Outline • Radiological physics and radiation Ionizing Radiation dosimetry • Types and sources of ionizing radiation Chapter 1 • Description of ionizing radiation fields – Random nature of radiation F.A. Attix, Introduction to Radiological – Non-stochastic quantities Physics and Radiation Dosimetry Introduction Ionizing radiation • Radiological physics studies ionizing radiation and its interaction with matter • By general definition ionizing radiation is characterized by its ability to excite and • Began with discovery of x-rays, ionize atoms of matter radioactivity and radium in 1890s • Lowest atomic ionization energy is ~ eV, • Special interest is in the energy absorbed with very little penetration in matter • Energies relevant to radiological physics • Radiation dosimetry deals with and radiation therapy are in keV – MeV quantitative determination of the energy range absorbed in matter Types and sources of ionizing Types and sources of ionizing radiation radiation • g-rays: electromagnetic radiation (photons) emitted • Fast electrons (positrons) emitted from nuclei (b- from a nucleus or in annihilation reaction rays) or in charged-particle collisions (d-rays). – Practical energy range from 2.6 keV (Ka from electron capture Other sources: Van de Graaf generators, linacs, in 37 Ar) to 6.1 and 7.1 MeV (g-rays from 16 N) 18 7 betatrons, and microtrons • x-rays: electromagnetic radiation (photons) emitted by charged particles (characteristic or bremsstrahlung • Heavy charged particles emitted by some processes). Energies: radioactive nuclei (a-particles), cyclotrons, heavy particle linacs (protons, deuterons, ions of heavier – 0.1-20 kV “soft” x-rays elements, etc.) – 20-120 kV diagnostic range – 120-300 kV orthovoltage x-rays • Neutrons produced by nuclear reactions (cannot be accelerated electrostatically) – 300 kV-1 MV intermediate energy x-rays – 1 MV and up megavoltage x-rays 1 Description of ionizing Types of interaction radiation fields • To describe radiation field at a point P need to • ICRU (The International Commission on Radiation define non-zero volume around it Units and Measurements; established in 1925) • Can use stochastic or non-stochastic physical terminology quantities • Directly ionizing radiation: by charged particles, delivering their energy to the matter directly through multiple Coulomb interactions along the track • Indirectly ionizing radiation: by photons (x-rays or g- rays) and neutrons, which transfer their energy to charged particles (two-step process) Stochastic quantities Stochastic quantities • Values occur randomly, cannot be predicted • For a “constant” radiation field a number of x-rays observed at point P per unit area and time interval • Radiation is random in nature, associated physical follows Poisson distribution quantities are described by probability distributions • For large number of events it may be approximated • Defined for finite domains (non-zero volumes) by normal (Gaussian) distribution, characterized by • The expectation value of a stochastic quantity (e.g., standard deviation s (or corresponding percentage number of x-rays detected per measurement) is the standard deviation S) for a single measurement mean of its measured value for infinite number of s Ne N measurements 100s 100 100 N Ne for n S Ne Ne N Stochastic quantities Stochastic quantities • Normal (Gaussian) distribution is described by • For a given number of measurements n standard probability density function P(x) deviation is defined as • Mean N determines position of the maximum, standard s N N deviation s defines the width of the distribution s e n n n 100s 100 100 1 NN 2 /2s 2 S P(N) e Ne nN nN s 2 e • N will have a 68.3% chance of lying within interval s of Ne, 95.5% to be within 2 s , and 99.7% to be within interval 3 s . No experiment-related fluctuations 2 Stochastic quantities Stochastic quantities • In practice one always uses a detector. An estimated • An estimate of the precision (proximity to Ne) of the precision (proximity to Ne) of any single random mean value measured with a detector n times measurement Ni s s n n 1/ 2 2 1/ 2 1 n s N N 1 2 i n 1 i1 s Ni N nn 1 i1 N Ni n • Ne is as correct as your experimental setup • Determined from the data set of n such measurements Stochastic quantities: Example • A g-ray detector having 100% counting efficiency is positioned Non-stochastic quantities in a constant field, making 10 measurements of equal duration, Dt=100s (exactly). The average number of rays detected • For given conditions the value of non-stochastic (“counts”) per measurement is 1.00x105. What is the mean value quantity can, in principle, be calculated of the count rate C, including a statement of its precision (i.e., • In