phys 5012 radiation physics and dosimetry - lecture 1kuncic/lectures/rp1_slides.pdf · radiation...

Radiation PhysicsLecture 1

Background andFundamentalsThe Discovery of Radiation

X-rays

Radioactivity

Classification of Radiation

Types of Ionising Radiation

Radiation Units andProperties

Dose in Water

Atomic Physics andRadiation

The Rutherford-BohrModel

Multi-Electron Atoms

Production ofRadiationCharacteristic Radiation

Characteristic X-rays

Auger Electrons

Continuous Radiation

Bremsstrahlung Radiation

Synchrotron Radiation

Cerenkov Radiation

Particle Accelerators

X-ray Tubes

Cyclotrons

Linear Accelerators

PHYS 5012Radiation Physics and Dosimetry

Lecture 1

Tuesday 5 March 2013



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The Discovery of Radiation

Three main discoveries of radiation made at the turn ofthe 19th century, together with several major advances intheoretical physics, including quantum mechanics andspecial relativity, signalled the birth of Radiation Physics.The subsequent realisation that radiation can be harmfulto humans led to the the rapid development of radiationdosage measurements and quantification and commonlyaccepted standards for tolerable levels of radiation inhumans.



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X-raysX-rays are photons (i.e. electromagnetic radiation) withenergies typically above 1 keV. They were discovered byWilhelm Conrad Roentgen in 1895.

Roentgen discovered X-rays inadvertedly whilst studying fluoresenceusing a cathode ray tube. He explored the absorption properties of therays in soft tissue and bone using his wife’s hand (note the ring).



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RadioactivityNatural radioactivity is the spontaneous emission ofradiation by a material. It was discovered by AntoineHenri Becquerel in 1896.

Whilst Roentgen’s X-raysneeded to be induced bycathode rays (electrons),Becquerel found that somematerials, notably uranium ore,possessed their own source ofradiation energy. He discoveredthis after placing some uraniummineral on a photographic platewrapped in black paper into adark drawer, finding afterwardsthat the uranium had indeedleft an image on the plate.



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RadioactivityMarie Curie coined the term "radioactivity" for thephenomenon Becquerel found associated with uraniumore. Together with her husband Pierre, they beganinvestigating radioactivity. Marie found that afterextracting pure uranium from ore, the residual materialwas even more radioactive than the uranium. She haddiscovered polonium and radium.



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Radiation can be broadly classified into two maincategories, based on its ability to ionise matter:

I Non-ionising radiation cannot ionise matter becauseits energy is lower than the ionisation potential of thematter.

I Ionising radiation has sufficient energy to ionisematter either directly or indirectly.

Although non-ionising radiation can transfer some of itsenergy to matter, the low energies involved result innegligible effects compared to those of ionising radiation.Henceforth, only ionising radiation will be considered.



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Ionising radiation can be further subdivided into twoclasses:

I Directly ionising - charged particles (electrons,protons, α particles, heavy ions); deposits energy inmatter directly through Coulomb collisions withorbital electrons.

I Indirectly ionising - neutral particles (photons,neutrons); deposit energy indiectly through atwo-step process: 1. release of charged particlesand 2. charged particle energy deposition throughColoumb interactions.



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Types of Directly Ionising Radiation

Charged particles are described as light (electrons andpositrons), heavy (protons, deutrons, α particles) orheavier (e.g. carbon-12). Some of the commonnomenclature is as follows:

Light charged particlesI photoelectrons – produced by photoelectric effectI recoil electrons – produced by Compton effectI delta rays – electrons produced by charged particle

collisionsI beta particles – electrons or positrons emitted from

nuclei by β− or β+ decay:10n −→1

1 p + 0−1 e or 1

1p −→10 n + 0

+1 e + ν



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Types of Directly Ionising Radiation

Heavy charged particlesI protons – nucleus of hydrogen-1 (1

1H) atomI deuteron – nucleus of deuterium (2

1H) atomI triton – nucleus of tritium (3

1H) atomI helium-3 – nucleus of helium-3 (3

2He) atomI α particle – nucleus of helium-4 (4

2He) atom

Heavier charged particles include nuclei or ions ofheavier atoms such as carbon-12 (12

6 C), nitrogen-14 (147 N),

or neon-20 (2010Ne).



