PHYS 5012 Radiation Physics and Dosimetry

Radiation Physics Lecture 1

Background and Fundamentals The Discovery of Radiation X-rays Radioactivity Classiﬁcation of Radiation Types of Ionising Radiation PHYS 5012 Radiation Units and Properties Radiation Physics and Dosimetry Dose in Water Atomic Physics and Radiation Lecture 1 The Rutherford-Bohr Model Multi-Electron Atoms

Production of Radiation Characteristic Radiation Characteristic X-rays Auger Electrons Continuous Radiation Bremsstrahlung Radiation Tuesday 5 March 2013 Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1 The Discovery of Radiation

Background and Fundamentals The Discovery of Radiation X-rays Radioactivity Classification of Radiation Types of Ionising Radiation Three main discoveries of radiation made at the turn of Radiation Units and Properties the 19th century, together with several major advances in Dose in Water Atomic Physics and theoretical physics, including quantum mechanics and Radiation The Rutherford-Bohr special relativity, signalled the birth of Radiation Physics. Model Multi-Electron Atoms The subsequent realisation that radiation can be harmful Production of Radiation to humans led to the the rapid development of radiation Characteristic Radiation Characteristic X-rays dosage measurements and quantification and commonly Auger Electrons accepted standards for tolerable levels of radiation in Continuous Radiation Bremsstrahlung Radiation humans. Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1 X-rays X-rays are photons (i.e. electromagnetic radiation) with Background and energies typically above 1 keV. They were discovered by Fundamentals The Discovery of Radiation Wilhelm Conrad Roentgen in 1895. X-rays Radioactivity Classification of Radiation Types of Ionising Radiation Radiation Units and Properties Dose in Water Atomic Physics and Radiation The Rutherford-Bohr Model Multi-Electron Atoms

Production of Radiation Characteristic Radiation Characteristic X-rays Auger Electrons Continuous Radiation Bremsstrahlung Radiation Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Roentgen discovered X-rays inadvertedly whilst studying fluoresence using a cathode ray tube. He explored the absorption properties of the rays in soft tissue and bone using his wife’s hand (note the ring). Radiation Physics Lecture 1 Radioactivity Natural radioactivity is the spontaneous emission of Background and radiation by a material. It was discovered by Antoine Fundamentals The Discovery of Radiation Henri Becquerel in 1896. X-rays Radioactivity Classification of Radiation Types of Ionising Radiation Radiation Units and Properties Dose in Water Atomic Physics and Radiation Whilst Roentgen’s X-rays The Rutherford-Bohr Model needed to be induced by Multi-Electron Atoms cathode rays (electrons), Production of Becquerel found that some Radiation materials, notably uranium ore, Characteristic Radiation possessed their own source of Characteristic X-rays radiation energy. He discovered Auger Electrons Continuous Radiation this after placing some uranium Bremsstrahlung Radiation mineral on a photographic plate Synchrotron Radiation wrapped in black paper into a Cerenkov Radiation dark drawer, finding afterwards Particle Accelerators X-ray Tubes that the uranium had indeed Cyclotrons left an image on the plate. Linear Accelerators Radiation Physics Lecture 1 Radioactivity Marie Curie coined the term "radioactivity" for the Background and phenomenon Becquerel found associated with uranium Fundamentals The Discovery of Radiation ore. Together with her husband Pierre, they began X-rays Radioactivity investigating radioactivity. Marie found that after Classification of Radiation Types of Ionising Radiation extracting pure uranium from ore, the residual material Radiation Units and Properties was even more radioactive than the uranium. She had Dose in Water Atomic Physics and Radiation discovered polonium and radium. The Rutherford-Bohr Model Multi-Electron Atoms

Background and Fundamentals The Discovery of Radiation X-rays Radiation can be broadly classified into two main Radioactivity Classification of Radiation categories, based on its ability to ionise matter: Types of Ionising Radiation Radiation Units and Properties I Non-ionising radiation cannot ionise matter because Dose in Water Atomic Physics and its energy is lower than the ionisation potential of the Radiation The Rutherford-Bohr Model matter. Multi-Electron Atoms I Ionising radiation has sufficient energy to ionise Production of Radiation matter either directly or indirectly. Characteristic Radiation Characteristic X-rays Auger Electrons Although non-ionising radiation can transfer some of its Continuous Radiation Bremsstrahlung Radiation energy to matter, the low energies involved result in Synchrotron Radiation Cerenkov Radiation negligible effects compared to those of ionising radiation. Particle Accelerators X-ray Tubes Henceforth, only ionising radiation will be considered. Cyclotrons Linear Accelerators Radiation Physics Lecture 1 Types of Ionising Radiation