general, it is a “point function” defined for standard deviation)? infinitesimal volumes N 1.00105 C 1.00103 c/s – It is a continuous and differentiable function of space and Dt 100 time; with defined spatial gradient and time rate of change C 1.00103 • Its value is equal to, or based upon, the expectation s 1 c/s C n 10 value of a related stochastic quantity, if one exists C 1.00103 1 c/s – In general does not need to be related to stochastic quantities, they are related in description of ionizing • Here the standard deviation is due entirely to the stochastic nature radiation of the field, since detector is 100% efficient Description of radiation fields Non-stochastic quantities: by non-stochastic quantities Fluence • A number of rays crossing an infinitesimal • Fluence area surrounding point P, define fluence as • Flux Density (or Fluence Rate) dN • Energy Fluence e • Energy Flux Density (or Energy Fluence da Rate) -2 -2 •NUnits of m or cm 3 Non-stochastic quantities: Non-stochastic quantities: Flux density (Fluence rate) Energy fluence • An increment in fluence over an infinitesimally small • For an expectation value R of the energy carried by all time interval the Ne rays crossing an infinitesimal area surrounding point P, define energy fluence as d d dNe dR dt dt da • Units of m-2 s-1 or cm-2 s-1 da • Fluence can be found through integration: • Units of J m-2 or erg cm-2 t1 • If all rays have energy E t ,t tdt 0 1 R EN e t 0 E Differential distributions by Differential distributions energy and angle of incidence • More complete description of radiation field • Differential flux density as a is often needed function of energy and angles of • Generally, flux density, fluence, energy flux incidence: distribution density, or energy fluence depend on all ,b, E variables: , b, or E • Typical units are m-2 s-1sr-1keV-1 • Simpler, more useful differential • Integration over all variables gives the flux density: distributions are those which are functions 2 Emax of only one of the variables , b, EsinddbdE 0 b 0 E0 (x,y,z) > (r,,b) Differential distributions: Differential distributions: Energy spectra Energy spectrum example • If a quantity is a function of energy only, such • A “flat” distribution distribution is called the energy spectrum (e.g. E ) of photon flux density • Typical units are m-2 s-1keV-1 or cm-2 s-1keV-1 • Energy flux density • Integration over angular variables gives flux density spectrum is found by spectrum E EE 2 E E , b, Esinddb 0 b 0 • Typically units for E • Similarly, may define energy flux density E are joule or erg, so that [’] = Jm-2s-1keV-1 4 Example: Problem 1.8 Example: Problem 1.8 Energy spectrum of a flux density ( E ) 7.5x108 photons/m2-sec-keV a) Photon flux density EE E 8 max min An x-ray field at a point P contains 7.5x10 8 10 2 2 7.510 90 6.7510 photons/m s photons/(m -sec-keV), uniformly b) The photon fluence in one hour distributed from 10 to 100 keV. t 1 hour Dt a) What is the photon flux density at P? 6.751010 3600 2.431014 photons/m2 b) What would be the photon fluence in one hour? c) The corresponding energy fluence, in J/m2 and erg/cm2 E100 E 2 c) What is the corresponding energy fluence, in Dt E EdE Dt 100 2 10 J/m2 and erg/cm2? E10 1 36007.5108 1002 102 1.3361016 keV/m2 2 1.3361016 1.6021016 2.14 J/m2 2.14103 erg/cm2 Differential distributions: Summary Angular distributions • Types and sources of ionizing radiation • Full differential distribution integrated – g-rays, x-rays, fast electrons, heavy charged over energy leaves particles, neutrons only angular dependence • Description of ionizing radiation fields • Often the field is – Due random nature of radiation: expectation symmetrical with respect to a certain values and standard deviations direction, then only – Non-stochastic quantities: fluence, flux density, dependence on polar angle or azimuthal energy fluence, energy flux density, differential a) b) http://newsroom.varian.com http://cerncourier.com/cws/article/cern/28653 angle b distributions Azimuthal symmetry: a) accelerator beam after primary collimator; b) brachytherapy surface applicator Outline Quantities for Describing the Interaction of Ionizing • Kerma, components of kerma Radiation with Matter • Absorbed dose • Exposure Chapter 2 • Quantities for use in radiation protection F.A. Attix, Introduction to Radiological Physics and Radiation Dosimetry 5 Introduction Definitions • Need to describe interactions of ionizing • Most of the definitions are by ICRU radiation with matter • Energy transferred by indirectly ionizing • Special interest is in the energy absorbed in radiation leads to the definition of kerma matter, absorbed dose – delivered by • Energy imparted by ionizing radiation leads directly ionizing