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Types of Indirectly Ionising Radiation

Ionising photons can be classified into four groups:I characteristic X-rays – due to electronic transitions

between discrete atomic energy levelsI bremsstrahlung emission – due to electron-nucleus

Coulomb interactionsI gamma rays – resulting from nuclear decaysI annihilation radiation – resulting from

electron-positron pair annihilation



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Radiation Units and Properties

Accurate measurement of radiation is critical to anyindustry or profession that involves regular use ofradiation. Several units have been defined to quantifydifferent types of radiation measurements. These aresummarised in the following table.



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Quantity Definition SI unitExposure X = ∆Q/∆mair 2.58× 10−4C kg−1

Dose D = ∆Eab/∆m 1 Gy = 1 J kg−1

Equivalent dose H = DwR 1 SvActivity A = λN 1 Bq = 1 s−1

I Exposure measures the ability of photons to ioniseair (its original unit of measurement was theroentgen, R); ∆Q is the collected charge.

I Dose is the energy absorbed per mass of matter; itsunit is the gray (Gy); ∆Eab is the energy absorbed ina medium.

I Equivalent dose is the dose mulitplied by a radiationweighting factor wR for different types of radiation(wR = 1 for photons and electrons); its unit ofmeasurement is the sievert (Sv).

I Activity is the number of decays per unit time of aradioactive substance; λ is the decay constant and Nis the number of radioactive atoms.



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Dose in Water for Different Radiation Beams

Dose deposition in water is extremely important becausesoft tissue is mostly made up of water. Different types ofradiation deposit their energy at different depths in water.In general, indirectly ionising radiation deposits energy inan exponential-like fashion, while directly ionisingradiation deposits virtually all its energy in a localisedregion, as is evident in the figure below.



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Depth dose curves for different radiation beams in water and for differ-ent energies, normalised to 100% at depth dose maximum (reproduced fromPodgoršak, Fig. 1.2).



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Dose distributions for photon beams:I build-up region from surface to depth dose maximum

zmax followed by approximate exponential attenuationI dose deposition determined by secondary electrons;

zmax proportional to beam energyI skin sparing effect: low surface dose for high energy

beamsDose distributions for neutron beams:

I similar to photon case, but dose deposition due tosecondary protons or heavier nuclei



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Dose distributions for electron beams:I high surface dose and build-up to zmax, followed by

rapid fall-off to a low-level dose bremsstrahlung taildue to radiative losses of the beam

I zmax does not depend on beam energy, but beampenetration depends on beam energy

Dose distributions for heavy charged particle beams:I exhibit a range in distance traversed before very

localised energy deposition; this is because ofnegligible changes in heavy particle trajectoriesresulting from Coulomb interactions with orbitalelectrons in absorber

I maximum dose is called Bragg peak



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Atomic Physics and RadiationWith the discovery of electrons as well as alpha, beta andgamma rays by 1900 came their use as probes to studythe atomic structure of matter. In 1911, Ernest Rutherfordproposed the atomic model that we retain today, in whichall positive charge is concentrated in a small massivenucleus, with the electrons orbiting around. This modelwas vindicated in 1913 by Rutherford’s students, Geigerand Marsden, in their famous alpha particle scatteringexperiment (now known as "Rutherford scattering").



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The Rutherford-Bohr ModelNeils Bohr further postulated that electrons only exist incertain fixed orbits that were related to the quantisation ofelectromagnetic radiation shown by Planck. Bohr’s atomicmodel successfully explains single-electron atoms.



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Bohr’s model breaks down for multi-electron atomsbecause it does not take into account the repulsiveCoulomb interactions between electrons. DouglasHartree proposed an approximation that adequatelypredicts the energy levels En and radii rn of atomic orbitsin multi-electron systems:

En = −ER

(Zeff

n

)2

, rn =a0n2

Zeff(1)

where n is the principal quantum number, ER = 13.61 eVis the Rydberg energy, Zeff is the effective atomic numberand a0 = 5.292× 10−11 m is the Bohr radius of asingle-electron atom.



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Energy level diagram for lead (Z = 82). The n = 1, 2, 3, 4... shells inmulti-electron atoms are referred to as the K, L,M,N... shells.



