Dissolve volatile green lion in the central salt of Venus and distill. This spirit is the green lion the blood of the green lion Venus, the Babylonian Dragon that kills everything with its poison, but conquered by being assuaged by the Doves of Diana, it is the Bond of Mercury.Isaac Newton, from his alchemical notebooks

This page is presented as an exercise in technical writing. It is an adaption of a written report that was part of the qualifying exam topic for my PhD. The code that accompanies this project is called AIR.

## Contents

### I. Introduction

This report describes the radiation environment in the atmosphere, and an empirical model used to calculate absorbed dose rate within this environment as a function of altitude and geomagnetic location. This study complements the student education/outreach portion of a recent NASA EPSCoR grant that measures absorbed dose rate from cosmic radiation at altitudes up to approximately 100k feet using inexpensive ionization chambers flown on standard weather balloons. A simple computer program called Atmospheric Ionizing Radiation (AIR) verifies the results from such flights. This empirical model calculates absorbed dose rate based on the following considerations: time; latitude; longitude; altitude; galactic cosmic ray (GCR) spectrum; ionization rate; neutron contribution; geomagnetic field and cutoff; solar cycle phase.

The AIR model was modified to make use of neutron count rates and vertical cutoff rigidities provided by the Climax Neutron Monitor in Colorado, the nearest operating neutron monitor to Stillwater, Oklahoma. In this report, we describe this model and show comparisons with actual balloon flight data.

The radiation environment within the Earth's atmosphere is complex and changes with altitude, geomagnetic position, and time. The radiation environment is dominated by cosmic radiation at all but the lowest altitudes. This is not due to primary cosmic radiation, but rather cosmic ray secondaries produced through nuclear interactions. These secondary particles are the result of air showers or particle cascades initiated when primary cosmic rays interact with the constituent nuclei of the atmosphere. An understanding of the radiation environment at high altitudes can be obtained by considering the sources of cosmic radiation and the different physical processes that affect this radiation. For high altitudes, one must first consider propagation of this radiation field through the Earth's magnetosphere before taking into account its propagation in the atmosphere.

For the most part, life is shielded against this radiation by approximately 1,033 g/cm2 of air, which is comparable to a water depth of roughly 10 m. On the ground, cosmic rays contribute less than 10% of the total absorbed dose rate of natural background radiation. While not a health issue on the ground, exposure to cosmic radiation may be a health concern at altitudes greater than 30k ft. At these altitudes, airline pilots and flight attendants are considered radiation workers since they can accumulate a biologically-weighted absorbed dose of approximately 9 mSv/yr, assuming 600 hr/yr exposure time. This is compared to approximately 0.3 mSv/yr for the average person at sea level. Prolonged exposure to high altitude cosmic radiation may increase the risk of fatal cancer as well as the development of cataracts in the eyes. Exposure to ionizing radiation can also adversely affect aircraft electronics (avionics). In addition to practical concerns, atmospheric ionizing radiation is part of our environment and thus intrinsically interesting.

### II. Radiation Environment in the Atmosphere

#### 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.

### Footnotes

1. E.R. Benton, E.G. Yukihara, A.S. Arena, Jr., and A.C. Lucas, Tissue Equivalent Detectors for Space Crew Dosimetry and Characterization of the Space Radiation Environment, A NASA Experimental Program to Stimulate Competitive Research (EPSCoR) Project (2007).Back to standard weather balloons
2. W. Heinrich, S. Roesler, and H. Schraube, "Physics of Cosmic Radiation Fields," Radiation Protection Dosimetry 86(4), 253 (1999).Back to natural background radiation
3. E.A. Blakely, "Biological Effects of Cosmic Radiation: Deterministic and Stochastic," Health Physics 79(5), 495 (2000).Back to 600 hr/yr exposure time
4. F. Spurný and Ts. Dachev, "Measurements in an Aircraft during an Intense Solar Flare, Ground Level Event 60, on April 15, 2001," Radiation Protection Dosimetry 95, 273 (2001).Back to average person at sea level
5. E. Ron, "Ionizing Radiation and Cancer Risk: Evidence from Epidemiology," Radiation Research 150, S30 (1998).Back to fatal cancer
6. V. Rafnsson, E. Olafsdottir, J. Hrafnkelsson, H. Sasaki, A. Arnarsson, and F. Jonasson, "Cosmic Radiation Increases the Risk of Nuclear Cataract in Airline Pilots," Arch Ophthalmol 123(8), 1102 (2005).Back to cataracts in the eyes
7. T. Foelsche, R.B. Mendell, J.W. Wilson, and R.R. Adams, "Measured and Calculated Neutron Spectra and Dose Equivalent Rates at High Altitudes; Relevance to SST Operations and Space Research," NASA Technical Note D-7715 (1974).Back to near solar maximum
8. J.A. Simpson, "Elemental and Isotropic Composition of the Galactic Cosmic Rays," Annual Review of Nuclear and Particle Science 33, 323 (1983).Back to broken down as follows
9. E.R. Benton, "Radiation Dosimetry at Aviation Altitudes and in Low-Earth Orbit," PhD dissertation (2004).Back to adapted from
10. G.D. Badhwar, "The Radiation Environment in Low-Earth Orbit," Radiation Research 148, S3 (1997).Back to model calculation
11. G.D. Badhwar and P.M. O'Neill, "An Improved Model of Galactic Cosmic Radiation for Space Exploration Missions," Nuclear Tracks and Radiation Measurements 20, 403 (1992).Back to time-dependent solar adjustment of the GCR spectrum
12. B. Rossi, Cosmic Rays, New York, McGraw-Hill (1964).Back to latitude effect
13. T.H. Johnson, "A Note on the Nature of the Primary Cosmic Radiation," Physical Review 54, 385 (1938).Back to dominate proton component in the GCR spectrum