Radiation Physics Lecture 5 Interactions of Charged Particles with Matter Radiation Yield Bremsstrahlung Targets Thin Targets PHYS 5012 Thick Targets Restricted Stopping Power Straggling and Scattering Radiation Physics and Dosimetry Electron Range Dose Linear Energy Transfer Lecture 5 Tuesday 3 April 2012 Radiation Physics Lecture 5 Charged Particle Interactions (cont.) Interactions of Charged Particles with Matter Radiation Yield Bremsstrahlung Targets Thin Targets Thick Targets Restricted Stopping Power Straggling and Scattering Electron Range Dose Linear Energy Transfer Stopping power of water for 10 MeV electrons: 2 −1 2 −1 Scol = 1.968 MeV cm g , Srad = 0.1814 MeV cm g , 2 −1 Stot = Scol + Srad = 2.149 MeV cm g −2 Range: RCSDA = 4.975 g cm ⇒ average path length of 10 MeV electrons in water is ≈ 5 cm. Radiation yield: −2 2 −1 Y = 4.072 × 10 ⇒ S¯col = 1.928 MeV cm g Radiation Physics Lecture 5 Bremsstrahlung (Radiation) Yield Recall the mean collision stopping power (c.f. eqn. 32, Interactions of Lec. 4): Charged Particles with Matter 1 − Y(EK,0) Radiation Yield Scol(EK,0) = EK,0 Bremsstrahlung Targets RCSDA Thin Targets Thick Targets which takes into account the continuous degradation in Restricted Stopping Power Straggling and Scattering energy of an initially monoenergetic beam of radiation. Electron Range Dose Linear Energy Transfer I Y(EK,0) = radiation yield = fraction of initial kinetic energy EK,0 emitted as bremsstrahlung radiation through continuous slowing down of charged particle in a medium I Y(EK,0) ≈ 0 for heavy charged particles I for light charged particles (electrons and positrons), Z EK,0 1 Srad(E) Y(EK,0) = dE (1) EK,0 0 Stot(E) I electron-positron annilhilation radiation is generally negligible compared to bremsstrahlung emission Radiation Physics Lecture 5 Interactions of Charged Particles with Matter Radiation Yield Bremsstrahlung Targets Thin Targets Thick Targets Restricted Stopping Power Straggling and Scattering Electron Range Dose Linear Energy Transfer Bremsstrahlung yield for electrons in different media plotted against initial elec- tron kinetic energy. (Fig. 6.12 in Podgoršak.) Recall from Lec. 4 (c.f. eqn. 22), the formula for radiative stopping power: N S (E) = A σ E rad A rad i 2 where σrad ∝ Z Brad(Z, Ei) is the Bethe-Heitler total radiative cross section derived from the quantum mechanical theory for bremsstrahlung radiation, and 2 where Ei = EK,0 + mec . Radiation Physics Lecture 5 Interactions of Charged Particles with Matter Radiation Yield Bremsstrahlung Targets I energy radiated per charged particle: Thin Targets Thick Targets Restricted Stopping Power Z EK,0 Straggling and Scattering Srad(E) Electron Range Erad = EK,0Y(EK,0) = dE (2) Dose 0 Stot(E) Linear Energy Transfer I energy lost to ionisation per charged particle: Z EK,0 Scol(E) Ecol = EK,0 − Erad = EK,0 [1 − Y(EK,0)] = dE 0 Stot(E) (3) Radiation Physics Lecture 5 Example: Radiation yield for 10 MeV electrons. 1. In water (Z = 10): Y ≈ 4.1% (from NIST/estar) =⇒ Interactions of Charged Particles I energy radiated per charged particle: with Matter Radiation Yield Bremsstrahlung Targets Erad = EK,0Y(EK,0) ≈ 0.41 MeV Thin Targets Thick Targets Restricted Stopping Power Straggling and Scattering I energy lost to ionisation per charged particle: Electron Range Dose Linear Energy Transfer Ecol = EK,0 [1 − Y(EK,0)] ≈ 9.59 MeV 1. In tungsten (Z = 74): Y ≈ 30% (from NIST/estar) =⇒ I energy radiated per charged particle: Erad = EK,0Y(EK,0) ≈ 3.0 MeV I energy lost to ionisation per charged particle: Ecol = EK,0 [1 − Y(EK,0)] ≈ 7.0 MeV Radiation Physics Lecture 5 Radiation Yield and Radiative Fraction Interactions of Charged Particles with Matter I Y(EK,0) = radiation yield = fraction of initial kinetic Radiation Yield energy EK,0 of an electron (or positron) lost to Bremsstrahlung Targets Thin Targets radiative (bremsstrahlung) losses Thick Targets Restricted Stopping Power Straggling and Scattering I g¯ = radiative fraction = average fraction of energy Electron Range Dose transferred to light charged particles by photons that Linear Energy Transfer is subsequently lost to radiation (predominantly bremsstrahlung); c.f. µ µ ab = tr (1 − g¯) ρ ρ I photon interactions produce electrons (and positrons) with a spectrum of kinetic energies EK,i ⇒ g¯ = average value of Y(EK,i) for all light charged particles produced by photon interactions Radiation Physics Lecture 5 Bremsstrahlung Targets Interactions of Charged Particles with Matter I monoenergetic electron beams incident on solid Radiation Yield Bremsstrahlung Targets target material commonly used to generate Thin Targets Thick Targets (bremsstrahlung) radiation beams Restricted Stopping Power Straggling and Scattering Electron Range Dose Linear Energy Transfer Radiation