Production of X-rays

1. The X-ray tube

1.1. Introduction

X-rays are generated when high velocity electrons are suddenly decelerated on impact with a metal target, losing its kinetic energy in the emission of a quantum of x-ray radiation. This occurs within a vacuum-sealed x-ray tube which principally contains a cathode and an anode. The cathode, which contains a tungsten filament, provides a source of electrons and is therefore the negative terminal of the x-ray tube. The anode is the target for the negatively charged electrons and is therefore the positive terminal of the x-ray tube. The anode is the site where electron kinetic energy is converted into x-ray radiation.

The process of converting electrical energy to useful diagnostic x-rays, however, is inefficient with the vast majorty (95 – 99%) of energy being converted to heat. The design of x-ray tubes must therefore account for effective heat dissipation to allow for higher electrical input, prevent equipment damage and promote the longevity of x-ray machine. 

The cathode as described in chemistry refers to the positive terminal. Likewise, the anode refers to the negative terminal.

1.2. Photons and Energy

Photons travel at the speed of light c in a vacuum, where c = 3 x 10⁸ ms^-1

c = ƒ × λ

Photon energy can be calculated with the following equation:

E = h × ƒ

This equation can be re-arranged as follows:

$E = \frac{h \times c}{\lambda }$

where E = photon energy (J), h = 6.626 x 10-34 J.s (Planck’s constant), λ = photon wave length.

Worked example

For a typical x-ray photon with λ = 1 x 10^-11m

$E = \frac{6.626 x {10}^{–34} J.s\times 3 x {10}^8 m.s^{–1}}{1 x {10}^{–11} m} = 2 x {10}^{–14} J$

1 eV = 1.6 x 10^-19 J

∴ 2 x 10^-14 J = 1.2 x 10⁵ eV = 120 keV

2. Generation of an X-ray Photon

The production of the x-ray spectrum involves the interaction of electrons with the nucleus or electrons of the target anode. 

2.1. Electron interactions with the target anode

2.1.1. Inelastic collisions with the nuclei – Bremsstrahlung radiation

When negatively charged electrons from the cathode interact with atoms of the tungsten anode, its trajectory is influenced by the larger mass of the tungsten nucleus and coloumbic force exerted by the positive charge of the nucleus.

The deflection of the electron results in a loss of total kinetic energy. This loss of kinetic energy is transformed in the emission of a quantum of radiation in the x-ray band of the electromagnetic spectrum. This is an example of an inelastic collision as the total kinetic energy of the electron and nucleus is not conserved.

As incident electrons lose kinetic energy as their original path is deflected, their velocity is reduced and therefore the x-ray radiation is termed Bremsstrahlung or braking radiation. As there are differences in the degrees of inelastic collisions and therefore resultant x-ray radiation, a spectrum of x-ray photons results. The closer the proximity of interactions and therefore greater the coloumbic force, the greater the energy given. The maximum energy of the x-ray photon is equal to the maximum kinetic energy of the incident electron, as all energy is transformed.

Bremsstrahlung interactions produce a continuous spectrum of radiation, with a maximum energy determined by the peak kilovoltage (kVp). Bremsstrahlung x-ray production increases with accelerating voltage and atomic number of the anode. The number of Bremsstrahlung X-ray photons emitted decreases linearlywith energy. The probability of interaction increases with distance from the nucleus. Increased distance from nucleus => more interactions => lower energy xrayphotons

2.1.2. Elastic collisions with the nuclei

It is also possible that elastic interactions occur with the nuclei where the kinetic energy of the incident electron is mostly conserved, resulting in only small deflections from its original trajectory. This electron will continue to propagate through the anode until it eventually undergoes an inelastic collision

2.1.3. Inelastic collisions with the electrons – Characteristic x-rays

The incident electron transfers a fraction of its energy to an orbital electron. Depending on the energy transferred to the orbital electron, the collision will result in either excitation of the atom or ionisation of the atom.

With sufficient energy, an incident electron can promote or excite an inner shell electron to a higher energy and more unstable outer electron shell. 

If the energy transferred by the incident electron exceeds the binding energy of an inner electron shell, the orbital electron will be ejected, thereby positively ionising the atom.

In both excitation or ionisation, a inner shell vacancy is created which is then immediately occupied by an outer electron undergoing a quantum jump. As these electrons perform this quantum jump, they emit a quantised photon of discrete energy equivalent to the energy difference between the orbital shells. These discrete photons are characteristic to the target atom, and therefore are termed characteristic x-rays.

3. The Spectrum

• The number of Bremsstrahlung X-ray photons emitted decreases linearly with energy
• The probability of interaction increases with distance from the nucleus
• Increased distance from nucleus => more interactions => lower energy xray photons.

Increasing kVp;

• improves radiative interaction probability
• reduces heat loss
• more photons have the energy to eject k shell electrons
• Increase beam Quantity (more so than increasing mAs)
• Increase beam Quality

Radiation output (and dose) ∝  kVp2

If AEC is used, there may be a patient dose reduction as mAs will be modulated.

Next chapter: Beam Quality

Quiz