Interaction of GCRs with the Interplanetary Medium

Galactic cosmic rays (GCRs) are charged particles that originate from sources beyond our solar system. At least outside of the heliosphere, the distribution of GCRs is believed to be isotropic throughout interstellar space. The energy range of GCRs varies considerably, from a few tens of MeV/nucleon to as high as 10¹⁶ MeV/nucleon. The total flux of GCRs is very low, being about 0.53 (cm²‑sec‑sr)^-1 near solar minimum, and about half that value near solar maximum. This illustrates the effect of the solar cycle, which indirectly modulates the flux of high energy GCRs entering the solar system via the solar wind. The solar cycle is an 11-year periodic trend in the number of sunspots visible on the surface of the Sun and is indicative of solar activity. The GCR spectrum consists of two main components: baryonic and leptonic. The baryon component is composed of 98% protons and heavy ions. A heavy ion refers to an ionized atom which is usually heavier than beryllium ($Z$ = 4). The lepton component makes up the remaining 2% with electrons and positrons. The 98% baryon portion of the spectrum is broken down as follows:

1. 87% protons;
2. 12% helium ions (alpha particles);
3. 1% heavy ions with atomic numbers ranging from $Z$ = 3 (Li) to 92 (U).

Highly energetic particles in the heavy ion component, or HZE particles, are important from a radiobiological standpoint because they possess a high linear energy transfer (LET) and are highly penetrating. LET is the amount of energy deposited per unit path length of a charged particle on transit through a medium (units: keV/μm). Figure 2.1 shows relative abundances of various GCR species both as a function of $Z$ and $Z^2$. The fundamental dosimetric quantity of absorbed dose, in units of gray (Gy = gray; 1 Gy = 1 J/kg), is proportional to LET, and LET is proportional to $Z^2$. Energetic iron nuclei are the most important HZE particles, as Figure 2.1 demonstrates, since they are relatively plentiful compared to other high $Z$ particles.

Figure 2.2 shows the measured energy spectra of various components of the GCR spectrum⁸. The general shape of the observed differential energy spectra in this plot is typical of measurements at the orbit of Earth. Figure 2.3 details the attenuating effect of solar activity on the GCR spectrum via a model calculation. This model contains improvements in the treatment of the time-dependent solar adjustment of the GCR spectrum. This improved treatment predicts that the flux is relatively insensitive to variables such as solar wind velocity. However, the large scale structure of the interplanetary magnetic field (IMF) is important, which the solar wind transports. The solar wind is a stream of charged particles that is electrically conductive so that magnetic field lines from the Sun are carried along with it. The solar wind creates the heliosphere, which can be thought of as a vast "bubble" in the interstellar medium surrounding the solar system. The lower energy component of the GCR flux entering the heliosphere is partially attenuated as these particles are scattered by irregularities in the IMF embedded in the solar wind. The large scale structure of the IMF changes in shape through the 11-year solar cycle, causing variations in the GCR spectrum over solar maximum and minimum as shown by Figure 2.3. In general, the changes in the spectra of Figure 2.3 are indirect responses to the level of solar activity that is manifested in the large scale changes of the IMF carried by the solar wind.

Interaction of GCRs with the Earth's Magnetic Field

Since GCRs are charged particles, they are affected by the Earth's magnetic field. These charged particles tend to follow lines of the geomagnetic field, which are parallel to the Earth's surface near the equator. All but the most energetic particles are deflected away by the Earth's magnetic field. Cosmic ray primaries enter the Earth's magnetic field before entering the atmosphere; the shape of this dipole field is such that both a latitude effect and an angular dependence (east-west effect) is present in its shielding properties. Since geomagnetic field lines are perpendicular to the Earth's surface at the poles, GCR particles have the tendency to be funneled towards these locations, while particles arriving near the equator are deflected away. From the poles to the equator, particles of increasingly high energy are prevented by the magnetic field from reaching the surface. This is referred to as the latitude effect. This magnetic deflection creates an asymmetry in the distribution of the arrival directions of cosmic ray particles entering the atmosphere. Moreover, positively charged particles—protons—arrive with greater abundance from the west than the east. This is referred to as the east-west effect¹². The east-west effect accounts for a dominate proton component in the GCR spectrum.