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Production of RadiationRadiation is produced in a variety of different ways byboth natural and man-made processes. Atoms in anexcited state de-excite by emitting electromagneticradiation at discrete energies. For high-Z atoms, this lineemission typically occurs at X-ray energies and is referredto as characteristic radiation. Under some conditions, anexcited atom can also de-excite by emitting an Augerelectron, which is analogous to a photoelectron.Continuous emission of electromagnetic radiation isproduced by charged particle (usually electron)acceleration, either by an electrostatic (Coulomb) field,resulting in bremsstrahlung radiation, or by a magneticfield, resulting in synchrotron radiation. Radiation canalso be produced by naturally radioactive sources. Thiswill not be covered here. Finally, man-made acceleratormachines are designed to produce radiation with specificdesired properties.



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Characteristic RadiationA vacancy in an atomic shell occurs as a result of severaldifferent processes (e.g. photoelectric effect, Coulombinteractions – to be discussed later in the course). Whenit occurs in an inner shell, the atom is in a highly excitedstate and returns to its ground state through electronictransitions which are usually accompanied bycharacteristic X-ray emission (formerly also referred to asfluorescent emission). Some transitions result in theejection of other orbital electrons. This is the Auger effect.



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Electronic transitions that result in electromagneticradiation are fully described using spectroscopic notationfor the electronic configurations, which take the form nljwritten in terms of the quantum numbers:

I n = principal quantum number, or shell:n = 1, 2, 3, ...

I l = azimuthal quantum number, or subshell(specifying an electron’s orbital angular momentum):l = 0, 1, 2, 3, ..., n− 1 (corresponding to s, p, d, f orbitalstates)

I s = spin quantum number : s = 12

I mj = total (orbital+spin) angular momentum quantumnumber: mj = −j,−j + 1,−j + 2, ...j− 2, j− 1, j, wherej = |l− s|, |l− s + 1|, ...|l + s|



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Radiative transitions can only proceed between adjacentangular momentum states:

∆l = ±1 , ∆j = 0 or 1 (2)

but not j = 0→ j = 0. These are referred to as theselection rules for allowed transitions and are based onthe condition that electrostatic interactions alwaysdominate. Forbidden transitions are those which occur asa result of other interactions, the most important beingspin-orbit (or L− S) coupling. Forbidden transitions violatethe selection rules. For example, the Kα3 transition2s1/2 −→ 1s1/2 is forbidden because ∆l = 0. The Kα1

transition 2p3/2 −→ 1s1/2 is allowed because ∆l = 1 and∆j = 1.



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Linear AcceleratorsTypical energy level diagram for a high-Z atom showing sub-shell structure forK, L and M shells. Allowed (solid lines) and forbidden (dashed lines) Kα and Kβ

transitions are also shown. Numbers in parentheses indicate maximum numberof electrons in that sub-shell, 2j + 1.



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Characteristic X-ray SpectraCharacteristic emission produces line spectra at discreteenergies corresponding to the difference between energystates. The strongest lines are usually the Kα(n = 2→ n = 1) and Kβ (n = 3→ n = 1) transitions.



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Auger Electrons

When forbidden transitions occur, sometimes it results inthe ejection of an electron, called an Auger electron,instead of characteristic X-rays. The energy differencebetween the two shells is thus transferred to the Augerelectron, which is ejected with kinetic energy equal to thedifference between its binding energy and the energyreleased in the electronic transition. In the exampleshown below, for instance, the Auger electron’s kineticenergy is: Ekin = (EK − EL1)− EL2



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The Auger effect usually occurs between L and K shellsand is more common in low-Z atoms, which tend to havea lower fluorescence yield (number of characteristicphotons emitted per vacancy) than high-Z atoms. Thissuggests the effect cannot be simply explained in termsof the photoelectric effect and photon reabsorption. Insome cases, a cascade effect occurs, whereby inner shellvacancies are successively filled by the Auger process,with ejections of more loosely bound electrons. Atomswhich produce mulitple Auger electrons are referred to asAuger emitters.



