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Gennaro Miele » 11.Cosmic Rays - I

Cosmic Rays I

Cosmic rays continually bombard the Earth.

In fact, about 100 000 cosmic rays pass through a person every hour!

Cosmic Rays I – Outlines

  • The discovery of cosmic rays
  • Cosmic ray and particle physics
  • CR deflections in magnetic field
  • CR from the Sun
  • Shower theory
Energy spectrum of cosmic radiation

Energy spectrum of cosmic radiation

Just before…

When scientists first started studying radiation in the early 1900s, they found 3 different types of rays:

  • α rays: turned out to be Helium nuclei
  • β rays: turned out to be electrons and positrons
  • γ rays: turned out to be e.m. radiation

Of the known radiation, the one emitted by radioactive substances had the highest energies (MeV). Cosmic ray physics had to involve much greater energies, till 1020 eV!

The Discovery

“At six o’clock on the morning of August 7, 1912, a balloon ascended from a field near the town of Aussig, in Austria…”from Cosmic rays, Bruno Rossi

Victor F. Hess took with him three electroscopes up to an altitude of about 16000 feet (without oxygen!).

“The results of my observations are best explained by the assumption that a radiation of very great penetrating power enters our atmosphere from above.”

from Physikalische Zeitschrift, November 1912

Hess won the Nobel prize in 1936 for his discovery of cosmic rays. Millikan gave the name cosmic rays to the new radiation.

Atmospheric depth

When comparing radiation absorbers of different substances, it becomes necessary to consider the density as well as the thickness of the absorber. Thus, it is customary to define an absorber not by its geometrical thickness, but by the mass of a column of unit cross sectional area.

This quantity – the mass per unit area – is usually measured in grams per square centimeters (g/cm2). For an absorber of constant density, the mass per unit area is just the product of its thickness and its density: so, it’s like a length which takes into account the density. The mass per unit area of the atmosphere above a given level is known as atmospheric depth.

New particles

Colombo, searching for a new route to India, discovered America. In the same way physicists, searching for a solution to the cosmic ray puzzle, discovered a zoo of new particles, opening an entirely new field of research: at the beginning, cosmic ray physics and elementary particle physics were strictly connected.

The instrument which made possible these discovers is the cloud (or expansion) chamber, invented by Wilson in 1911.

Photo of alpha-particles emitted by radioactive source

Photo of alpha-particles emitted by radioactive source

photon conversion in electron/positron couple

photon conversion in electron/positron couple

Cloud chamber

The cloud (or expansion) chamber was invented by Wilson in 1911. The expansion of the gas in the chamber causes condensation around the ions present, producing avisible track along the trajectory of a charged particle. However, to be detected, the particle must traverse the chamber at some time during the so-called expansion phase: so the chamber, in its early version, was sensitive for a period of about 0.01 second at each expansion.

A major technical achievement was the counter controlled chamber, which was triggered by Geiger-Müller counters when they were hitted by a CR particle (Blackett & Occhialini, 1932).For a given velocity, the density of ions per unit length increases with increasing charge of the initial particle. For a given charge, it decreases with increasing velocity. The ion trail of smallest possible density isone left by a singly charged particle moving at nearly the velocity of light (minimum-ionizing particle).

An elementary zoo: the positron

  • Anderson 1932

The positron in the figure is identified as the particle that enters the cloud chamber from below and curves sharply to the left after traversing the lead plate.

At first Anderson thought the positive particles were protons. But the ionizing power estimated by the observation should have been greater for a particle of mass larger than the electron one.

An elementary zoo: the muon

  • Anderson & Neddermayer, 1937

Physicists observed that cosmic rays contained a soft and hard component; the particles of the latter could penetrate as much as 1 m of lead. They could not be e+- e-, since their estimated energy should have been absurd, and their energy losses did not agree with the Bethe-Heitler theory.

Moreover, the penetrating particles often occurred in groups, as they were secondary products of the interaction of primary cosmic rays.

Muon decay

In measuring the numbers of CR at various altitudes in the atmosphere, physicists found a very puzzling result: contrary to the earlier findings of Millikan, it looked as if air absorbed CR more effectively than solid or liquid matter. Moreover, the low density air at very high altitudes appeared to be a better absorber then the denser layer in the lower atmosphere.

