Bremsstrahlung radiation

Bremsstrahlung is a German term meaning “braking radiation.” It occurs when a high-speed electron is deflected by the strong electrostatic field of the atomic nucleus.

Here’s a detailed step by step breakdown of how Bremsstrahlung photons are produced:

(There’s a lot to go through here. This is one of the most high yield sections of the course. It is worth knowing this in detail. My advice, spend some time here, don’t just skim this section 🙂)

1. Electron acceleration: Electrons are emitted from the filament (thermionic emission) and accelerated through the tube potential (kVp). Each electron arrives at the target with kinetic energy approximately Eₑ ≈ e · V (e.g. 100 kVp → ~100 keV per electron).
2. Entry into target lattice: The electron penetrates the target material, moving through the atomic lattice. It experiences Coulomb forces from nuclei (positive) and bound electrons (negative).
3. Near nucleus interaction (Coulomb deceleration): Passing near a nucleus, the electron’s path is deflected (bent) by the strong nuclear electric field. During this rapid change in velocity (deceleration), the electron loses kinetic energy.
4. Emission of an X-ray photon: The lost kinetic energy is emitted as a single photon of electromagnetic radiation. Photon energy (Eγ) equals the electron’s kinetic energy loss in that interaction.
5. Energy range and probability: The deflection varies from glancing to very close passes: Small deflection → small energy loss → low-energy photon. Close pass → large energy loss → high-energy photon (up to the incident electron’s full energy). Therefore, Bremsstrahlung forms a continuous spectrum from near 0 up to Emax = kVp. The average photon energy of the beam is approximately 1/3 of E_max.
6. Dependence on target atomic number: Intensity (number of photons) ∝ Z² (approximately): high-Z targets (tungsten) produce Bremsstrahlung more efficiently.
7. Dependence on kVp: Increased electron kinetic energy → more Bremsstrahlung photons and higher average and maximum photon energy.

These are the fundamental steps in Bremsstrahlung radiation production. I want to mention a few more details that I have seen mention/tested in exams. I’ve kept these separate because I don’t want these to be a primary focus. The 7 steps above are more important. The are just for those looking to get top marks.

• In the diagnostic energy range, Bremsstrahlung photons are emitted with a forward bias (more intense in the general direction of the incident electron). The bias increases with increasing electron energy.
• A single incident electron can undergo many sequential small deflections most of which produce very low energy photons.
• Most of these very low energy photons are absorbed in the anode and never leave the tube. We will look at absorption later when we look at X-ray interaction with matter.
• The most common interaction in the anode is inelastic collisions between incident electrons and orbital electrons in the target. This produces heat.

The second mechanism for producing X-ray photons at the anode is Characteristic radiation.

Characteristic radiation

Characteristic radiation arises when an incoming electron ejects an inner-shell electron (usually from the K-shell) of a target atom.

Here’s a detailed step by step breakdown of how Characteristic photons are produced:

(The same goes for this step-by-step description of characteristic radiation. It’s a must know)

1. Electron acceleration: Electrons are emitted from the filament (thermionic emission) and accelerated through the tube potential (kVp). Each electron arrives at the target with kinetic energy approximately Eₑ ≈ e · V (e.g. 100 kVp → ~100 keV per electron).
2. Electron impact: On impact with the target, some electrons interact directly with the orbital electrons of tungsten atoms rather than the nucleus.
3. Inner shell ionisation: If the incident electron’s kinetic energy exceeds the binding energy (E_b) of an inner-shell electron (e.g. K-shell), it can eject that electron completely from the atom. The process leaves a vacancy (hole) in the inner shell, and the atom becomes ionised and unstable.
4. Electron transition: To regain stability, an electron from a higher-energy shell (e.g. L, M, or N) drops down to fill the vacancy. The energy difference between the two shells is released as a photon of electromagnetic radiation/ X-ray.
5. Photon energy: The emitted photon energy is discrete and equals: E_{b (outer shell)} – E_{b (inner shell)}. For tungsten: K_α = 59 keV (L → K transition). K_β = 67 keV (M → K transition). These values are characteristic of the element, hence the name.
6. Photon emission: The released X-ray photon leaves the atom with a specific, characteristic energy unique to the target element’s atomic structure. These photons form sharp, discrete peaks on the X-ray spectrum, known as characteristic lines.
7. Threshold dependence: The incident electron must have kinetic energy greater than the binding energy of the target shell for characteristic X-rays to be produced. Below that threshold, only Bremsstrahlung occurs.
8. Emission probability: Probability of K-shell ionisation increases with incident electron energy and atomic number of the target (Z).

Again, some minor points:

• Filling a K-shell vacancy often creates secondary vacancies in outer shells. These may, in turn, be filled by electrons from even higher shells, producing additional (lower-energy) characteristic X-rays or Auger electrons. These a very low energy and rarely leave the tube. This is called the cascade effect. This cascade continues until the atom returns to its ground state.
• Instead of emitting an X-ray photon, the transition energy between shells may be transferred to another orbital electron, which is then ejected (an Auger electron). This is more common in biological tissue (low-Z) and minimal in the anode (high-Z).

Summary of target interactions:

Different target materials are used depending on the type of X-ray spectrum required.

We will discuss these again later (The X-ray spectrum and Mammography sections).

Key takeaways and exam tips:

• Bremsstrahlung radiation: continuous spectrum; produced by electron deceleration near nucleus. Continuous from ~0 to Emax = e·V; average energy ≈ ~⅓ Emax.
• Characteristic radiation: discrete peaks; produced by inner-shell electron transitions.
• Characteristic X-rays appear only if electron energy > shell binding energy. Photon energy = difference between shell binding energies.
• Tungsten Kα = 59 keV, Kβ = 67 keV.
• Mammography targets: Mo (17–20 keV) and Rh (20–23 keV) produce softer X-rays suited for breast tissue.
• Efficiency of X-ray production increases with kVp and Z but remains <1%.