Background and Fundamentals The Discovery of Radiation X-rays Radioactivity Ionising radiation can be further subdivided into two Classiﬁcation of Radiation Types of Ionising Radiation classes: Radiation Units and Properties I Directly ionising - charged particles (electrons, Dose in Water Atomic Physics and protons, α particles, heavy ions); deposits energy in Radiation The Rutherford-Bohr Model matter directly through Coulomb collisions with Multi-Electron Atoms orbital electrons. Production of Radiation I Indirectly ionising - neutral particles (photons, Characteristic Radiation Characteristic X-rays neutrons); deposit energy indiectly through a Auger Electrons Continuous Radiation two-step process: 1. release of charged particles Bremsstrahlung Radiation Synchrotron Radiation and 2. charged particle energy deposition through Cerenkov Radiation Particle Accelerators Coloumb interactions. X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1 Types of Directly Ionising Radiation

Background and Fundamentals The Discovery of Radiation Charged particles are described as light (electrons and X-rays Radioactivity positrons), heavy (protons, deutrons, α particles) or Classiﬁcation of Radiation Types of Ionising Radiation heavier (e.g. carbon-12). Some of the common Radiation Units and Properties nomenclature is as follows: Dose in Water Atomic Physics and Radiation Light charged particles The Rutherford-Bohr Model Multi-Electron Atoms I photoelectrons – produced by photoelectric effect Production of Radiation I recoil electrons – produced by Compton effect Characteristic Radiation Characteristic X-rays I delta rays – electrons produced by charged particle Auger Electrons Continuous Radiation collisions Bremsstrahlung Radiation Synchrotron Radiation I beta particles – electrons or positrons emitted from Cerenkov Radiation − + Particle Accelerators nuclei by β or β decay: X-ray Tubes 1 1 0 1 1 0 Cyclotrons n −→ p + e or p −→ n + e + ν Linear Accelerators 0 1 −1 1 0 +1 Radiation Physics Lecture 1 Types of Directly Ionising Radiation

Background and Fundamentals The Discovery of Radiation X-rays Radioactivity Heavy charged particles Classiﬁcation of Radiation Types of Ionising Radiation 1 I protons – nucleus of hydrogen-1 ( H) atom Radiation Units and 1 Properties 2 Dose in Water I deuteron – nucleus of deuterium ( H) atom Atomic Physics and 1 Radiation 3 The Rutherford-Bohr I triton – nucleus of tritium ( H) atom Model 1 Multi-Electron Atoms 3 I helium-3 – nucleus of helium-3 (2He) atom Production of 4 Radiation I α particle – nucleus of helium-4 ( He) atom Characteristic Radiation 2 Characteristic X-rays Auger Electrons Heavier charged particles include nuclei or ions of Continuous Radiation 12 14 Bremsstrahlung Radiation heavier atoms such as carbon-12 ( C), nitrogen-14 ( N), Synchrotron Radiation 6 7 20 Cerenkov Radiation or neon-20 ( Ne). Particle Accelerators 10 X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1 Types of Indirectly Ionising Radiation

Background and Fundamentals The Discovery of Radiation X-rays Radioactivity Classiﬁcation of Radiation Ionising photons can be classiﬁed into four groups: Types of Ionising Radiation Radiation Units and Properties I characteristic X-rays – due to electronic transitions Dose in Water Atomic Physics and between discrete atomic energy levels Radiation The Rutherford-Bohr Model I bremsstrahlung emission – due to electron-nucleus Multi-Electron Atoms Coulomb interactions Production of Radiation Characteristic Radiation I gamma rays – resulting from nuclear decays Characteristic X-rays Auger Electrons I annihilation radiation – resulting from Continuous Radiation Bremsstrahlung Radiation electron-positron pair annihilation Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1 Radiation Units and Properties

Background and Fundamentals The Discovery of Radiation X-rays Radioactivity Classiﬁcation of Radiation Types of Ionising Radiation Radiation Units and Properties Dose in Water Accurate measurement of radiation is critical to any Atomic Physics and Radiation industry or profession that involves regular use of The Rutherford-Bohr Model radiation. Several units have been deﬁned to quantify Multi-Electron Atoms

Production of different types of radiation measurements. These are Radiation Characteristic Radiation summarised in the following table. Characteristic X-rays Auger Electrons Continuous Radiation Bremsstrahlung Radiation Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Quantity Deﬁnition SI unit Lecture 1 −4 −1 Exposure X = ∆Q/∆mair 2.58 × 10 C kg −1 Background and Dose D = ∆Eab/∆m 1 Gy = 1 J kg Fundamentals Equivalent dose H = Dw 1 Sv The Discovery of Radiation R −1 X-rays Activity A = λN 1 Bq = 1 s Radioactivity Classiﬁcation of Radiation Types of Ionising Radiation I Exposure measures the ability of photons to ionise Radiation Units and Properties air (its original unit of measurement was the Dose in Water Atomic Physics and Radiation roentgen, R); ∆Q is the collected charge. The Rutherford-Bohr Model I Dose is the energy absorbed per mass of matter; its Multi-Electron Atoms

