Quantities, Units and Ionising Radiation Fundamentals

Transcription

1 Ionising Radiation Metrology Forum Quantities, Units and Ionising Radiation Fundamentals Mark Bailey Additional information from Clare Lee November 2010

2 Contents 1. Fundamentals 2. Radioactivity 3. Radiation field 4. Dosimetry Absorbed Dose 5. Dosimetry Kerma 6. Stopping powers 7. Protection quantities

3 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 m 2 Energy joule SI derived unit with special name Absorbed dose Absorbed dose gray SI derived unit with special name (restricted use) J (= kg m 2 s -2 ) Gy (= m 2 s -2 ) Rad Non-SI unit rad (= 0.01 Gy)

4 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.

5 Radiation field: Fluence Φ Φ = dn da 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

6 and Energy fluence ψ Ψ = de 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

7 Dosimetry - Absorbed Dose Absorbed dose D D = dε 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).

8 Relative interaction probabilities Interactions in water or tissue

9 KERMA: Kinetic Energy Released per unit MAss Kerma is defined as: Where de tr 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 detr dm The special name for the unit of kerma is gray (Gy) K = Should note that for a beam of charged particles, the quantity Cema is used: Converted energy per unit mass.

10 Kerma relationship to fluence Kerma is usually expressed in terms of the distribution Ψ E (E) of the uncharged energy fluence with respect to energy. Kerma K is then given by K = Ψ µ tr ( E) E de E ( ) ρ µ tr (E) Where is the mass energy transfer coefficient of the material for ρ uncharged particles of energy E Unit: m 2 kg -1 but it is often quoted in cm 2 /g

11 Collisional kerma Total kerma can be split into two parts: collisional kerma K coll and radiative kerma K rad. Collisional kerma K col : Production of electrons that dissipate their energy as ionisation near electron tracks in the medium. Radiative kerma K ra : Production of bremsstrahlung photons, taking energy far from the region of interest. K total = K coll + K rad K coll = K total (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 ; however, g increases as energy increases.

12 Collisional kerma relationship to fluence The collisional kerma K coll is given by µ en(e) ρ Where is the mass energy absorption coefficient of the material for uncharged particles of energy E Unit: m 2 kg -1 K coll but it is often quoted in cm 2 /g = Ψ µ en( E) ( E) ρ de

13 Electrons: Unrestricted stopping power Linear stopping power Unit: J m -1 often quoted in kev µm -1 or MeV cm -1 S = (Unrestricted) Mass stopping power Unit: J m 2 kg -1 often quoted in MeV cm 2 /g de dx S ρ = 1 de ρ dx Total stopping power is the sum of the collisional and radiative stopping powers S = S coll + S rad

14 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 - e - Energy loss by ionisation Dominates for low energy, low Z Absorbed dose delivered to material via this process

15 Radiative stopping power Interactions of charged particles with nuclear electric field, lead to bremsstrahlung photon production: Scattering, mainly by nuclei Energy loss by photon emission e - e - γ Dominates for higher energies and high-z material 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.

16 Relationship of fluence and stopping power to absorbed dose For a differential fluence Φ med,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 D med is given by: D med S coll ( E) = Φmed, E ( E) de ρ med Where S coll /ρ is the mass collisional stopping power. Integrating over the fluence spectrum for a given medium, D med = Φ med S coll ρ med

17 Relating collisional kerma to absorbed dose Beam of Co photons into water Actually 800here, EGSnrc Monte Carlo calculation 700 K coll Gamma dose, arbitrary D D < K coll D = K coll z max (for no attenuation) CPE Depth in water, mm

18 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 = R H w D, w R = radiation weighting factor T R T Effective Dose absorbed dose to the whole body R E = T w T H T w T = tissue weighting factor Unit: J kg -1 The special name for the unit of equivalent and of effective dose is sievert (Sv) (1 Sv = 100 rem)

19 Radiation weighting factors Radiation type and energy Photons 1 w R (ICRP60) 1 w R (IRCP103) Electrons & muons Protons & charged pions, energy >2 MeV Alphas, fission fragments & heavy ions Neutrons Continuous function of energy

20 w R for neutrons 25 Radiation weighting factor w R ICRP 103 ICRP Neutron energy (MeV) Radiation weighting factor, w R, for neutrons as a function of neutron energy

21 Tissue weighting factors

22 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 H p (d) d is the depth of tissue beneath specified point on body Unit: J kg -1 (Sv)

23 For internal exposure Committed equivalent dose, H T (τ) Where τ is the integrating time in years following the intake Committed effective dose, E(τ) Collective equivalent dose, S T Collective effective dose, S Unit: J kg -1 (Sv)

24 Summary Have discussed: Measurement fundamentals: Quantities, Units Radiation fundamentals: Radiation interactions: Kerma Collisional and radiative kerma Absorbed dose: Stopping powers Protection quantities: Equivalent dose Effective dose Operational quantities: Ambient dose equivalent Directional dose equivalent Personal dose equivalent