Production of X-Rays. Yoichi Watanabe, Ph.D. Masonic Memorial Building M10-M (612) MPHY 5170/TRAD 7170, Fall semester

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1 Production of X-Rays Yoichi Watanabe, Ph.D. Masonic Memorial Building M10-M (612) MPHY 5170/TRAD 7170, Fall semester

2 Contents 1) Physics of X-ray production 2) The X-ray tube 3) X-ray energy spectra 4) Basic X-ray circuit 5) Voltage rectification

3 Physics of X-ray production Electrons are focused on a thick target (metals) to produce x-rays. Electrons lose the energy through ionization and radiative collisions with target atoms. The interactions produce Bremsstrahlung and characteristic X-rays.

4 Bremsstrahlung Process Electron or charge particle m, z, E 0 r Nucleus M, Z Photon Force F Ze ze k 2 r = F = ma Acceleration Ze ze a m X-ray intensity I ( a ze) 2 rad = 2 4 Z z e 6 m 2

5 Bremsstrahlung Bremsstrahlung = breaking radiation (in German), white light. An electron may have one or more bremsstrahlung interactions. The bremsstrahlung photon may have any energy up to the initial energy of the electron. 2 Radiation energy EE 0

6 Bremsstrahlung (cont ) The energy loss per atom by electrons Z 2 The efficiency of x-ray production in thick target Z E Actually Efficienty, η = total X ray intensity input energy deposited by electrons 2 σ 0 2 E Z BS E Z E [ MeV ] Mean path length of electrons: S 1 NZ (Note) For E=0.1 MeV and Z=74 (tungsten), η=0.5%.

7 Bremsstrahlung Process Photon Angular Distribution

8 Characteristic X-rays Characteristic radiation are emitted at discrete energies hv = E k -E l E k and E l are the electron binding energies of the K shell and the L shell.

9 Characteristic x-ray production K electron Ε -E K Primary electron E 0 Characteristics radiation K L M Primary electron E 0 - Ε

10 Characteristic x-ray from Tungsten

11 X-ray energy spectra Heterogeneous in energy: bremsstrahlung photons superimposed by characteristic radiation of discrete energies. The maximum possible energy that a bremsstrahlung photon can have is equal to the energy of the incident electron. The average X-ray energy is approximately 1/3 of the maximum energy.

12 Spectral distribution of X-ray thick tungsten target F.Khan, 3rd ed. Figure 3.9

13 Kramer s equation I E = K Z ( E E) m I E : intensity of photons with energy E Z : atomic number of the target E m : maximum photon energy K : constant I E = 0 when E = E m

14 Diagnostic x-ray tube Ref: Figure 2-8, Physics of Radiology, 4 th ed. (1983)

15 Therapy X-ray tube Tungsten shield

16 The X-ray tube (1) Anode: target material=high atomic number and high melting point, Tungsten Copper anode tube: conduction of heat Anode hood: prevents stray electrons from striking the walls or other non-target components; absorbs the secondary electrons (copper shield); absorbs the unwanted X-ray (tungsten shield) Z s of copper (Cu) and tungsten (W) are 29 and 74. Cu is good to stop electrons without producing much Bremmstrahlung radiation and W is good to attenuate the photons.

17 The X-ray tube (2) Cathode: wire filament, circuit to provide filament current and a negatively charged focusing cup Cathode cup: direct the electrons toward the anode Beryllium window for therapy tubes: stop secondary electrons.

18 Target (anode) design Focal spot, A, must be small, but the size cannot be too small because of heating problem. Apparent size (a) is smaller than A. Apparent beam size is approximately square. Diagnostics: θ=5 to 17 (0.1x0.1 to 2x2 mm) Therapy: θ=30 (5x5 to 7x7 mm) Heal effect : the x-ray intensity decreases in the cathode to the anode direction.

19 Heat generation in target: Example Calculate temperature rise of a rotating anode after an exposure of 100 ma for 2 sec at constant potential of 100 kv. Target volume = 500 g Bombarded surface area=30 cm 2 Tungsten target: 19.3 g/cm 3 and specific heat = 0.03 cal/g/ºc. 1) Energy input = 100,000 [V] x 0.1 [A] x 2 [s] = 2x10 4 J. 2) Heat input to anode = 2x10 4 /4.18 = 5x10 3 cal. 3) Thermal capacity of anode = 500 [g]x0.03 [cal/g/ºc]=15 cal/ºc. 4) Mass of bombarded volume = 30 [cm 2 ] x 0.1 [cm] x 19.3 [g/cm 3 ]=58 g. 5) Rise of local temperature = 5x10 3 [cal]/(58x0.03) [cal/ºc]= 2870 ºC. (Note) Melting point of tungsten = 3400 ºC.

20 Tube operation limit due to heat Ref: Figure 2-11, Physics of Radiology, 4 th ed. (1983)

21 Heat Unit (HU) HU = average tube current [ma] x peak voltage [kv] x exposure time [s] Energy deposited = f x HU [J] f = 0.75 for single phase, full wave rectification. f = 1.35 for three phase, 6 or 12 pulse systems. Example: A tube is given 10 exposures each for 2.0 s at 150 ma and 100 kvp. For a single phase full-wave system, HU 100 x 150 x 10 x 2 = 3 x 10 5 HU Energy deposited = 0.75 x 3 x 10 5 HU = 2.2 x 10 5 J.

22 Filtration Inherent filtration due to absorption in target, glass walls of the tube, or thin beryllium window ( 0.5 to 1 mm Al). The filtration is to enrich the beam with higher energy photons by absorbing the lower energy components of the spectrum hardens, higher average energy and greater penetrating power.

23 X-ray spectra: filtration effects Inherent filtration K charact. X-ray Tungsten target No external filtration 1.52-mm Cu filter The effect of current. Ref: L.H.J.Peaple et al, Phys Med Biol 14:73 (1969)

24 Basic X-ray circuit High-voltage circuit: provides the accelerating potential for the electrons Low-voltage (filament) circuit: supplies heating current to the filament Transformer: step-up and step-down. Autotransformer: provides a selected voltage for the primary of the high-voltage transformer. Rectifier: change alternating current to direct current. Rheostat: a variable register used to continuously vary the voltage.

25 Self-rectified X-ray unit 10V X V, 60 Hz

26 p-n Silicon rectifier Ref: Figure 2-4, Physics of Radiology, 4 th ed. (1983)

27 Physics of p-n diode n p-n junction p - + Depletion layer V

28 Half-wave rectification Temporal variation of the line voltage, the tube kilovoltage, the tube current V 2

29 Full-wave rectification

30 Three-phase six-pulse generator

31 Operating Characteristics A small change in the filament current leads to a large change in exposure rate. Hence, the constancy of the filament current is critical. Exposure rate is linearly proportional to the tube current. Exposure rate varies approximate as a function of V 2.

32 Relative Exposure Rate Relative Exposure Rate Filament current V 2 Tube current Tube voltage

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