The German physicist H. Kuhlenkampff proposed a solution based on the fact that the newly discovered cosmic ray meson were unstable, with a decay time of the order of μs. In a 10 cm layer of water, equivalent to a 16000 cm layer of the high atmosphere air, none of the mesons will have the time to decay.

The muon enters the cloud chamber from above, loses most of its energy in traversing an aluminum plate, then decays giving an electron track (minimum ionizing track)

The muon enters the cloud chamber from above, loses most of its energy in traversing an aluminum plate, then decays giving an electron track (minimum ionizing track)

An elementary zoo: the pion

  • Lattes, Occhialini, & Powell, 1947

In 1935, H. Yukawa had postulated the existence of a subatomic particle associated with the nuclear forces, like the photon was associated to the e.m. ones. Physicists thought that the μ meson was such a particle. Next, Tomonaga and Araki pointed out that positive and negative μ mesons should behave differently after coming at rest in matter.

But, the results of an experiment made by Conversi, Pancini and Piccioni, using a magnetic lens, and different materials (lead, carbon, magnesium), showed that in light elements negative mesons could escape nuclear capture. Only later, Lattes, Occhialini and Powell identified the π meson in emulsions.

An elementary zoo: the kaon

  • Rochester & Butler, 1947

Just a few months after the discovery of the π meson, Rochester and Butler published two cloud-chamber photographs. Neither the neutral particle invoked to explain the first event, nor the charged particle in the second could possibly be identified as any known particle.

Two years later, Powell’s group found in nuclear emulsion a particle, with mass intermediate between that of a π meson and a proton, which appeared to decay in three particles, one of which was a π meson.

An elementary zoo: more and more…

For a while there was a great deal of confusion about the number and properties of the particles required to explain all the experimental data. Then a classification was made in mesons, baryons, and leptons.

Magnetic rigidity

A moving charged particle in a magnetic field experiences a deflecting force. The radius, R, of the circle described in a uniform field (Larmor radius) is obtained from the condition that the centrifugal force and the Lorentz force must balance.

\frac{m \, v^2}{R} = Z \, e\, B, v  \,\,\,\, \Longrightarrow \,\,\,\, B\, R = \frac{p}{Z\, e}

where p is relativistically corrected.

The product B R is called magnetic rigidity. From the definition of eV it follows that:

c \, B \, R = \frac{E({\mbox{eV}})}{Z}

and inserting unity of measure:

B({\mbox{gauss}}) \, R({\mbox{cm}}) = \frac{E({\mbox{eV}})}{300 \, Z}

Magnetic field deflections: latitude effect

In 1930 the notions about the possible effects of the Earth’s magnetic field  upon cosmic rays were still rather nebulous. Consider a particle that circles the Earth at the geomagnetic equator: it has to move from east to west if it is positive and on the contrary if it is negative. The product BR, known as magnetic rigidity of the particle, has to be

B \, R = 0.32 \, {\mbox{gauss}} \cdot 6.38 \, 10^8 \, {\mbox{cm}} = 2 \cdot 10^8 \, {\mbox{gauss cm}}

which corresponds to an energy of about 60 GeV. This means that charged particles with energies of this order or less must be strongly deflected by the earth’s magnetic field at the geomagnetic equator, and CR should somehow be channeled toward the poles (latitude effect).

Magnetic field deflections: E-W effect

Then, the Norwegian physicist Carl Störmer computed the trajectories of particles with different magnetic rigidities approaching the Earth, and distinguished them in allowed (a) and forbidden (b) ones.

He found that there existed a special class of trajectories, called bounded ones, with the property of remaining forever in the vicinity of the Earth. For each point on the Earth, there exists a Störmer cone with the axis pointing to the East (West), which contains the bounded (so forbidden) directions for positive (negative) CR.

Störmer cone for positive particles (a). Störmer cone for negative particles (b).

Störmer cone for positive particles (a). Störmer cone for negative particles (b).

Van Allen radiation belt

On November 3, 1957, USSR launched Sputnik II, and USA satellites Explorer I and III followed on February 1 and March 26, 1958.  At  every  revolution, Explorer  I and III swung from several hundred km to several thousands km. Above 2000 km, the counters, installed aboard by the CR group under J. Van Allen, apparently stopped working and started again at lower altitudes. The only explanation was that they become “jammed” when were exposed to a radiation of excessive strength.

