma Rays

The flux of primary gamma rays is low at high energies. At 1 GeV the ratio of gamma rays to protons is about 10^–6. The arrival directions of these gamma rays are strongly concentrated in the plane of the Milky Way although there is a diffuse, near isotropic background flux and some point sources have been detected.

Since the absorption cross section for gamma rays above 100 MeV is approximately 20 mbarn/electron, less than 10% of gamma rays reach mountain altitudes (Refs. 19, 24).

Sea-Level Cosmic Radiation

The sea-level cosmic ray dose is 300 millirad⋅yr^–1 and the sea-level ionization is 2.2 × 10⁶ ion pairs m^–3s^–1. The sea-level flux has a soft component, which can be absorbed in about 100 mm of lead (about 100 g⋅cm^–2 of absorber) and a more penetrating (largely muon) hard component. The sea-level radiation is largely produced in the atmosphere and is a secondary component from interactions of the primary particles. The steep primary energy spectrum means that most secondaries at sea level are from rather low-energy primaries. Thus, the secondary flux is dependent on the solar cycle and the geomagnetic latitude of the observer.

Absolute Flux of the Hard Component

• Vertical Integral Intensity I(0) ~100 m^–2 s^–1 sr^–1
• Angular Dependence I(θ) ~ I(0) cos²(θ)
• Integrated Intensity ~200 m^–2 s^–1
• (O. C. Allkofer, 1975b)

Flux of the Soft Component

In free air, the soft component comprises about one-third of the total cosmic ray flux.

Latitude Effect

The geomagnetic field influences the trajectories of lower-energy cosmic rays approaching the Earth. As a result, the background flux is reduced by about 7% at the geomagnetic equator. The effect decreases toward the poles and is negligible at latitudes above about 40°.

Flux of Protons

The proton component is strongly attenuated by the atmosphere with an attenuation length (reduction by a factor of e) of about 120 g⋅cm^–2, constituting about 1% of the total vertical sea-level flux.

Absorption

The soft component is absorbed in about 100 g⋅cm^–2 of matter. The hard component is absorbed much more slowly:

• Absorption in lead, 6% per 100 g⋅cm^–2
• Absorption in rock, 8.5% per 100 g⋅cm^–2
• Absorption in water, 10% per 100 g⋅cm^–2
• (Absorption for depths less than 100 g⋅pd cm^–2 is given by K. Greisen, 1943)

Altitude Dependence

The cosmic ray background in the atmosphere has a maximum intensity of about 15 times that at sea level at a depth of about 150 g⋅cm^–2 (15 km altitude). At maximum intensity, the soft and hard components contribute roughly equally but the hard component is then attenuated more slowly (Ref. 14).

Cosmic Ray Showers

High-energy cosmic rays produce particle cascades in the atmosphere which can be detected at sea level provided that their energy exceeds about 100 GeV (such low-energy cascades may be detected by using the most sensitive atmospheric Cerenkov detectors). The primary particle progressively loses energy which is transferred through the production of successive generations of secondary particles to a cascade of hadrons, an electromagnetic shower component (both positively and negatively charged electrons and gamma rays) and muons. The secondary particles are relativistic and all travel effectively at the speed of light. As a result, they reach sea level at approximately the same time but, due to Coulomb scattering (for the electrons) and production angles (for the pions producing the muons), are spread laterally into a disk-like shower front with a characteristic lateral width of several tens of meters and thickness (near the central shower core) of 2 to 3 m. The number of particles at sea level is roughly proportional to the primary particle energy:

Number of particles at sea level ~10^–10 × energy (eV).

At altitudes below a few kilometers, the number of particles in a shower attenuates with an attenuation length of about 200 g⋅cm^–2, i.e.,

particle number = original number × exp(–(depth increase)/200)

The above applies to an individual shower. The rate of observation of showers of a given size (particle number at the detector) at different depths of absorber attenuates with an absorption length of about 100 g⋅cm^–2 (Ref. 23).

Atmospheric Background Light from Cosmic Rays

Cosmic ray particles produce Cerenkov light in the atmosphere and produce fluorescent light through the excitation of atmospheric molecules.