Production of unit is the gray (Gy); ∆Eab is the energy absorbed in Radiation Characteristic Radiation a medium. Characteristic X-rays Auger Electrons I Equivalent dose is the dose mulitplied by a radiation Continuous Radiation Bremsstrahlung Radiation weighting factor wR for different types of radiation Synchrotron Radiation Cerenkov Radiation (wR = 1 for photons and electrons); its unit of Particle Accelerators X-ray Tubes measurement is the sievert (Sv). Cyclotrons Linear Accelerators I Activity is the number of decays per unit time of a radioactive substance; λ is the decay constant and N is the number of radioactive atoms. Radiation Physics Lecture 1 Dose in Water for Different Radiation Beams

Background and Fundamentals The Discovery of Radiation X-rays Radioactivity Classiﬁcation of Radiation Types of Ionising Radiation Radiation Units and Dose deposition in water is extremely important because Properties Dose in Water soft tissue is mostly made up of water. Different types of Atomic Physics and Radiation The Rutherford-Bohr radiation deposit their energy at different depths in water. Model Multi-Electron Atoms In general, indirectly ionising radiation deposits energy in Production of an exponential-like fashion, while directly ionising Radiation Characteristic Radiation radiation deposits virtually all its energy in a localised Characteristic X-rays Auger Electrons region, as is evident in the ﬁgure below. Continuous Radiation Bremsstrahlung Radiation Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1

Production of Radiation Characteristic Radiation Characteristic X-rays Auger Electrons Continuous Radiation Bremsstrahlung Radiation Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Depth dose curves for different radiation beams in water and for differ- Linear Accelerators ent energies, normalised to 100% at depth dose maximum (reproduced from Podgoršak, Fig. 1.2). Radiation Physics Lecture 1 Dose in Water for Different Radiation Beams

Background and Fundamentals The Discovery of Radiation X-rays Radioactivity Dose distributions for photon beams: Classiﬁcation of Radiation Types of Ionising Radiation I build-up region from surface to depth dose maximum Radiation Units and Properties zmax followed by approximate exponential attenuation Dose in Water Atomic Physics and Radiation I dose deposition determined by secondary electrons; The Rutherford-Bohr Model zmax proportional to beam energy Multi-Electron Atoms Production of I skin sparing effect: low surface dose for high energy Radiation Characteristic Radiation beams Characteristic X-rays Auger Electrons Dose distributions for neutron beams: Continuous Radiation Bremsstrahlung Radiation Synchrotron Radiation I similar to photon case, but dose deposition due to Cerenkov Radiation Particle Accelerators secondary protons or heavier nuclei X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1 Dose in Water for Different Radiation Beams

Background and Fundamentals Dose distributions for electron beams: The Discovery of Radiation X-rays Radioactivity I high surface dose and build-up to zmax, followed by Classiﬁcation of Radiation Types of Ionising Radiation rapid fall-off to a low-level dose bremsstrahlung tail Radiation Units and Properties due to radiative losses of the beam Dose in Water Atomic Physics and Radiation I zmax does not depend on beam energy, but beam The Rutherford-Bohr Model penetration depends on beam energy Multi-Electron Atoms

Production of Dose distributions for heavy charged particle beams: Radiation Characteristic Radiation I exhibit a range in distance traversed before very Characteristic X-rays Auger Electrons localised energy deposition; this is because of Continuous Radiation Bremsstrahlung Radiation negligible changes in heavy particle trajectories Synchrotron Radiation Cerenkov Radiation resulting from Coulomb interactions with orbital Particle Accelerators X-ray Tubes electrons in absorber Cyclotrons Linear Accelerators I maximum dose is called Bragg peak Radiation Physics Lecture 1 Atomic Physics and Radiation

Background and With the discovery of electrons as well as alpha, beta and Fundamentals gamma rays by 1900 came their use as probes to study The Discovery of Radiation X-rays the atomic structure of matter. In 1911, Ernest Rutherford Radioactivity Classification of Radiation proposed the atomic model that we retain today, in which Types of Ionising Radiation Radiation Units and Properties all positive charge is concentrated in a small massive Dose in Water Atomic Physics and nucleus, with the electrons orbiting around. This model Radiation The Rutherford-Bohr was vindicated in 1913 by Rutherford’s students, Geiger Model Multi-Electron Atoms and Marsden, in their famous alpha particle scattering Production of experiment (now known as "Rutherford scattering"). Radiation Characteristic Radiation Characteristic X-rays Auger Electrons Continuous Radiation Bremsstrahlung Radiation Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1 The Rutherford-Bohr Model Neils Bohr further postulated that electrons only exist in Background and Fundamentals certain fixed orbits that were related to the quantisation of The Discovery of Radiation X-rays electromagnetic radiation shown by Planck. Bohr’s atomic Radioactivity Classification of Radiation model successfully explains single-electron atoms. Types of Ionising Radiation Radiation Units and Properties Dose in Water Atomic Physics and Radiation The Rutherford-Bohr Model Multi-Electron Atoms