Physics Lecture 5 Thin Targets Interactions of Charged Particles with Matter Radiation Yield Bremsstrahlung Targets thin X-ray targets – thickness ∆x R sufficiently Thin Targets I Thick Targets small such that incident electrons experience Restricted Stopping Power Straggling and Scattering I no ionisation losses Electron Range Dose I no elastic collisions Linear Energy Transfer I only one bremsstrahlung interaction I total energy radiated: dE (E ) = ρN ∆x S = N ∆x − rad rad tot e rad e dx where Ne = no. of incident electrons Radiation Physics Lecture 5 I intensity spectrum, IE (where E = hν = ~ω), obtained Interactions of by taking Fourier transform of classical Larmor Charged Particles with Matter formula (c.f. Lec. 1) for electromagnetic power Radiation Yield −2 Bremsstrahlung Targets I → dI(b)/dω ∝ b ⇒ more photons emitted for Thin Targets small-b interactions of monoenergetic electrons Thick Targets Restricted Stopping Power I integrate over all impact parameters: Straggling and Scattering R Electron Range IE ∝ (dI(b)/dω) bdb ∝ ln(bmax/bmin) → approx. Dose Linear Energy Transfer independent of E = hν ⇒ thin-target bremsstrahlung spectrum is approximately flat up to a cut-off hνmax = EK,0 I also consistent with Bethe-Heitler quantum mechanical differential cross-section, which predicts Iω ∝ hω dσrad ∝ Brad(ω) where Brad(ω) is almost independent of ω R 1 n.b. Brad = 0 Brad d(hω/EK,0) Radiation Physics Lecture 5 Thick Targets Interactions of Charged Particles with Matter Radiation Yield ∆x ∼ R such that Bremsstrahlung Targets I Thin Targets I no incident electrons can traverse the medium Thick Targets Restricted Stopping Power I attenuation of bremsstrahlung photons is minimised Straggling and Scattering Electron Range Dose I intensity spectrum is a superposition of multiple Linear Energy Transfer thin-target spectra for different EK,i, since incident monoenergetic electrons gradually lose energy through multiple collisions IE = CZ (EK,0 − hν) Kramer’s spectrum (4) where C = constant and EK,0 = initial kinetic energy of electrons incident on thick target Radiation Physics Lecture 5 I filtration of resulting X-ray beam through attenuators Interactions of preferentially removes low enegy photons and Charged Particles with Matter hardens the spectrum; used for clinical applications Radiation Yield Bremsstrahlung Targets Thin Targets Thick Targets Restricted Stopping Power Straggling and Scattering Electron Range Dose Linear Energy Transfer Typical bremsstrahlung spectra produced by 100 keV electrons striking a target: 1. thin target; 2. thick target (unfiltered) showing superposition of multiple thin target spectra; 3. thick target, with resulting beam filtered by an X-ray tube window; 4. thick target with additional filtration. In general, spectra should also include characteristic emission from the target and filters. (Fig. 6.19 Podgorsak) Radiation Physics Lecture 5 2 I for EK,0 mec , Interactions of Charged Particles with Matter 2 2 NA 2 2 NA Radiation Yield Srad = αre Z Brad(EK,0 + mec ) ∝ Z Brad Bremsstrahlung Targets A A Thin Targets Thick Targets Restricted Stopping Power ⇒ energy radiated: Straggling and Scattering Electron Range Dose Z EK,0 Z EK,0 Linear Energy Transfer Srad(E) dE Erad = dE ≈ Srad 0 Stot(E) 0 Stot(E) and Stot ≈ Scol ∝ ZNA/A ⇒ Erad ∝ Z ⇒ production of kilovoltage X-ray beams determined by high-Z targets, but independent of initial electron energy Radiation Physics Lecture 5 Interactions of Charged Particles with Matter Radiation Yield 2 Bremsstrahlung Targets I for EK,0 mec , Thin Targets Thick Targets Restricted Stopping Power Srad Srad EK,0 Straggling and Scattering = = Electron Range Dose Stot (Scol + Srad) (n/Z + EK,0) Linear Energy Transfer where n = n(Z, EK,0) is a weak function of Z and EK,0 ⇒ production of megavoltage X-ray beams largely independent of target Z, but more efficient for higher initial electron energies Radiation Physics Lecture 5 radiation pattern Interactions of Charged Particles with Matter Radiation Yield Bremsstrahlung Targets Thin Targets Thick Targets Restricted Stopping Power Straggling and Scattering Electron Range Dose Linear Energy Transfer 2 ◦ I for EK mec , most radiation emerges at θmax ≈ 90 (dipole pattern) 2 ◦ I for EK mec , most radiation emerges at θmax ' 0 (forward beaming) Radiation Physics Lecture 5 Interactions of Charged Particles This is why X-ray tubes, which produce kilovoltage with Matter Radiation Yield X-rays, have an exit window positioned at an angle to the Bremsstrahlung Targets Thin Targets target, while medical linacs, which produce megavoltage Thick Targets Restricted Stopping Power X-rays, have an X-ray window placed on the other side of Straggling and Scattering Electron Range the target: Dose Linear Energy Transfer Radiation Physics