It is generally understood that the inner and outer Van Allen belts result from different processes. The inner belt, consisting mainly of energetic protons, is the product of the decay of albedo neutrons which are themselves the result of cosmic ray collisions in the upper atmosphere. The outer belt consists mainly of electrons that are injected from the geomagnetic tail following geomagnetic storms.

Low energy CR from the Sun

When systematic measurements were undertaken at altitudes and latitudes where primary CR particles of lower energy could also be observed, it became apparent that the low-energy portion of the cosmic radiation had to do primarily with events in the sun.

The CR particles from these events, recorded at Earth, have energies of the order of tens of GeV, since the effect is usually much smaller near the geomagnetic equator than at high latitudes. The same conclusion is indicated by the fact that neutron detectors record a much greater increase than μ detectors, since μ leptons are produced abundantly only by protons with greater energies.

SOHO images of the flare that occurred on the 15 July 2002

SOHO images of the flare that occurred on the 15 July 2002

The solar cycle

The general pattern of solar activity follows an 11-year cycle. When cosmic ray observations began to accumulate, it was found that the flux of cosmic rays also changes systematically during this cycle.

In the plot (lower figure) it is reported the intensity of CR measured at a geomagnetic latitude of 88° N by H.V.Neher of CalTech in 1954 and 1958. At the highest altitude, the intensity doubles. The interpretation of these data is that the plasma emitted by the Sun carries materially away with it the magnetic field, which acts as a partial screen against CR particles entering the solar system from the outside.

Solar cycle from 1991 (on the left) to 1995 (on the right)

Solar cycle from 1991 (on the left) to 1995 (on the right)

A changing perspective

During several years physicists belief on cosmic rays changed continuously. At the beginning, Millikan though that they were mainly photons and resulted from the synthesis of heavy elements like nitrogen, oxygen or silicon. But the coincidences observed by Bothe and Kohlhörster in Geiger-Müller counters were difficult to explain by double Compton effects. The observations seemed to indicate that the primary cosmic radiation consisted of charged particles.

Then, other experiments showed that high-energy cosmic rays occasionally produced secondary ionizing  particles in the matter of the shields. It soon became clear that this was not inusual, but a characteristic of these particles, which arrived to Earth in showers.

Photograph by the MIT cosmic ray group

Photograph by the MIT cosmic ray group

Photograph by Blackett and Occhialini

Photograph by Blackett and Occhialini

A changing perspective

Experimental set-up by Bruno Rossi

Experimental set-up by Bruno Rossi

The discovery of extensive air showers

Extensive air showers were discovered in the 1930’s by the French physicist Pierre Victor Auger. In addition to his contributions to the field of cosmic rays, Pierre Auger was most well known for his discovery in the 1920’s of a spontaneous process by which an atom with a vacancy in the K-shell achieves a more stable state by the emission of an electron instead of an X-ray photon, commonly known as the Auger Effect.

After physicists began to experiment with coincidences, it became a common practice to test the operation of the equipment by placing the counters out of line, usually on a horizontal plane. Several experimenters noticed that the number of coincidences recorded was too large to be accounted for entirely by chance. In 1938 Pierre Auger and collaborators undertook a systematic study that established beyond any doubt the occurrence of air showers and provided preliminary information about their properties.

Shower development

A high-energy primary CR particle (e.g. a proton) collides with a nucleus (O, N, Ar) in the atmosphere producing other particles, mainly pions and kaons. These particles have energies high enough to produce more particles (mainly hadrons). This is called air shower (or hadronic cascade). At very high energies this is an Extensive Air Shower (EAS).

Neutral pions quickly decay into two photons, which start electromagnetic cascade. Photons produce e+e--pairs, which generate photons in their turn via bremsstrahlung radiation. Eventually, π, K and other unstable particles decay into muons and neutrinos (or electrons and neutrinos), whereas low energy electrons lose energy via ionization without generating more photons.

Branching models

As a result, at first the particles increase in number while their energy decreases. Eventually, as the original energy is shared among more and more particles, individual particles have so little energy that they no longer produce new particles (they arrive to the so called critical energy, Ec), but lose energy by ionization: the shower particle number stops increasing and gradually goes to zero.

