2.3.1 - Photon Beam Spectrum

## Fluence and Spectrum

### Monoenergetic Beams

A beam of photons is most easily thought of as a containing a single energy of photons. This simplifies calculation of energy within the beam. Numerous descriptors can be used to classify this beam.

#### Fluence

The fluence of a beam is the number of photons (N) that enter an imaginary sphere, with a cross-sectional area of A m2. The units of fluence are m-2.

(1)
\begin{align} \Phi = \frac{N}{A} \text{m}^{-2} \end{align}

#### Fluence Rate

The fluence rate describes the fluence per unit time, with units of m-2.s-1.

(2)
\begin{align} \phi = \frac{\Phi}{t} \text{m}^{-2}\text{s}^{-1} \end{align}

#### Energy Fluence

Instead of particles, the energy fluence is the amount of energy (in Joules) that enters the imaginary sphere with cross-sectional area of A m2. It has units of $\frac{J}{m^2}$

(3)
\begin{align} \Psi = \frac{E}{A} \frac{\text{J}}{\text{m}^2} \end{align}

Energy fluence can be found by multiplying the particle fluence by the energy (E) of individual photons:

(4)
\begin{align} \Psi = \Phi.E = \frac{N \times E}{A} \end{align}

#### Energy Fluence Rate

This has a similar usage to Fluence Rate, and is the energy fluence per unit time.

(5)
\begin{align} \psi = \frac{\Psi}{t} \frac{\text{J}}{\text{m}^2 \text{s}} \end{align}

### Polyenergetic Beams

The above values are not suitable descriptions of a polyenergetic beam (which all therapeutic beams are).

#### Fluence Spectrum

The fluence spectrum describes the number of particles of different energies that enter the imaginary sphere.

#### Energy Spectrum

The energy fluence spectrum describes the amount of energy that enters the sphere of area A m2, accounting for the different energies of the representative particles.

## Describing Photon Beams

It is difficult to describe a photon beam as 'containing a spectrum of energies, from 0 to a maximum of 200 keV, following a particular curve…' etc etc. Therefore there are shorter ways of describing a beam without going into all the specifics.

### Half Value Layer

The half value layer is a useful descriptor of (particularly low energy) photon beams. However, it does not always describe the distribution of dose within a volume well.
HVL values are often given for kilovoltage beams, often as a metal type and a thickness. This is the thickness of a particular metal that will attenuate half of the beam. Low kilovoltage beams will typically use a thickness of aluminium (Z = 13); orthovoltage beams typically use HVL of copper.

### Peak Voltage (kVp)

The peak voltage is the voltage potential that exists within the x-ray tube. This is typically under 150 keV for superficial beams and under 500 keV for orthovoltage beams.
By combining the peak voltage and the HVL, a clinically useful description of the beam is generated.

### Effective Energy

The effective energy is the equivalent energy of a theoretical monoenergetic photon beam that would be attenuated at the same rate as the beam in question. For megavoltage beams, this is usually quoted as a HVL of lead to attenuate half of the theoretical beam. This is not a very useful description as the distance for the first and second HVL of a beam are not equal.

### Mean Energy

The mean energy is the average fluence or energy fluence of a beam. It is not commonly used to describe photon beams.

### TPR20,10

The TPR20,10 is the method recommended by the IAEA to describe a megavoltage photon beam. This is the absorbed dose at a depth of 20 cm divided by the dose at a depth of 10 cm within a water phantom. This ratio gives a number under 1 which provides a useful description of how the photon beam is attenuated in water, the most commonly irradiated material in radiotherapy.