Ionising Radiation Metrology Forum
Quantities, Units and Ionising Radiation
Fundamentals
Mark Bailey
Additional information from Clare Lee
November 2010
Contents
1.
Fundamentals
2.
Radioactivity
3.
Radiation field
4.
Dosimetry – Absorbed Dose
5.
Dosimetry – Kerma
6.
Stopping powers
7.
Protection quantities
Fundamentals: Quantities and units
A physical quantity is a phenomenon capable of expression as the product of
a number and a unit.
A unit is a selected reference sample of a quantity.
So we measure some number of unit things…
Quantity
Unit
Type of unit
Symbol
Length
metre
SI base unit
m
Area
metre square
SI derived unit
m2
Energy
joule
SI derived unit
with special name
J (= kg m2 s-2)
Absorbed
dose
gray
SI derived unit
with special name
(restricted use)
Gy (= m2 s-2)
Absorbed
dose
Rad
Non-SI unit
rad (= 0.01 Gy)
The measurement of ionising radiation
•
To measure the absorbed dose from ionising radiation within
a medium, we need to know
1. The number of particles or photons, or the quantity of
energy, passing through the medium (the fluence)
2. The quantity of energy transferred from initial particles
(often photons, which are uncharged) to charged
particles in the medium: Kerma
3. The rate at which energy is transferred from the charged
particles in the medium, to the medium itself (stopping
power, leading to absorbed dose).
•
These quantities are explained in the next sections.
Radiation field: Fluence Φ
da
dN
Φ=
da
Fluence Φ is defined as the number dN of particles incident on a sphere of
cross-sectional area da. By using a sphere, the area perpendicular to the
direction of each particle is accounted for so that all particles passing through
this volume of space are included.
Unit: m-2
…and Energy fluence ψ
dE
Ψ=
da
Energy fluence Ψ is defined as the energy dE incident on a sphere of
cross-sectional area da.
If you have a fluence Φ of particles all of energy E, then the energy fluence
Ψ = ΦE.
Unit: J m-2
Dosimetry - Absorbed Dose
Absorbed dose D
dε
D=
dm
Where dε is the mean energy imparted to matter of mass dm.
Energy imparted is the energy incident minus the energy leaving a given
region. The medium should always be specified – water, air, for example.
The National Standard in the UK is realised with a graphite calorimeter, giving
absorbed dose to water after some conversions.
Unit: J kg-1
Special name for the unit of absorbed dose is gray (Gy).
Relative interaction probabilities
Interactions in
water or
tissue
KERMA: Kinetic Energy Released per unit
MAss
Kerma is defined as:
dEtr
K=
dm
Where dEtr is the mean kinetic energy transferred to charged particles from
uncharged particles in a mass dm of a given material. There are different
primary standards to realise air kerma for different particle types and energies.
Unit: J kg-1
The special name for the unit of kerma is gray (Gy)
Should note that for a beam of charged particles, the quantity Cema is used:
Converted energy per unit mass.
Kerma relationship to fluence
Kerma is usually expressed in terms of the distribution ΨE(E) of the
uncharged energy fluence with respect to energy. Kerma K is then given by
µtr ( E )
K = ∫ ΨE ( E )
dE
ρ
µtr (E )
Where
is the mass energy transfer coefficient of the material for
ρ
uncharged particles of energy E
Unit: m2 kg-1
but it is often quoted in cm2/g
Collisional kerma
Total kerma can be split into two parts: collisional kerma Kcoll and radiative
kerma Krad.
• Collisional kerma Kcol: Production of electrons that dissipate their energy
as ionisation near electron tracks in the medium.
• Radiative kerma Kra: Production of bremsstrahlung photons, taking
energy far from the region of interest.
Ktotal = Kcoll + Krad
Kcoll = Ktotal(1-g)
…where g is the fraction of the initial kinetic energy of the particles
transferred to bremsstrahlung. For cobalt-60, g is small – about 0.0032;
however, g increases as energy increases.