Background and Fundamentals The Discovery of Radiation Bohr’s model breaks down for multi-electron atoms X-rays Radioactivity because it does not take into account the repulsive Classiﬁcation of Radiation Types of Ionising Radiation Coulomb interactions between electrons. Douglas Radiation Units and Properties Hartree proposed an approximation that adequately Dose in Water Atomic Physics and Radiation predicts the energy levels En and radii rn of atomic orbits The Rutherford-Bohr Model in multi-electron systems: Multi-Electron Atoms Production of 2 2 Radiation Zeff a0n Characteristic Radiation En = −ER , rn = (1) Characteristic X-rays n Zeff Auger Electrons Continuous Radiation n E = . Bremsstrahlung Radiation where is the principal quantum number, R 13 61 eV Synchrotron Radiation is the Rydberg energy, Z is the effective atomic number Cerenkov Radiation eff − Particle Accelerators and a = 5.292 × 10 11 m is the Bohr radius of a X-ray Tubes 0 Cyclotrons single-electron atom. Linear Accelerators Radiation Physics Lecture 1

Energy level diagram for lead (Z = 82). The n = 1, 2, 3, 4... shells in multi-electron atoms are referred to as the K, L, M, N... shells. Radiation Physics Lecture 1 Production of Radiation Radiation is produced in a variety of different ways by Background and Fundamentals both natural and man-made processes. Atoms in an The Discovery of Radiation X-rays excited state de-excite by emitting electromagnetic Radioactivity Classification of Radiation radiation at discrete energies. For high-Z atoms, this line Types of Ionising Radiation Radiation Units and emission typically occurs at X-ray energies and is referred Properties Dose in Water to as characteristic radiation. Under some conditions, an Atomic Physics and Radiation The Rutherford-Bohr excited atom can also de-excite by emitting an Auger Model Multi-Electron Atoms electron, which is analogous to a photoelectron. Production of Continuous emission of electromagnetic radiation is Radiation Characteristic Radiation produced by charged particle (usually electron) Characteristic X-rays Auger Electrons acceleration, either by an electrostatic (Coulomb) field, Continuous Radiation Bremsstrahlung Radiation resulting in bremsstrahlung radiation, or by a magnetic Synchrotron Radiation Cerenkov Radiation field, resulting in synchrotron radiation. Radiation can Particle Accelerators X-ray Tubes also be produced by naturally radioactive sources. This Cyclotrons Linear Accelerators will not be covered here. Finally, man-made accelerator machines are designed to produce radiation with specific desired properties. Radiation Physics Lecture 1 Characteristic Radiation A vacancy in an atomic shell occurs as a result of several Background and different processes (e.g. photoelectric effect, Coulomb Fundamentals The Discovery of Radiation interactions – to be discussed later in the course). When X-rays Radioactivity it occurs in an inner shell, the atom is in a highly excited Classification of Radiation Types of Ionising Radiation state and returns to its ground state through electronic Radiation Units and Properties transitions which are usually accompanied by Dose in Water Atomic Physics and Radiation characteristic X-ray emission (formerly also referred to as The Rutherford-Bohr Model fluorescent emission). Some transitions result in the Multi-Electron Atoms ejection of other orbital electrons. This is the Auger effect. Production of Radiation Characteristic Radiation Characteristic X-rays Auger Electrons Continuous Radiation Bremsstrahlung Radiation Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1 Characteristic X-rays

