Production of X-Rays
Yoichi Watanabe, Ph.D.
Masonic Memorial Building M10-M
(612)626-6708
watan016@umn.edu
MPHY 5170/TRAD 7170, Fall semester
Contents
1)
2)
3)
4)
5)
Physics of X-ray production
The X-ray tube
X-ray energy spectra
Basic X-ray circuit
Voltage rectification
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.

Bremsstrahlung Process
Force
Electron or
charge particle
m, z, E0
F=k
Ze ⋅ ze
r
2
F = ma
Acceleration
r
Photon
Nucleus
M, Z
Ze ⋅ ze
a∝
m
X-ray intensity
2 z 4e6
Z
I rad ∝ (a ⋅ ze )2 =
m2
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

Bremsstrahlung (cont’)


The energy loss per atom by electrons ∝ Z2
The efficiency of x-ray production in thick
target ∝ Z×E
total X − ray intensity
Efficienty, η =
input energy deposited by electrons
Actually
E 2 ⋅ σ 0Z 2B S
∝
E
≅ 0.0007 ⋅ Z ⋅ E [MeV ]
Mean path length of electrons: S ∝
1
NZ
(Note) For E=0.1 MeV and Z=74 (tungsten), η=0.5%.
Bremsstrahlung Process
Photon Angular Distribution
Characteristic X-rays
Characteristic radiation are emitted at
discrete energies
 hv = Ek-El
 Ek and El are the electron binding
energies of the K shell and the L shell.

Characteristic x-ray production
K electron
∆Ε -EK
Primary electron
E0
Characteristics
radiation
K
L
M
Primary electron
E0 -∆Ε
Characteristic x-ray from Tungsten
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.

Spectral distribution of X-ray
thick tungsten target
F.Khan, 3rd ed. Figure 3.9
Kramer’s equation
I E = K ⋅ Z ⋅ ( Em − E )
 IE




: intensity of photons with energy E
Z : atomic number of the target
Em : maximum photon energy
K : constant
IE = 0 when E = Em
Diagnostic x-ray tube
Ref: Figure 2-8, Physics of Radiology, 4th ed. (1983)
Therapy X-ray tube
Tungsten
shield
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.
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.

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.
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 cm2
• Tungsten target: 19.3 g/cm3 and specific heat = 0.03 cal/g/ºC.
1)
2)
3)
4)
5)
Energy input = 100,000 [V] x 0.1 [A] x 2 [s] = 2x104 J.
Heat input to anode = 2x104 /4.18 = 5x103 cal.
Thermal capacity of anode = 500 [g]x0.03 [cal/g/ºC]=15 cal/ºC.
Mass of bombarded volume = 30 [cm2] x 0.1 [cm] x 19.3 [g/cm3]=58 g.
Rise of local temperature = 5x103[cal]/(58x0.03) [cal/ºC]= 2870 ºC.
(Note) Melting point of tungsten = 3400 ºC.
Tube operation limit due to heat
Ref: Figure 2-11, Physics of Radiology, 4th ed. (1983)
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 105 HU
Energy deposited = 0.75 x 3 x 105 HU = 2.2 x 105 J.
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.

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)
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.
Self-rectified X-ray unit
10V
X 1000
110V, 60 Hz
p-n Silicon rectifier
Ref: Figure 2-4, Physics of Radiology, 4th ed. (1983)
Physics of p-n diode
p-n junction
n
p
-
+
Depletion layer
V
Half-wave rectification
Temporal variation of the line voltage, the
tube kilovoltage, the tube current
∝V2
Full-wave rectification
Three-phase six-pulse generator
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 V2.

Relative Exposure Rate
Relative Exposure Rate
Filament current
∝V2
Tube current
Tube voltage