Production of X-Rays
B. CHARACTERISTIC X-RAYS
Electrons incident on the target also produce characteristic x-rays. The mechanism of their production is illustrated in Figure 3.10. An electron, with kinetic energy E0, may interact with the atoms of the target by ejecting an orbital electron, such as a K, L, or M electron, leaving the atom ionized. The original electron will recede from the collision with energy E0 – ΔE, where ΔE is the energy given to the orbital electron. A part of ΔE is spent in overcoming the binding energy of the electron and the rest is carried by the ejected electron. When a vacancy is created in an orbit, an outer orbital electron will fall down to fill that vacancy. In so doing, the energy is radiated in the form of electromagnetic radiation. This is called characteristic radiation, i.e., characteristic of the atoms in the target and of the shells between which the transitions took place. With higher atomic number targets and the transitions involving inner shells such as K and L, the characteristic radiations emitted are of energies high enough to be considered in the x-ray part of the electromagnetic spectrum. Table 3.1 gives the major characteristic radiation energies produced in a tungsten target.
It should be noted that, unlike bremsstrahlung, characteristic x-rays are emitted at discrete energies. If the transition involved an electron descending from the L shell to the K shell, then the photon emitted will have energy hv = EK – EL, where EK and EL are the electron-binding energies of the K shell and the L shell, respectively.
The threshold energy that an incident electron must possess in order to first strip an electron from the atom is called critical absorption energy. These energies for some elements are given in Table 3.2.
3.6. X-RAY ENERGY SPECTRA
X-ray photons produced by an x-ray machine are heterogeneous in energy. The energy spectrum shows a continuous distribution of energies for the bremsstrahlung photons superimposed by characteristic radiation of discrete energies. A typical spectral distribution is shown in Figure 3.11.
M L K Primary
electron
Ejected K electron
∆E−EK
Primary electron after collision E0− ∆E K characteristic radiation Nucleus
E0
Figure 3.10. Diagram to explain the production of characteristic radiation.
TABLE 3.1 Principal Characteristic X-Ray Energies for Tungsten
Series Lines Transition Energy (keV)
K K2 NIII–K 69.09
K1 MIII–K 67.23
Ka1 LIII–K 59.31
Ka2 LII–K 57.97
L Lg1 NIV–LII 11.28
L2 NV–LIII 9.96
L1 MIV–LII 9.67
LaI MV–LIII 8.40
La2 MIV–LIII 8.33
(Data from U.S. Department of health, education, and Welfare. Radiological Health Handbook. rev. ed. Washington, DC:
U.S. Government printing Office; 1970.)
36 part I Basic physics
If no filtration, inherent or added, of the beam is assumed, the calculated energy spectrum will be a straight line (shown as dotted lines in Fig. 3.11) and mathematically given by Kramer’s equation (3):
IE= KZ(Em – E) (3.1)
where IE is the intensity of photons with energy E, Z is the atomic number of the target, Em is the maximum photon energy, and K is a constant. As pointed out earlier, the maximum possible energy that a bremsstrahlung photon can have is equal to the energy of the incident electron.
The maximum energy in kiloelectron volts (keV) is numerically equal to the voltage difference between the anode and the cathode in kilovolts peak (kVp). However, the intensity of such pho- tons is zero as predicted by the previous equation, that is, IE= 0 when E = Em.
The unfiltered energy spectrum discussed previously is considerably modified as the photons experience inherent filtration (absorption in the target, glass walls of the tube, or thin beryl- lium window). The inherent filtration in conventional x-ray tubes is usually equivalent to about 0.5- to 1.0-mm aluminum. Added filtration, placed externally to the tube, further modifies the spectrum. It should be noted that the filtration affects primarily the initial low-energy part of the spectrum and does not affect significantly the high-energy photon distribution.
The purpose of the added filtration is to enrich the beam with higher-energy photons by absorbing the lower-energy components of the spectrum. As the filtration is increased, the trans- mitted beam hardens, i.e., it achieves higher average energy and therefore greater penetrating power. Thus, the addition of filtration is one way of improving the penetrating power of the beam. The other method, of course, is by increasing the voltage across the tube. Since the total intensity of the beam (area under the curves in Fig. 3.11) decreases with increasing filtration and increases with voltage, a proper combination of voltage and filtration is required to achieve desired hardening of the beam as well as acceptable intensity.
The shape of the x-ray energy spectrum is the result of the alternating voltage applied to the tube, multiple bremsstrahlung interactions within the target, and filtration in the beam. How- ever, even if the x-ray tube were to be energized with a constant potential, the x-ray beam would still be heterogeneous in energy because of the multiple bremsstrahlung processes that result in different energy photons.
Because of the x-ray beam having a spectral distribution of energies, which depends on volt- age as well as filtration, it is difficult to characterize the beam quality in terms of energy, pen- etrating power, or degree of beam hardening. A practical rule of thumb is often used which states that the average x-ray energy is approximately one-third of the maximum energy or kVp.
TABLE 3.2 Critical Absorption Energies (keV)
Element
Level H C O Al Ca Cu Sn I Ba W Pb U
Z 1 6 8 13 20 29 50 53 56 74 82 92
K 0.0136 0.283 0.531 1.559 4.038 8.980 29.190 33.164 37.41 69.508 88.001 115.59
L 0.087 0.399 1.100 4.464 5.190 5.995 12.090 15.870 21.753
(Data from U.S. Department of health, education, and Welfare. Radiological Health Handbook. rev. ed. Washington, DC: U.S. Government printing Office; 1970.)
