Introduction to Ionizing Radiation

Since a large part of medical physics deals with the application of ionizing radiation to medicine, these tutorials begin with a brief description, both qualitative and quantitative, of ionizing radiation.

Ionizing Radiation Qualities

Qualitatively, ionizing radiation is the propagation of energy in the form of a wave or particle (see the wave-particle duality principle), although it will almost always be referred to as particles on this website. While radiation may be of any arbitrary energy, in this case we are only concerned with radiation that is energetic enough to ionize atoms, hence the name ionizing radiation. A group of radiation particles is often referred to as a radiation beam.

Ionizing radiation is typically classified by its particle type, which defines both its electric charge and mass. Some of these particles, such as photons (sometimes called x-rays or gamma rays) and electrons, are elementary (i.e. they cannot be broken into smaller particles). Others, such as protons and neutrons, are a combination of elementary particles and will have more mass than the elementary particles. Each particle either has an electric charge or does not, and this affects how the radiation will interact with matter. Charged particles such as electrons and protons will interact directly with nearby electric fields in matter via Coulomb's law. In contrast to charged particles, uncharged particles such as photons and neutrons cannot interact via Coulomb's law and have indirect, probabilistic interactions. This means that it is possible for uncharged particles to pass through matter without interacting, while charged particles will always interact with the nearby electric fields of atoms and molecules. When uncharged particles do interact, they transfer their energy to charged particles, which then interact with matter directly; this is what we mean by the indirect interaction of uncharged particles.

Ionizing Radiation Quantities

Radiation particles are typically quantified by four parameters: amount, energy, time, and position. Describing each of these quantities will help set a foundation for the subsequent tutorials when other derived quantities, such as radiation dose, are defined.

Radiation Amount

The basic quantity of radiation amount is the radiation fluence, defined as the number of radiation particles N passing through an area A:

\Phi = N / A

By definition, the units of fluence are inverse area (e.g. particles/cm2).

Radiation Energy and Energy Fluence

Radiation particles are also quantified by the physical property of energy. While the SI units for energy, joules (J), can be used to quantify radiation energy, the energy of a single particle is often many orders of magnitude less that 1 J. Thus the concept of the electron volt (eV) was introduced, which is defined as the energy of a single electron with charge e accelerating through a 1 volt potential:

1 \ eV = e \times (1 \ V) = (1.6022 \times 10^{-19} \ C) \times (1 \ J/C) = 1.6022 \times 10^{-19} \ J

Given the binding energy of atomic electrons to the nucleus, the energy for ionizing radiation is typically greater than approximately 10 eV, although this will certainly depend on the atomic properties of the material being exposed to the radiation.

Radiation energy and amount can be combined with the concept of energy fluence, which is defined as the amount of radiation energy E passing through an area A:

\Psi = EN / A = E \Phi

Similar to fluence, the units for energy fluence are energy divided by area (e.g. J/cm2). In all the definitions above it was assumed that the energy of all the particles in a beam are the same, i.e. E is constant and the radiation beam is monoenergetic. However, we will often encounter radiation beams that are polyenergetic, containing a varying spectrum of energies. In this case the fluence energy-dependent and denoted as \Phi (E), and the total fluence and energy fluence can be obtained by integrating over all energies in the spectrum:

\Psi = \int^{E_{max}}_{E_{min}} \Psi (E) \ dE

\Psi = \int^{E_{max}}_{E_{min}} E \Phi (E) \ dE

Radiation vs. Time

We are also certainly interested in how radiation changes over time. Is it constant over time? Does it vary periodically? Both the fluence and the energy fluence can be quantified with respect to their change over time, defined as the fluence rate and energy fluence rate, respectively:

\phi = d\Phi / dt

\psi = d\Psi / dt

The total fluence and energy fluence can be calculated from their respective rates by simply integrating over the elapsed time T:

\Phi = \int^{T}_{0} \phi \ dt

\Psi = \int^{T}_{0} \psi \ dt

Radiation vs. Position

Finally, we are also concerned with radiation as a function of position. Where did the radiation originate from (also called the radiation source)? Which direction is the radiation traveling? In addition to energy or time, we can also define fluence in terms of position, for example Cartesian coordinates, \Phi(x,y,z), or spherical coordinates, \Psi(r,\phi,\theta). Integrating over all spatial dimensions would result in the total fluence:

\Phi = \int^{x_{max}}_{x_{min}} \int^{y_{max}}_{y_{min}} \int^{z_{max}}_{z_{min}} \Phi(x,y,z) \ dx \ dy \ dz

\Phi = \int^{r_{max}}_{r_{min}} \int^{\phi_{max}}_{\phi_{min}} \int^{\theta_{max}}_{\theta_{min}} \Phi(r,\phi,\theta) \ dr \ d\phi \ d\theta

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