Background and Fundamentals Electronic transitions that result in electromagnetic The Discovery of Radiation X-rays radiation are fully described using spectroscopic notation Radioactivity Classification of Radiation for the electronic configurations, which take the form nlj Types of Ionising Radiation Radiation Units and written in terms of the quantum numbers: Properties Dose in Water I n = principal quantum number, or shell: Atomic Physics and Radiation The Rutherford-Bohr n = 1, 2, 3, ... Model Multi-Electron Atoms I l = azimuthal quantum number, or subshell Production of Radiation (specifying an electron’s orbital angular momentum): Characteristic Radiation l = 0, 1, 2, 3, ..., n − 1 (corresponding to s, p, d, f orbital Characteristic X-rays Auger Electrons states) Continuous Radiation Bremsstrahlung Radiation 1 Synchrotron Radiation I s = spin quantum number: s = 2 Cerenkov Radiation Particle Accelerators I mj = total (orbital+spin) angular momentum quantum X-ray Tubes Cyclotrons number: mj = −j, −j + 1, −j + 2, ...j − 2, j − 1, j, where Linear Accelerators j = |l − s|, |l − s + 1|, ...|l + s| Radiation Physics Lecture 1 Radiative transitions can only proceed between adjacent Background and Fundamentals angular momentum states: The Discovery of Radiation X-rays Radioactivity Classification of Radiation ∆l = ±1 , ∆j = 0 or 1 (2) Types of Ionising Radiation Radiation Units and Properties Dose in Water but not j = 0 → j = 0. These are referred to as the Atomic Physics and Radiation selection rules for allowed transitions and are based on The Rutherford-Bohr Model the condition that electrostatic interactions always Multi-Electron Atoms dominate. Forbidden transitions are those which occur as Production of Radiation a result of other interactions, the most important being Characteristic Radiation Characteristic X-rays spin-orbit (or L − S) coupling. Forbidden transitions violate Auger Electrons Continuous Radiation the selection rules. For example, the Kα transition Bremsstrahlung Radiation 3 Synchrotron Radiation 2s1/2 −→ 1s1/2 is forbidden because ∆l = 0. The Kα Cerenkov Radiation 1 Particle Accelerators transition 2p3/2 −→ 1s1/2 is allowed because ∆l = 1 and X-ray Tubes Cyclotrons ∆j = 1. Linear Accelerators Radiation Physics Lecture 1

Background and When forbidden transitions occur, sometimes it results in Fundamentals The Discovery of Radiation the ejection of an electron, called an Auger electron, X-rays Radioactivity instead of characteristic X-rays. The energy difference Classiﬁcation of Radiation Types of Ionising Radiation between the two shells is thus transferred to the Auger Radiation Units and Properties electron, which is ejected with kinetic energy equal to the Dose in Water Atomic Physics and difference between its binding energy and the energy Radiation The Rutherford-Bohr released in the electronic transition. In the example Model Multi-Electron Atoms shown below, for instance, the Auger electron’s kinetic Production of Radiation energy is: Ekin = (EK − EL1 ) − EL2 Characteristic Radiation Characteristic X-rays Auger Electrons Continuous Radiation Bremsstrahlung Radiation Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1

Background and Fundamentals The Discovery of Radiation The Auger effect usually occurs between L and K shells X-rays Radioactivity and is more common in low-Z atoms, which tend to have Classification of Radiation Types of Ionising Radiation a lower fluorescence yield (number of characteristic Radiation Units and Properties photons emitted per vacancy) than high-Z atoms. This Dose in Water Atomic Physics and Radiation suggests the effect cannot be simply explained in terms The Rutherford-Bohr Model of the photoelectric effect and photon reabsorption. In Multi-Electron Atoms some cases, a cascade effect occurs, whereby inner shell Production of Radiation vacancies are successively filled by the Auger process, Characteristic Radiation Characteristic X-rays with ejections of more loosely bound electrons. Atoms Auger Electrons Continuous Radiation which produce mulitple Auger electrons are referred to as Bremsstrahlung Radiation Synchrotron Radiation Auger emitters. Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1 Continuous Radiation

Background and Fundamentals The Discovery of Radiation Unbound charged particles that are accelerated emit X-rays Radioactivity electromagnetic radiation. The emitted photons can have Classification of Radiation Types of Ionising Radiation any energy up to the kinetic energy of the radiating Radiation Units and Properties Dose in Water charged particle. Thus, the emission is continuous, rather Atomic Physics and Radiation than discrete as occurs for characteristic radiation. The Rutherford-Bohr Model Emission of electromagnetic radiation is most efficient for Multi-Electron Atoms electrons. The most common form of continous emission Production of Radiation occurs when an electron is deaccelerated by the Characteristic Radiation Characteristic X-rays Coulomb field of a nearby atomic nucleus. This is called Auger Electrons Continuous Radiation bremsstrahlung radiation. The radiation emitted by an Bremsstrahlung Radiation Synchrotron Radiation electron accelerated by an external magnetic field is Cerenkov Radiation Particle Accelerators called synchrotron radiation. Radiative losses of X-ray Tubes < Cyclotrons high-energy particles are typically ∼ 10%. Linear Accelerators Radiation Physics Lecture 1

