9.1 - Measurement Of Electron Beams

## Measurement of Beam Quality

Electrons are mono-energetic as they exit the beam transport system. Upon hitting the scattering foil and passing through the treatment head and electron applicator, their spectrum broadens due to collisions and ionisations. There are several different methods of classifying an electron beam.

### Most Probable Energy

An electron beam may be specified by the most probable energy at the phantom surface. The Nordic Association of Clinical Physics recommends the use of the formula:

(1)
$$E_{p,0}=C_1 + C_2.R_p + C_3.R^2_p$$

In water, C1 = 0.22 MeV, C2 = 1.98 MeV.cm-1, and C3 = 0.0025 MeV.cm-2. Rp is the practical range of electrons, given by the intersection of an imaginary line drawn through the linear part of the depth dose curve would intersect the depth axis.

### Mean Energy

An alternate method of describing an electron beam is that the mean energy of the electron beam at the phantom surface is related to the R50 (depth at which dose falls to 50%). The relationship is:

(2)
\begin{align} \bar{E_0}=C_4.R_50 \end{align}

For water, C4 = 2.33 MeV.cm-1.

### Energy at Depth

It has been shown that the most probable energy and mean energy of the spectrum decreases linearly with depth, expressed by the relationship:

(3)
\begin{align} (E_p)_z=(E_p)_0.(1-\frac{z}{R_p}) \end{align}
(4)
\begin{align} \bar{E_z}=\bar{E_0}(1-\frac{z}{R_p}) \end{align}

The upper equation states that the most probable energy at depth z is equal to the probable energy at the surface, multiplied by the one minus the depth divided by the practical range. The lower states that the mean energy at depth is equal to the mean energy at the surface multiplied by the same correction factor.
These equations allow dose measurement in ionisation chambers at depth, which require the mean electron energy.

## Measurement of Beam Output

The beam output of each linear accelerator is variable for different beam energies, field sizes and applicators. It also varies between machines. For each machine, beam energy, field size and applicator used the output should be measured. The output for a standard field (usually 10 x 10 cm) is measured for each energy, and then a correction factor is determined for other field sizes and applicators.

## Dosimeters for measuring Electron Beams

Depth dose, isodose distributions may be measured by ionisation chambers, silicon diodes or film. Beam energy and output measurements should be made by ionisation chambers as they are less likely to be damaged and are less dependent on beam energy and temperature.

### Ionisation chambers

A correction needs to be applied when measuring dose with ionisation chambers, due to the different stopping powers of water and air. They are typically used for absolute dosimetry.

### Silicon Diodes

Unlike ionisation chambers, no correction needs to be applied for silicon diodes as the stopping power of silicon is similar to water at the energies used in radiotherapy. Due to their potential for damage from radiation it is recommended that silicon diodes are only used for relative dosimetry.

### Film Dosimetry

Film is most useful in determining an isodose distribution on the plane of the film, which correlates closely with ionisation chamber measurements. Film is not energy dependent but the presence of multiple variables means that they are useful only in relative dosimetry. Film is also not used in water phantoms.

## Measurement Protocols

The IAEA TRS 398 is used in my department. It defines conditions under which beam quality and output should be measured. The TRS 398 recommends that electron beams be specified by the R50 value instead of the probable or mean energy at depth. Reference conditions vary depending on beam energy – higher energy beams need larger field sizes in most cases to ensure uniform dose along the central axis.