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Unbound charged particles that are accelerated emitelectromagnetic radiation. The emitted photons can haveany energy up to the kinetic energy of the radiatingcharged particle. Thus, the emission is continuous, ratherthan discrete as occurs for characteristic radiation.Emission of electromagnetic radiation is most efficient forelectrons. The most common form of continous emissionoccurs when an electron is deaccelerated by theCoulomb field of a nearby atomic nucleus. This is calledbremsstrahlung radiation. The radiation emitted by anelectron accelerated by an external magnetic field iscalled synchrotron radiation. Radiative losses ofhigh-energy particles are typically <∼ 10%.



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The emission of electromagnetic radiation represents anirreversible flow of energy from a source (acceleratedelectron) to infinity. This is possible only because theelectromagnetic fields associated with acceleratingcharges fall off as 1/r, instead of 1/r2, as is the case forcharges at rest or charges moving uniformly. Thisproduces a finite total electromagnetic power (Poyntingflux integrated over surface area ∝ r2E2) at arbitrarily fardistances r.The 1/r dependence arises because electromagneticwaves have a finite propagation time to reach a field pointP from a source point S, so the radiation field measured atP at time t depends on the time at emission, called theretarded time: t′ = t −∆r/c.



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The electromagnetic radiation field produced by anaccelerated, nonrelativistic charge q is:

Erad =q

4πε0

1c2

[r× (r× v)

r

](3)

Brad =1c

r× Erad (4)

where v is the particle’s acceleration and r is thedisplacement vector from the charged particle at time t′ tothe field point at which the radiation is being measured attime t. Note: Erad, Brad and r are mutually perpendicular.

Problem: Derive an expression for the magnitude of thePoynting flux, S = |E × B|/µ0, in terms of angle θ be-tween the acceleration v and displacement unit vector r.In what directions is the radiative power a maximum and aminimum?



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Solution:

S =1µ0|E× B| = EB

µ0=

E2

µ0c

since Erad, Brad and r are mutually perpendicular. We canwrite E in terms of θ as follows:

E =q

4πε0c2v sin θ

r

so

S =1µ0c

(q

4πε0c2

)2 a2 sin2 θ

r2

=⇒ Maximum radiation is emitted in directions perpendic-ular to the particle’s acceleration (i.e. θ = ±π/2). No radi-ation is emitted in directions aligned with the acceleration(forward or backward). This is known as a dipole radiationpattern.



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The total electromagnetic power P radiated is obtained byintegrating the Poynting flux, S = EradBrad/µ0, over asurface area in all directions: P =

∫Sr2dΩ, where

dΩ = sin θdθdφ. This gives the following:

P =µ0q2a2

6πcLarmor formula (5)

This famous result shows that the total power emitted intoelectromagnetic radiation is directly proportional to thesquare of a charged particle’s acceleration a and chargeq.



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Bremsstrahlung RadiationWhen charged particles of mass m and charge e areincident on a target material, they experience inelasticCoulomb interactions with the orbital electrons and withthe nuclei (charge Ze) of the target. Coulomb collisionswith the orbital electrons usually results in ionisationlosses. Coulomb encounters with nuclei results inradiative bremsstrahlung losses.



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The acceleration a experienced by an incident charge q inthe vicinity of a nucleus is obtained from the Coulombforce:

ma =q Ze

4πε0r2 =⇒ a ∝ qZem

The Larmor formula then implies that radiative losses forincident electrons is more efficient, by a factor(mp/me)

2 ' 4× 106, than for protons, which lose kineticenergy more quickly via collisional ionisation losses.

The emission spectrum forbremsstrahlung radiation iscontinuous up to the kineticenergy of the emitting elec-tron and the power spec-trum dIω/dω falls off as ω−1.



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Synchrotron radiation is electromagnetic radiation emittedby charged particles accelerated by a magnetic field thatmaintains a circular particle trajectory, so there is acentripetal acceleration perpendicular to theinstantaneous particle momentum. Because particles canbe accelerated to very high energies, it is necessary toconsider the relativistic generalisation of the Larmorformula:

P =µ0q2

6πcγ4(γ2a2

‖+a2⊥) relativistic Larmor formula (6)

where γ = (1− β2)−1/2 is the particle’s Lorentz factor,corresponding to its energy E = γmc2, and where a‖ anda⊥ are the components of the particle’s accelerationparallel and perpendicular to its velocity βc.