The Earth's magnetic field, from the perspective of an incident GCR, can be understood in terms of a "stiffness" that varies with geomagnetic position. An incoming GCR can contribute to the radiation environment in the atmosphere only if the particle has sufficient momentum per unit charge, or rigidity, to penetrate the Earth's magnetic field and interact with air nuclei. That rigidity, which is a function of the particle's charge combined with the zenith and azimuthal angles its entrance makes with the Earth's surface, is called the cutoff rigidity and is expressed in gigavolts (GV), which is equivalent to GeV/c per unit charge. The rigidity is given by

$\displaystyle{ R = \frac{p c}{Z e} \text{.} }$

(2.

The Earth's magnetic field is characterized by a cutoff rigidity for a given geomagnetic position. It is a measure of the amount by which a particle of electric charge $Z$ and relativistic momentum $\mathbf{p} = \gamma m \mathbf{v}$ is deflected by a magnetic field. Particles of the same rigidity should be deflected by the same amount and therefore have similar trajectories in a given magnetic field configuration. The term "cutoff rigidity" refers to the ability of the Earth's magnetic field to act as a high-pass filter for incoming cosmic rays. Galactic cosmic rays usually arrive somewhat normal to the Earth's surface, and because of this, tables of vertical cutoff rigidities are compiled for a given magnetic epoch. The latitude effect and the east-west effect are illustrated by the contour plots of vertical cutoff rigidities in Figures 4 and 5 for solar minimum and solar maximum, respectively.

Interaction of GCRs with the Atmosphere

An incoming GCR can interact with the nuclei of the atmosphere once it has traversed the Earth's magnetic field. The particle can interact with air (or target) nuclei in two ways: 1) ionization and 2) nuclear fragmentation. Ionization is an electromagnetic phenomenon that results in the slowing of a charged particle when it interacts with electrons in the air that are also charged. Nuclear interactions, on the other hand, occur when a nucleon (a proton or neutron) interacts with a target nucleus, causing the production of secondary nucleons, pions, muons, and more. These interactions, both electromagnetic and nuclear, cease once the quantity of kinetic energy carried by the primary GCR has been dissipated.

Ionization vs. Nuclear Reactions

LET is the amount of energy deposited by a particle to the surrounding medium per unit path length, which is directly related to the amount of energy deposited per unit mass by electromagnetic processes (absorbed dose). LET is proportional to the square of the projectile charge, and inversely proportional to the square of the projectile velocity. A lower velocity translates into a higher LET, meaning that a particle is imparting more energy per unit path length to the medium (units: keV/μm).

A classical picture of target fragmentation, shown in Figure 2.6, typically involves nucleon-nucleus reactions. The usual scenario involves the interaction of an incident proton or neutron with a target oxygen or nitrogen nucleus in the atmosphere. The incident nucleon is commonly a primary GCR proton, but a secondary proton or neutron resulting from an earlier nuclear interaction within the atmosphere may also be the case. A target fragmentation event can result in a number of different scenarios depending on the kinetic energy of the incident nucleon and the proximity of the interaction. For high energy interactions greater than 1 GeV, neutral and charged pions may be produced. Neutral pions quickly decay into gamma rays; these gamma rays can participate in pair production, provided they have enough energy to do so (~1.022 MeV). This leads to an electromagnetic cascade. Charged pions, on the other hand, undergo energy loss through ionization and can decay into charged muons, which themselves decay into electrons and positrons.

At intermediate energies above 50 MeV, the incident nucleon interacts with individual nucleons within the target nucleus, thereby producing knock-out protons, neutrons, alpha particles, and occasional light nuclei ($Z$ > 4). This is referred to as an intra-nuclear cascade. The emission of these nucleons during the cascade is usually in the forward direction. The emitted particles, having charge, will be slowed through ionization, but are still free to undergo additional nuclear interactions in what is known as an extra-nuclear cascade. The target nucleus is often left in an excited, unstable state—called a compound nucleus—after the initial collision and the resulting cascade. This compound nucleus can return to stability through the evaporation, or prompt emission, of protons, neutrons, and alpha particles. The evaporation of particles is nearly isotropic, with the nucleus recoiling in a direction conforming to conservation of momentum. These evaporation events of excited nuclei are more biologically damaging than energetic lightly ionizing particles.

The target nucleus may be in a final state of radioactivity following these events. Proton- or neutron-induced radioactivity will require either alpha, beta, or gamma decay to achieve stability in the long term (i.e., a time frame measured in seconds). The radioactive decay products will be emitted nearly isotropically, as in the case of the compound nucleus.