Background and The emission of electromagnetic radiation represents an Fundamentals The Discovery of Radiation irreversible flow of energy from a source (accelerated X-rays Radioactivity electron) to infinity. This is possible only because the Classification of Radiation Types of Ionising Radiation electromagnetic fields associated with accelerating Radiation Units and 2 Properties charges fall off as 1/r, instead of 1/r , as is the case for Dose in Water Atomic Physics and charges at rest or charges moving uniformly. This Radiation The Rutherford-Bohr produces a finite total electromagnetic power (Poynting Model 2 2 Multi-Electron Atoms flux integrated over surface area ∝ r E ) at arbitrarily far Production of Radiation distances r. Characteristic Radiation /r Characteristic X-rays The 1 dependence arises because electromagnetic Auger Electrons Continuous Radiation waves have a finite propagation time to reach a field point Bremsstrahlung Radiation P from a source point S, so the radiation field measured at Synchrotron Radiation Cerenkov Radiation P at time t depends on the time at emission, called the Particle Accelerators 0 X-ray Tubes retarded time: t = t − ∆r/c. Cyclotrons Linear Accelerators Radiation Physics Lecture 1 The electromagnetic radiation field produced by an accelerated, nonrelativistic charge q is: Background and Fundamentals The Discovery of Radiation q 1 ˆr × (ˆr × v˙) X-rays Erad = 2 (3) Radioactivity 4π0 c r Classification of Radiation Types of Ionising Radiation Radiation Units and Properties 1 Dose in Water Brad = ˆr × Erad (4) Atomic Physics and c Radiation The Rutherford-Bohr Model where v˙ is the particle’s acceleration and r is the Multi-Electron Atoms displacement vector from the charged particle at time t0 to Production of Radiation the field point at which the radiation is being measured at Characteristic Radiation Characteristic X-rays time t. Note: Erad, Brad and ˆr are mutually perpendicular. Auger Electrons Continuous Radiation Bremsstrahlung Radiation Problem: Derive an expression for the magnitude of the Synchrotron Radiation Cerenkov Radiation Poynting flux, S = |E × B|/µ0, in terms of angle θ be- Particle Accelerators X-ray Tubes tween the acceleration v˙ and displacement unit vector ˆr. Cyclotrons Linear Accelerators In what directions is the radiative power a maximum and a minimum? Radiation Physics Lecture 1 Solution: 1 EB E2 Background and S = |E × B| = = Fundamentals µ0 µ0 µ0c The Discovery of Radiation X-rays Radioactivity since Erad, Brad and ˆr are mutually perpendicular. We can Classification of Radiation Types of Ionising Radiation write E in terms of θ as follows: Radiation Units and Properties Dose in Water q v˙ sin θ Atomic Physics and E = 2 Radiation 4π0c r The Rutherford-Bohr Model Multi-Electron Atoms so Production of 1 q 2 a2 sin2 θ Radiation S = Characteristic Radiation µ c π c2 r2 Characteristic X-rays 0 4 0 Auger Electrons Continuous Radiation =⇒ Maximum radiation is emitted in directions perpendic- Bremsstrahlung Radiation Synchrotron Radiation ular to the particle’s acceleration (i.e. θ = ±π/2). No radi- Cerenkov Radiation Particle Accelerators ation is emitted in directions aligned with the acceleration X-ray Tubes Cyclotrons (forward or backward). This is known as a dipole radiation Linear Accelerators pattern. Radiation Physics Lecture 1

Background and Fundamentals The Discovery of Radiation The total electromagnetic power P radiated is obtained by X-rays Radioactivity integrating the Poynting flux, S = EradBrad/µ0, over a Classification of Radiation R 2 Types of Ionising Radiation surface area in all directions: P = Sr dΩ, where Radiation Units and Properties dΩ = sin θdθdφ. This gives the following: Dose in Water Atomic Physics and Radiation 2 2 The Rutherford-Bohr µ0q a Model P = Larmor formula (5) Multi-Electron Atoms 6πc Production of Radiation This famous result shows that the total power emitted into Characteristic Radiation Characteristic X-rays electromagnetic radiation is directly proportional to the Auger Electrons Continuous Radiation square of a charged particle’s acceleration a and charge Bremsstrahlung Radiation Synchrotron Radiation q. Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1 Bremsstrahlung Radiation When charged particles of mass m and charge e are Background and incident on a target material, they experience inelastic Fundamentals The Discovery of Radiation Coulomb interactions with the orbital electrons and with X-rays Radioactivity the nuclei (charge Ze) of the target. Coulomb collisions Classification of Radiation Types of Ionising Radiation with the orbital electrons usually results in ionisation Radiation Units and Properties losses. Coulomb encounters with nuclei results in Dose in Water Atomic Physics and Radiation radiative bremsstrahlung losses. The Rutherford-Bohr Model Multi-Electron Atoms

Production of Radiation Characteristic Radiation The emission spectrum for Characteristic X-rays Auger Electrons bremsstrahlung radiation is Continuous Radiation Bremsstrahlung Radiation continuous up to the kinetic Synchrotron Radiation Cerenkov Radiation energy of the emitting elec- Particle Accelerators X-ray Tubes tron and the power spec- Cyclotrons −1 Linear Accelerators trum dIω/dω falls off as ω . Radiation Physics Lecture 1 Synchrotron Radiation