Cerenkov Light

High-energy charged particles will cause the emission of Cerenkov light in air if their energies are above about 30 MeV (electrons). This threshold is pressure (and hence altitude) dependent. A typical Cerenkov light pulse (at sea level, 100 m from the central shower core) has a time spread of a few nanoseconds. Over this time, the photon flux between 430 and 530 nm would be ~10¹⁴ m^–2s^–1 for a primary particle energy of 10¹⁶ eV. For comparison, the night sky background flux is ~6 × 10¹¹ photons m^–2s^–1sr^–1 in the same wavelength band (Ref. 15).

Fluorescence Light

Cosmic ray particles in the atmosphere excite atmospheric molecules which then emit fluorescence light. This is weak compared to the highly collimated Cerenkov component when viewed in the direction of the incident cosmic ray particle but is emitted isotropically. Typical pulse widths are longer than 50 ns and may be up to several microseconds for the total pulse from distant large showers (Ref. 6).

Effects of Cosmic Rays

Cerenkov Effects in Transparent Media

Background cosmic ray particles will produce Cerenkov light in transparent material with a photon yield between wavelengths λ₁ and λ₂

$\sim (2\pi /137){\sin }^2({\theta }_c){\displaystyle {\int }_{{\lambda }_1}^{{\lambda }_2}d}\lambda /{\lambda }^2{\text{photons(unit length)}}^{-\text{1}}$

where θ_c (the Cerenkov angle) = cos^–1 (1/refractive index).

This background light is known to affect light detectors, e.g., photomultipliers, and can be a major source of background noise (Ref. 10).

Effects on Electronic Components

If background cosmic ray particles pass through electronic components, they may deposit sufficient energy to affect the state of, e.g., a transistor flip-flop. This effect may be significant where reliability is of great importance or the background flux is high. For instance, it has been estimated that, in communication satellite operation, an error rate of about 2 × 10^–3 per transistor per year may be found. Permanent damage may also result. A significant error rate may be found even at sea level in large electronic memories. This error rate is dependent on the sensitivity of the component devices to the deposition of electrons in their sensitive volumes (Ref. 26).

Biophysical Significance

When cosmic rays interact with living tissue, they produce radiation damage. The amount of the damage depends on the total dose of radiation. At sea level, this dose is small compared with doses from other sources, but both the quantity and quality of the radiation change rapidly with altitude. Approximate dose rates under various conditions are:

• Dose rates (mrem⋅yr^–1)
• Sea-level cosmic rays, 30
• Cosmic rays at 10 km (subsonic jets), 2000
• Cosmic rays at 18 km (supersonic transports), 10,000
• (c.f., mean total sea-level dose, 300)

Astronauts would be subject to radiation from galactic (0.05 rads per day) and solar (a few hundred rads per solar flare) cosmic rays as well as large fluxes of low-energy radiation when passing through the Van Allen belts (about 0.3 rads per traverse).

Both astronauts and SST travelers would be subject to a small flux of low-energy heavy nuclei stopping in the body. Such particles are capable of destroying cell nuclei and could be particularly harmful in the early stages of the development of an embryo. The rates of heavy nuclei stopping in tissue in supersonic transports and spacecraft are approximately as follows:

• Stopping nuclei ((cm³ tissue)^–1 hr^–1)
• Supersonic transport (16 km), 0.0005
• Supersonic transport (20 km), 0.005
• Spacecraft, 0.15
• (Refs. 3, 4)

Carbon Dating

Radiocarbon is produced in the atmosphere due to the action of cosmic ray slow neutrons. Solar cycle modulation of the very low-energy cosmic rays causes an anticorrelation of the atmospheric ¹⁴C activity with sunspot number with a mean amplitude of about 0.5%. In the long term, modulation of cosmic rays by a varying magnetic field may be important (Ref. 8).

Practical Uses of Cosmic Rays

There are few direct practical uses of cosmic rays. Their attenuation in water and snow have, however, enabled automatic monitors of water and snow depth to be constructed. A search for hidden cavities in pyramids has been carried out using a muon “telescope.”

Other Effects

Stellar x-rays have been observed to affect the transmission times of radio signals between distant stations by altering the depth of the ionospheric reflecting layer. It has also been suggested that variations in ionization of the atmosphere due to solar modulation may have observable effects on climatic conditions.

References

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