Collisional kerma relationship to fluence
The collisional kerma Kcoll is given by
K coll
µen ( E )
= ∫ Ψ(E)
dE
ρ
µen (E )
Where
is the mass energy absorption coefficient of the material
ρ
for uncharged particles of energy E
Unit: m2 kg-1
but it is often quoted in cm2/g
Electrons: Unrestricted stopping power
dE
S=
dx
Linear stopping power
Unit: J m-1
often quoted in keV µm-1 or MeV cm-1
(Unrestricted) Mass stopping power
S
1 dE
=
ρ ρ dx
Unit: J m2 kg-1
often quoted in MeV cm2/g
Total stopping power is the sum of the collisional and radiative stopping powers
S = S coll + S rad
Collisional stopping power
Interactions of charged particles with atomic electrons:
Soft:
b >> a: Bethe theory
Hard:
b ~ a:
Møller theory (electrons)
Bhabha theory (positrons)
e-
e-
Energy loss by ionisation
Dominates for low energy, low Z
e-’
Absorbed dose delivered to
material via this process
Radiative stopping power
Interactions of charged particles with nuclear electric field, lead to
bremsstrahlung photon production:
Scattering, mainly by nuclei
e-
Energy loss by photon emission
e-
Dominates for higher energies
and high-Z material
γ
Radioactivation may occur for high
energy, if the bremsstrahlung
photon interacts directly with the
nucleus, for example knocking out
a neutron, which will then itself be
absorbed elsewhere.
Relationship of fluence and stopping
power to absorbed dose
For a differential fluence Φmed,E(E) of identical charged particles in a medium
(if radiative photons escape the volume of interest and secondary electrons
are absorbed locally), the absorbed dose Dmed is given by:
Dmed
 S coll ( E ) 
 dE
= ∫ Φ med , E ( E )
 ρ  med
Where Scoll/ρ is the mass collisional stopping power.
Integrating over the fluence spectrum for a given medium,
Dmed
 S coll
= Φ med 
 ρ


 med
Relating collisional kerma to absorbed
dose
• Beam of 60900Co photons into water
Kcoll
– Actually800here,
EGSnrc Monte Carlo calculation
Gamma dose, arbitrary
700
600
500
400
D < Kcoll
D
300
D = Kcoll
(for no attenuation)
200
CPE
100
zmax
0
0
1
2
3
4
5
6
Depth in water, mm
7
8
9
10
Protection Quantities
• Equivalent Dose – average absorbed dose in the volume of an
organ or tissue due to radiation R, normalised to the equivalent
dose from photons or electrons
H T = ∑ wR
DT ,R
wR= radiation weighting factor
R
• Effective Dose – absorbed dose to the whole body
E = ∑ wT
HT
wT= tissue weighting factor
T
Unit: J kg-1
The special name for the unit of equivalent and of effective dose is sievert (Sv)
(1 Sv = 100 rem)
Radiation weighting factors
wR (ICRP60)
Radiation type
and energy
wR (IRCP103)
Photons
1
1
Electrons &
muons
1
1
Protons &
charged pions,
energy >2 MeV
5
2
Alphas, fission
fragments &
heavy ions
20
20
Neutrons
5 - 20
Continuous
function of energy
wR for neutrons
Radiation weighting factor wR
25
ICRP 103
ICRP 60
20
15
10
5
0
-6
10
10
-5
-4
10
-3
10
-2
10
10
-1
0
10
1
10
2
10
10
3
4
10
Neutron energy (MeV)
Radiation weighting factor, wR, for neutrons as a
function of neutron energy
Tissue
weighting
factors
Operational quantities for external
exposure
• For area monitoring:
– Ambient dose equivalent H*(10)
– Directional dose equivalent H’(0.07, Ω)
– Ω is a specified direction
• For individual monitoring:
– Personal dose equivalent Hp(d)
– d is the depth of tissue beneath specified point on body
Unit: J kg-1 (Sv)
For internal exposure
• Committed equivalent dose, HT(τ)
Where τ is the integrating time in years following the intake
• Committed effective dose, E(τ)
• Collective equivalent dose, ST
• Collective effective dose, S
Unit: J kg-1 (Sv)
Summary
Have discussed:
Measurement fundamentals:
Quantities, Units
Protection quantities:
Equivalent dose
Effective dose
Radiation fundamentals:
Radiation interactions:
Kerma
Collisional and radiative
kerma
Absorbed dose:
Stopping powers
Operational quantities:
Ambient dose equivalent
Directional dose equivalent
Personal dose equivalent