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For synchrotron radiation, a‖ = 0 and a⊥ = v2/R, where Ris the fixed radius of the synchrotron accelerating device.The Larmor formula then implies

P =µ0q2c3β4γ4

6πR2 (7)

For a fixed magnetic field strength B, the particle orbitalangular momentum attained is γmv⊥ = eBR.The radiation intensity pattern emitted by relativisticcharged particles is highly directional and is beamedtowards the direction of motion of the particles in aforward beam. This effect, called relativistic beaming,results from relativistic aberration.

dipole emission (particle rest frame)P(θ) ∝ sin2 θ

forward beaming (observer rest frame)P(θ) ∝ (1− β cosϑ)−4



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Because P ∝ R−2 (c.f. eqn. 7), particle accelerators suchas CERN’s Large Hadronic Collider (LHC) and theAustralian synchrotron (shown below) have to be builtwith a large radius of curvature in order to minimisesynchrotron losses by the particles being accelerated.



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Cerenkov RadiationCerenkov radiation is most widely recognised as thecharacteristic blue glow emitted from water irradiated byhigh-energy particles. The optical radiation is producednot by the particles, which are moving at constant speed,but by the atoms which are excited by the passage ofcharged particles. This occurs in any dielectric(non-conducting) medium.

Cerenkov radiation from the water tank in theOPAL reactor at ANSTO.



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As a fast charged particle traverses a dielectric such aswater, it polarises the atoms. As the atoms relax back intotheir equilibrium state, energy is emitted in the form of anelectromagnetic pulse.

This only occurs if the charged particle is travelling fasterthan the phase velocity of light in the medium, i.e.

v >cn

where n = refractive index (8)

e.g. for water, n = 1.33, so Cerenkov radiation is emittedwhen v > 0.75c. For an electron, this corresponds to anenergy E = γmec2 = (1− β2)−1/2mec2 = 0.775 MeV.



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When the criterion v > c/n is satisfied, the chargedparticle moves faster than the emitted waves, so itovertakes the wavefronts. This results in the wavefrontsinterfering constructively, producing coherent radiationemitted on the surface of a forward cone directed alongthe particle’s trajectory.

For particles moving slower than the speed of light in themedium, the wavefronts always move ahead of theparticle and interfere destructively, so there is not netelectromagnetic field at large distances (i.e. no radiation).



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Various types of particle accelerator machines have beenbuilt for basic research in nuclear and high-energyphysics. Most of them have been modified for medicalapplication. All particle accelerators require an electricfield to accelerate charged particles. There are 2 types ofelectric field specifications:

1. electrostatic accelerators – particles accelerated by astatic electric field; maximum energy limited byvoltage drop; examples: superficial and orthovoltageX-ray tubes.

2. cyclic accelerators – particles accelerated by timevarying electric field and trajectories curved byassociated magnetic field; multiple crossings ofvoltage drop allows high energies to be attained;examples: cyclotrons, linear accelerators.



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X-ray Tubes

I electrons produced in heated filament (cathode)accelerated in vacuum tube toward target (anode)across electrostatic potential

I bremsstrahlung X-rays produced at high-Z target(∼ 1% efficiency typically)

I kinetic energy deposited in target mostly as heat;requires cooling



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I resulting X-ray beam energy determined by peakenergy of electron beam (voltage drop), often givenas peak voltage in kilovolts, kVp

Left: Spectra produced by an X-ray tube. Right: Angular distributionof bremsstrahlung emission by electron beams of different energies.



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Cyclotrons

I particles accelerated by crossing a radiofrequency(RF) voltage multiple times

I uniform B-field confines particle trajectories to spiralmotion

I proton cyclotrons used to produce fluorine-18radionuclide used in Positron Emission Tomography(PET)



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Linear Accelerators (linacs)

I used for radiotherapy treatment of cancer (externalbeam therapy)

I acceleration of electrons by pulsed, high power RFfields in an accelerating waveguide

I linear trajectories, multiple voltage crossingsI peak electron beam energies in range 4− 25 MeVI high energy (5− 20 MeV) photon beams also

produced with retractable thick X-ray targetI multiple configurations possible



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Schematic of a medical linac (from Podgoršak, Fig. 14.3).



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