0 50 100
Photon energy (keV) 65 kV
100 kV 150 kV
Excitation voltage Characteristic
radiation Unfiltered
200 kV
Relative intensity per energy interval
150 200
Figure 3.11. Spectral distribution of x-rays calculated for a thick tungsten target using equation 3.1. Dotted curves are for no filtration and the solid curves are for a filtration of 1-mm aluminum. (redrawn from Johns he, Cunningham Jr. The Physics of Radiology.
3rd ed. Springfield, IL: Charles C thomas; 1969, with permission.)
82453_ch03_p028-038.indd 36 1/7/14 8:28 PM
Chapter 3 production of X-rays 37
Of course, the one-third rule is a rough approximation since filtration significantly alters the average energy. Another quantity, known as half-value layer, has been defined to describe the quality of an x-ray beam. This topic is discussed in detail in Chapter 7.
3.7. OPERATING CHARACTERISTICS
In this section, the relationships between x-ray output, filament current, tube current, and tube voltage are briefly discussed. The output of an x-ray machine can also be expressed in terms of the ionization it produces in air. This quantity, which is a measure of ionization per unit mass of air, is called exposure.
The filament current affects the emission of electrons from the filament and, therefore, the tube current. Figure 3.12a shows the typical relationship between the relative exposure rate and the filament current measured in amperes (A). The figure shows that under typical operating conditions (filament current of 5 to 6 A), a small change in filament current produces a large change in relative exposure rate. This means that the constancy of filament current is critical to the constancy of the x-ray output.
In Figure 3.12b, the exposure rate is plotted as a function of the tube current. There is a linear relationship between exposure rate and tube current. As the current or milliamperage is doubled, the output is also doubled.
The increase in the x-ray output with increase in voltage, however, is much greater than that given by a linear relationship. Although the actual shape of the curve (Fig. 3.12c) depends on the filtration, the output of an x-ray machine varies approximately as a square of kilovoltage.
c a
b
Relative exposure rate
0 50
50
100 100
Tube voltage, kVp (c)
Tube current, MA (b) 150 150
200
5 10 15 20
Filament current, A (a)
3.0 4.0 5.0 6.0
Figure 3.12. Illustration of typical operating characteristics. plots of relative exposure rate versus (a) filament current at a given kVp, (b) tube current at a given kVp, and (c) tube voltage at a given tube current.
• The x-ray tube:
• X-ray tube is highly evacuated to prevent electron interactions with air.
• Choice of tungsten for filament (cathode) and target (anode) is based on its having a high melting point (3,370°C) and a high atomic number (Z = 74), which is needed to boost the efficiency of x-ray production.
• Heat generated in the target must be removed to prevent target damage, e.g., using a copper anode to conduct heat away, a rotating anode, fans, and an oil bath around the tube. The function of the oil bath is to provide electrical insulation as well as heat absorption.
K e Y p O I N t S
(continued )
38 part I Basic physics
K e Y p O I N t S
( c o n t i n u e d )• The function of a hooded anode (tungsten + copper shield around target) is to pre- vent stray electrons from striking the nontarget components of the tube and absorbing bremsstrahlung as a result of their interactions.
• Apparent focal spot size a is given as follows: a = A sin , where A is the side of actual focal spot presented at an angle with respect to the perpendicular to the direction of the electron beam (Fig. 3.2). The apparent focal spot size ranges from 0.1 × 0.1 to 2 × 2 mm2 for imaging, and 5 × 5 to 7 × 7 mm2 for orthovoltage therapy tubes.
• Peak voltage on an x-ray tube = √2 · line voltage · transformer turn ratio.
• Rectifiers conduct electrons in one direction only and can withstand reverse voltage up to a certain magnitude. Full-wave rectification increases effective tube current.
• X-ray output per mAs can be substantially increased by applying three-phase power to the x-ray tube. A three-phase, six-pulse generator delivers high-voltage pulses with a voltage ripple of 13% to 25%.
• A three-phase, 12-pulse generator is capable of providing high-voltage pulses to the x-ray tube with much less ripple (3% to 10%).
• A high-frequency generator provides nearly constant high-voltage potential (with a ripple of less than 2%). Consequently, it generates higher x-ray output per mAs and shorter exposure times.
• X-ray production:
• X-rays are produced by two different mechanisms: bremsstrahlung and characteristic x-ray emission.
• Bremsstrahlung x-rays have a spectrum of energies. The maximum energy is numeri- cally equal to the peak voltage. Average energy is about one-third of the maximum energy.
• Characteristic x-rays have discrete energies, corresponding to the energy level differ- ence between shells involved in the electron transition.
• The higher the energy of electrons bombarding the target, the more forward the direc- tion of x-ray emission.
• The efficiency of x-ray production is proportional to the atomic number Z of the tar- get and the voltage applied to the tube. The efficiency is less than 1% for x-ray tubes operating at 100 kVp (99% of input energy is converted into heat). The efficiency improves considerably for high-energy accelerator beams (30% to 95%, depending upon energy).
• Operating characteristics:
• Output (exposure rate) of an x-ray machine is very sensitive to the filament current.
The output increases proportionally with tube current and approximately with the square of the voltage.
R e f e r e n c e s
1. Botden P. Modern trends in diagnostic radiologic instru- mentation. In: Moseley R, Rust J, eds. The Reduction of Patient Dose by Diagnostic Instrumentation. Springfield, IL:
Charles C Thomas; 1964:15.
2. Hendee WR. Medical Radiation Physics. 2nd ed. Chicago:
Year Book Medical Publishers; 1979.
3. Kramers HA. On the theory of x-ray absorption and the continuous x-ray spectrum. Phil Mag. 1923;46:836.
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