Background and Synchrotron radiation is electromagnetic radiation emitted Fundamentals The Discovery of Radiation by charged particles accelerated by a magnetic field that X-rays Radioactivity maintains a circular particle trajectory, so there is a Classification of Radiation Types of Ionising Radiation centripetal acceleration perpendicular to the Radiation Units and Properties instantaneous particle momentum. Because particles can Dose in Water Atomic Physics and be accelerated to very high energies, it is necessary to Radiation The Rutherford-Bohr consider the relativistic generalisation of the Larmor Model Multi-Electron Atoms formula: Production of Radiation Characteristic Radiation Characteristic X-rays 2 Auger Electrons µ0q 4 2 2 2 Continuous Radiation P = γ (γ ak+a⊥) relativistic Larmor formula (6) Bremsstrahlung Radiation 6πc Synchrotron Radiation Cerenkov Radiation 2 −1/2 Particle Accelerators where γ = (1 − β ) is the particle’s Lorentz factor, X-ray Tubes 2 Cyclotrons corresponding to its energy E = γmc , and where ak and Linear Accelerators a⊥ are the components of the particle’s acceleration parallel and perpendicular to its velocity βc. Radiation Physics Lecture 1 2 For synchrotron radiation, ak = 0 and a⊥ = v /R, where R is the fixed radius of the synchrotron accelerating device. Background and Fundamentals The Larmor formula then implies The Discovery of Radiation X-rays 2 3 4 4 Radioactivity µ0q c β γ Classification of Radiation P = (7) Types of Ionising Radiation 6πR2 Radiation Units and Properties Dose in Water For a fixed magnetic field strength B, the particle orbital Atomic Physics and Radiation angular momentum attained is γmv⊥ = eBR. The Rutherford-Bohr Model The radiation intensity pattern emitted by relativistic Multi-Electron Atoms

Production of charged particles is highly directional and is beamed Radiation Characteristic Radiation towards the direction of motion of the particles in a Characteristic X-rays Auger Electrons forward beam. This effect, called relativistic beaming, Continuous Radiation Bremsstrahlung Radiation results from relativistic aberration. Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators dipole emission (particle rest frame) forward beaming (observer rest frame) P(θ) ∝ sin2 θ P(θ) ∝ (1 − β cos ϑ)−4 Radiation Physics Lecture 1 Because P ∝ R−2 (c.f. eqn. 7), particle accelerators such as CERN’s Large Hadronic Collider (LHC) and the Background and Fundamentals Australian synchrotron (shown below) have to be built The Discovery of Radiation X-rays with a large radius of curvature in order to minimise Radioactivity Classiﬁcation of Radiation synchrotron losses by the particles being accelerated. Types of Ionising Radiation Radiation Units and Properties Dose in Water Atomic Physics and Radiation The Rutherford-Bohr Model Multi-Electron Atoms

Cerenkov radiation from the water tank in the OPAL reactor at ANSTO. Radiation Physics Lecture 1 As a fast charged particle traverses a dielectric such as water, it polarises the atoms. As the atoms relax back into Background and their equilibrium state, energy is emitted in the form of an Fundamentals The Discovery of Radiation electromagnetic pulse. X-rays Radioactivity Classiﬁcation of Radiation Types of Ionising Radiation Radiation Units and Properties Dose in Water Atomic Physics and Radiation The Rutherford-Bohr Model Multi-Electron Atoms

Production of Radiation Characteristic Radiation This only occurs if the charged particle is travelling faster Characteristic X-rays Auger Electrons than the phase velocity of light in the medium, i.e. Continuous Radiation Bremsstrahlung Radiation Synchrotron Radiation c Cerenkov Radiation v > where n = refractive index (8) Particle Accelerators n X-ray Tubes Cyclotrons Linear Accelerators e.g. for water, n = 1.33, so Cerenkov radiation is emitted when v > 0.75c. For an electron, this corresponds to an 2 2 −1/2 2 energy E = γmec = (1 − β ) mec = 0.775 MeV. Radiation Physics Lecture 1 When the criterion v > c/n is satisﬁed, the charged particle moves faster than the emitted waves, so it

Background and overtakes the wavefronts. This results in the wavefronts Fundamentals The Discovery of Radiation interfering constructively, producing coherent radiation X-rays Radioactivity emitted on the surface of a forward cone directed along Classiﬁcation of Radiation Types of Ionising Radiation the particle’s trajectory. Radiation Units and Properties Dose in Water Atomic Physics and Radiation The Rutherford-Bohr Model Multi-Electron Atoms

