1.2.2: Attenuation & Scattering of Electron Beams

Attenuation of electrons

Electrons are attenuated through inelastic orbital or radiative collisions. Attenuation is based on the atomic number of the material and the beam energy, and is given the amount of kinetic energy Ek lost per unit of length x.

(1)
\begin{align} (\frac{S}{\rho})_{tot}=\frac{1}{\rho}.\frac{dE_k}{dx} \end{align}

The total mass stopping power is made up of the collisional and radiative mass stopping powers:

(2)
\begin{align} (\frac{S}{\rho})_{tot}=(\frac{S}{\rho})_{col} + (\frac{S}{\rho})_{rad} \end{align}

Where $(\frac{S}{\rho})_col$ is the collisional mass stopping power and of great interest in radiation therapy. This value is the amount of energy transferred to a material per unit length, and can determine the dose received if multiplied by the electron fluence.

Collisional Stopping Power

Importantly, electrons are more likely to undergo collisional interactions at lower energies and within low atomic number materials. This is due to the increased number of electrons per gram in low Z material and the increased binding energy of electrons in high Z atoms.

Radiative Stopping Power

Radiative losses increase as electron energy climbs above 1 MeV, and is also higher for high Z material - in general, radiative interactions are proportional to the beam energy and also proportional to the square of the atomic number. Therefore high Z materials and high electron energies will effectively produce bremsstrahlung radiation (explaining the tungsten target in the linear accelerator).

Scattering of electrons

Electrons are scattered as they pass through a medium, mostly through elastic 'collisions' with the nuclei of an atom. Scattering is more pronounced at lower beam energies and with higher atomic numbers.

As electrons move through a medium, they lose energy through attenuation. Lower energy electrons are more likely to scatter laterally. This is seen for high energy electron beams, where the penumbra is relatively narrow near the surface and broadens significantly at depth.

The mass scattering power of a medium is dependent on the incident electron energy as well as the material, and is given by:

(3)
\begin{align} \frac{T}{\rho}=\frac{\bar{\theta}^2}{\rho l} \end{align}

Where θ is the mean scattering angle and ρ is the density of the material.

Variation of Scattering Power

The scattering power is:

  • Proportional to the square of the atomic number Z
  • Inversely proportional to the square of the kinetic energy of the electron

Therefore, low energy electrons will be scattered more readily than high energy electrons; and high Z materials will cause more scattering than low Z material.

This explains two important concepts in physics:

  • Electrons passing through an inhomogeneity may be backscattered if the inhomogeneity is of higher atomic number than the medium. This can lead to increased dose on the low Z side of the inhomogeneity boundary
  • Electrons generated from a linear accelerator have high energy and travel in a pencil beam. By passing them through a scattering filter, they will be scattered in numerous directions. Scattering filters are made from thin, high Z material to produce the required scattering.

Range

The range of electrons is the distance travelled by an electron within a medium. In general, electrons with energies above 1 MeV will lose 2 MeV of energy per cm of water traversed. Below 1 MeV, electrons give up their energy relatively rapidly as they undergo more interactions with orbital electrons.

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