DOS 514 - Week 2 Discussion
Initial Post: Inefficient X-Ray Production
The basic concept behind the production of x-rays on demand is relatively simple, although the implementation can be very complex. In principle, you need an evacuated chamber with an electron source at one end, a target at the other end, and an extremely high voltage potential between the two.1 Khan explains that in most modern x-ray tubes, which are Coolidge-type constructions, the electron source (the cathode) is a glowing hot coiled filament of tungsten that throws off electrons through a process called thermionic emission. In order to help get the electrons moving in the correct direction, Khan goes on to explain that many designs feature a negatively charged cup around the filament that repels the produced electrons in the direction of the anode as soon as they are produced. An extremely large voltage potential, usually between 50-200 kV for imaging applications, rapidly accelerates the electrons down the length of the tube as they are drawn by their electric charge. At the other end of the tube is a target mounted on the anode, which is in the path of the high velocity electron stream. The anode itself is usually a large copper rod that is effective for conducting both electricity and waste heat. The target itself is usually made of tungsten, for several reasons.
As Khan explains, x-rays can be produced by electron streams in two primary ways:
- Bremsstrahlung, or "braking radiation". Since electrons have a negative charge, and atomic nuclei, which contain protons, have a positive charge, electrons that pass nearby an atomic nucleus will be deflected towards the nucleus by the force of Coulomb attraction.1 The degree of deflection will vary based on the proximity of the electron's path to the nucleus and based on the overall charge of the nucleus, which is determined by its Z-number (number of protons). The closer the path is, the higher the deflection, and the higher the Z-value is, the higher the deflection. Of these two factors, the Z-value of the target material is the only one that can be controlled by target construction. A high-Z-value material is optimal. Khan explains that tungsten is the best choice because it has both a high Z-value (74) and an extremely high heat tolerance (melting point of 3370 C). The reason that deflection is important is that the energy lost by the electron in the deflection must be conserved, so it is radiated out as an x-ray photon.
- Characteristic x-rays. Instead of interacting with the nucleus of a target atom, Khan points out that an incoming high speed electron may instead eject one of the target atoms' orbital electrons.1 As the vacancy is filled by an orbital electron from a higher orbit, the difference in binding energy will be emitted as a characteristic x-ray of predictable wavelength based on the orbit of the vacancy.
Khan explains that several factors affect the efficiency of conversion of high-speed electron energy into x-ray photon energy, but Z-number and tube voltage are the most important in the voltage ranges typically found in imaging systems and low-power therapy systems.1 In these ranges, efficiency can be modeled by the equation:
With a typical tungsten target (Z=74) and a 100 kV tube voltage, this comes out to:
Efficiency increases with tube voltage. In my department, we always scan at 120 kV, so we would expect an efficiency of around 0.8%
Khan points out that at tube voltages around 100 kV, the direction of the resulting x-rays is more or less evenly distributed, so x-rays going in the wrong direction must be filtered out, and x-rays of undesirable energies are also filtered, creating more waste.1 Since energy must be conserved, the 99+% of the electron stream's energy that isn't converted to useful x-rays is lost as heat, which results in extremely high cooling needs. Khan points out that the heavy copper construction of the anode allows effective transmission of this waste heat to an external cooling mechanism that can be based on oil, water, or air cooling.
- Khan FM, Gibbons JP. The physics of radiation therapy. 5th ed. Philadelphia, PA: Lippincott, Williams, and Wilkins; 2014:66-82