Production of Radiation Characteristic Radiation Characteristic X-rays Auger Electrons Continuous Radiation Bremsstrahlung Radiation Synchrotron Radiation Cerenkov Radiation Particle Accelerators X-ray Tubes Cyclotrons For particles moving slower than the speed of light in the Linear Accelerators medium, the wavefronts always move ahead of the particle and interfere destructively, so there is not net electromagnetic ﬁeld at large distances (i.e. no radiation). Radiation Physics Lecture 1 Particle Accelerators

Background and Various types of particle accelerator machines have been Fundamentals The Discovery of Radiation built for basic research in nuclear and high-energy X-rays Radioactivity physics. Most of them have been modified for medical Classification of Radiation Types of Ionising Radiation application. All particle accelerators require an electric Radiation Units and Properties field to accelerate charged particles. There are 2 types of Dose in Water Atomic Physics and Radiation electric field specifications: The Rutherford-Bohr Model 1. electrostatic accelerators – particles accelerated by a Multi-Electron Atoms

Production of static electric field; maximum energy limited by Radiation Characteristic Radiation voltage drop; examples: superficial and orthovoltage Characteristic X-rays X-ray tubes. Auger Electrons Continuous Radiation Bremsstrahlung Radiation 2. cyclic accelerators – particles accelerated by time Synchrotron Radiation Cerenkov Radiation varying electric field and trajectories curved by Particle Accelerators X-ray Tubes associated magnetic field; multiple crossings of Cyclotrons Linear Accelerators voltage drop allows high energies to be attained; examples: cyclotrons, linear accelerators. Radiation Physics Lecture 1 X-ray Tubes

Production of Radiation Characteristic Radiation Characteristic X-rays I electrons produced in heated ﬁlament (cathode) Auger Electrons Continuous Radiation accelerated in vacuum tube toward target (anode) Bremsstrahlung Radiation Synchrotron Radiation across electrostatic potential Cerenkov Radiation Particle Accelerators I bremsstrahlung X-rays produced at high-Z target X-ray Tubes Cyclotrons (∼ 1% efﬁciency typically) Linear Accelerators I kinetic energy deposited in target mostly as heat; requires cooling Radiation Physics Lecture 1

Background and Fundamentals I resulting X-ray beam energy determined by peak The Discovery of Radiation X-rays energy of electron beam (voltage drop), often given Radioactivity Classiﬁcation of Radiation as peak voltage in kilovolts, kVp Types of Ionising Radiation Radiation Units and Properties Dose in Water Atomic Physics and Radiation The Rutherford-Bohr Model Multi-Electron Atoms

Production of Radiation Characteristic Radiation Characteristic X-rays Auger Electrons Continuous Radiation Bremsstrahlung Radiation Synchrotron Radiation Cerenkov Radiation Particle Accelerators Left: Spectra produced by an X-ray tube. Right: Angular distribution X-ray Tubes of bremsstrahlung emission by electron beams of different energies. Cyclotrons Linear Accelerators Radiation Physics Lecture 1 Cyclotrons

Background and Fundamentals The Discovery of Radiation X-rays Radioactivity Classification of Radiation Types of Ionising Radiation Radiation Units and Properties Dose in Water Atomic Physics and Radiation The Rutherford-Bohr Model Multi-Electron Atoms Production of I particles accelerated by crossing a radiofrequency Radiation Characteristic Radiation (RF) voltage multiple times Characteristic X-rays Auger Electrons I uniform B-field confines particle trajectories to spiral Continuous Radiation Bremsstrahlung Radiation motion Synchrotron Radiation Cerenkov Radiation Particle Accelerators I proton cyclotrons used to produce fluorine-18 X-ray Tubes Cyclotrons radionuclide used in Positron Emission Tomography Linear Accelerators (PET) Radiation Physics Lecture 1 Linear Accelerators (linacs)

Background and Fundamentals The Discovery of Radiation X-rays Radioactivity Classification of Radiation I used for radiotherapy treatment of cancer (external Types of Ionising Radiation Radiation Units and beam therapy) Properties Dose in Water I acceleration of electrons by pulsed, high power RF Atomic Physics and Radiation The Rutherford-Bohr fields in an accelerating waveguide Model Multi-Electron Atoms I linear trajectories, multiple voltage crossings Production of Radiation I peak electron beam energies in range 4 − 25 MeV Characteristic Radiation Characteristic X-rays I high energy (5 − 20 MeV) photon beams also Auger Electrons Continuous Radiation produced with retractable thick X-ray target Bremsstrahlung Radiation Synchrotron Radiation Cerenkov Radiation I multiple configurations possible Particle Accelerators X-ray Tubes Cyclotrons Linear Accelerators Radiation Physics Lecture 1