After n branchings the number of particles is

N(X) = 2^{X/\lambda}

The energy per particle is

E(X) = \frac{E_0}{N(X)}

The number of particles at maximum is

N(X_{max}) = \frac{E_0}{E_c}

Then, Xmax is given by

X_{max} = \lambda \frac{\log(E_0/E_c)}{\log 2}

Longitudinal shower distribution

Longitudinal shower distribution

Simple branching model of an air shower (Heitler, 1944). Lambda is the collision length.

Simple branching model of an air shower (Heitler, 1944). Lambda is the collision length.

Particles and energy

The growth and decline of the number of charged particles of a shower can be defined using various mathematical models. One of these is the Gaisser-Hillas profile (1977):

N(X) = N_{max} \left( \frac{X - X_0}{X_{max} - X_0}\right)^{\frac{X_{max} - X_0}{\lambda}} \, \exp\left[ \frac{X_{max} - X}{\lambda} \right]

where X0 is the first interaction point. Note that the Slant depth reported in Figure is equal to

X = \frac{X_{Slant}}{\sin \alpha}

The primary energy is given by the track length integral plus the energy carried away by neutrinos:

E_0 = \alpha \int^\infty_0 dX \, N(X) + E_\nu

where α is the energy loss per unit length per particle.

Shower characteristics

Proton induced showers have larger fluctuations than iron or photon induced ones, and the average depth of the shower maximum is intermediate between them. The first thing is due to the fact that a heavy primary like an iron nucleus is viewed as a collection of independent nucleons (superposition model) and the  result of  collision is similar to an average on its constituents. On the other side, a photon primary produces an e.m. shower, where the fluctuations are reduced with respect to a hadronic shower.

The second feature depends on the fact that the interactions probabilities of the nucleons in the superposition model add, leading to a faster development of the shower and a somehow different formula for Xmax:

X_{max} \propto \lambda \, \log\left[ \frac{E_0} {A \, E_c}\right]

Proton FI: 70 g/cm2 Fe FI: 15 g/cm2 at PeV energies. The energy of primary is 3 10^20 eV.

Proton FI: 70 g/cm2 Fe FI: 15 g/cm2 at PeV energies. The energy of primary is 3 10^20 eV.

Elongation rate

The average of Xmax is related to the primary energy. For the simple Heitler branching model, for example:

X_{max} = \lambda \frac{\log(E_0/E_c)}{\log 2} \equiv \overline{X} \, \log E_0 + a = \overline{X} \, \log 10 \, \log E + a = 2.3 \,  \overline{X} \, \log E + a

The elongation rate is the increase of Xmax per decade of energy

E \, R = \frac{dX}{d \log E} = 2.3 \, \overline{X}

The elongation rate is different for different primaries and can be used for obtaining information on the composition of cosmic rays.

Shower distributions

The evolution of a shower is of statistical nature, since the exact point where a given photon materializes or a given electron radiates, or how the energy is shared between the two particles produced in a single event, is a matter of chance. One may, however, inquire into the average behavior of showers.

Three component: e.m., muonic, and hadronic. Longitudinal shower distribution.

Three component: e.m., muonic, and hadronic. Longitudinal shower distribution.

Lateral shower distribution.

Lateral shower distribution.

Fluorescence and Cherenkov light

A possible source of radiation, practically isotropic, from an air shower is the excitation of air nitrogen by the charged particles, mainly electrons (more correctly, it is scintillation light). First used by the experiment Fly’s Eye.

Moreover, as Blackett first realized in 1948, charged particles that travel faster than light in the atmosphere emit detectable Čerenkov radiation on a narrow cone around the direction of the particle. The opening angle is a function of the density of the air and, thus, of the height of emission.

Neutrinos as Universe messengers

High energy neutrino astronomy is one of the most promising research line in astroparticle physics. Similarly to photons and unlike charged cosmic rays, they keep directional information which can be used to perform astronomy. Differently from gamma rays, they are emitted only in hadronic processes and travel unimpeded to the Earth.

Vertical neutrino induced showers cannot be distinguished from ordinary CR showers. But in very inclined showers it is possible to identify different features for the different primaries.

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