Paolo Fornasini Department of Physics University of Trento Italy

Transcription

1 Paolo Fornasini Department of Physics University of Trento Italy

2

3 Mechanisms of X-ray production

4 X-rays are electromagnetic radiation Superposition of sinusoidal waves λ Electric field Magnetic field c = m/s X-rays λ Å ν Hz E kev

5 Two mechanisms of production of electromagnetic radiation 1. Emission from accelerated electric charges a 2. Emission as effect of quantum transitions

6 Non-accelerated charges Charge at rest Constant velocity E E B P t' t No power is emitted as electromagnetic radiation B E t

7 Accelerated charge: a tutorial example (a) a Charge at rest Short acceleration Constant velocity static E field B E static E field v=0 v acceleration

8 Accelerated charge: a tutorial example (b) a E B Acceleration acceleration Perturbation of static fields Electro-magnetic field Propagating with velocity Carrying energy c = m/s

9 Dipole approximation charge velocity: v << c charge size: d << λ observer distance: r >> λ a a E B Power flux E r,t ( ) = q B r,t ( ) = ˆ a ( t' ) 4πε 0 rc 2 r E r,t c ( ) a acceleration

10 Dipole approximation: radiated power The emitted power is: Zero in the direction of acceleration Maximum in the perpendicular plane a Angular emission profiles Linear motion Circular motion θ accel. acceleration θ

11 Examples Oscillating motion Average linear deceleration a Broadcasting antenna Relativistic circular motion a e - v Bremsstrahlung in X-ray tubes Synchrotron Radiation No dipole approximation Relativistic treatment necessary

12 Quantum transitions E p (ev) Copper E HIGH ω = E HIGH E LOW E LOW Atomic X-ray transitions ω kev

13 Characteristic lines 3s 3p 1/2 3p 3/2 3d 3/2 3d 5/2 M M 2 M 3 M 4 M 5 Transitions and X-ray lines 2s 2p 1/2 2p 3/2 L 1 L 2 L 3 K L 3 K L 2 Kα 1 Kα 2 Kα K M 3 K M 2 Kβ 1 Kβ 3 Kβ 1s K (Electric-dipole allowed transitions)

14 Laboratory X-ray sources

15 X-ray tubes Crookes tube, until 1920 Vacuum tube Anode Pt anode X-rays Cold Al cathode H.V. X rays Hot cathode Coolidge's tube (1913) Electrons Cathode Power supply of filament

16 Present-day laboratory tubes High vacuum sealed tubes Independent control of I and V Accelerating voltage < 100 kv Different anode metals: Cr, Cu, Mo, W,... Power: 1-4 kw ~ 1 % X-ray production ~99 % anode heating water cooling

17 X-ray emission Un-polarized X-rays Divergent beam Collimating slits

18 Emission spectrum Ag anode Characteristic lines Characteristic lines Ag anode Intensity Bremsstrahlung Bremsstrahlung E (kev) λ (Å) λ [Å] = 12.4 E [kev]

19 Continuous bremsstrahlung spectrum Electrons accelerating voltage: Maximum energy (minimum λ) Total intensity

20 Characteristic lines Moseley law λ 1 Z 2 Cr Cu Mo Kα Kα 1 Kα Kβ

21 Filters Mo emission spectrum Zr absorption coefficient Mo filtered spectrum

22 Rotating-anode tubes Snapshot emission: no liquid cooling Power ratings up to 100 kw Anode rotated by electromagnetic induction Almost all medical tubes are rotating anode tubes (exception: dental tubes)

23 Liquid cooled rotating-anode sources Power ratings kw For non-snapshot applications: diffraction, tomography, etc.

24 Synchrotron Radiation

25 Synchrotron radiation Electromagnetic radiation emitted by centripetally accelerated electrons moving at relativistic speed Storage rings Relative velocity β = v c 1 Electron energy A key parameter W 1 10 GeV γ = ( 1 v 2 /c 2 ) 1/ 2 = W /m 0 c

26 Storage rings as S.R. sources ID BM BM ID ID BM RF BM Basic components BM = bending magnets ID = insertion devices RF = radiofrequency cavity Synchrotron Radiation from: Bending magnets Insertion devices... - wigglers - undulators

27 Bending magnets and insertion devices Bending magnet Insertion device e -

28 S.R. Facilities - map

29 S.R. Facilities Name Site Year E (GeV) SPring8 Super Photon ring 8 GeV Hyogo (Japan) Large APS Advanced Photon Source Argonne, IL (USA) ESRF European S. R. Facility Grenoble (France) Name Site Year E (GeV) PETRA III Hamburg (D) DORIS III Hamburg (D) Europe Diamond Didcot (UK) Soleil S.Aubin (F) Elettra Trieste (I) ALBA Barcelona (E) SLS Villigen (CH)

30 E.S.R.F = European Synchrotron Radiation Facility Electron energy W = 6 GeV 300 m γ = Beamlines Diameter 300 m 32 bending magnets 32 straight sections 15 BM beamlines 32 ID beamlines

31 S. R. from bending magnets

32 Properties of Synchrotron Radiation Collimation I Θ 1/γ rad Photon energy High intensity continuous spectrum I E Polarisation Time structure time

33 S.R. angular distribution (a) v << c v a Classical dipole emission pattern v a v c a Top view v Perspective a v Relativistic emission pattern θ 1/γ

34 S.R. angular distribution (b) Instantaneous emission from one electron Electron beam in bending magnet v a θ 1/γ θ v 1/γ ESRF: W = 6 GeV γ = W m 0 c θ 1 γ 10 4 rad 0.005

35 Relativistic Doppler effect source v detector v = approaching velocity (detector.vs. source) ω s c ω d c = electrom. wave velocity (indep. of reference) Lorentz-invariance kx ωt = k' x' ω't' ω d / ω s Frequency (energy) shift ω d = ω s 1+ v /c 1 v /c = ω s γ 1+ v /c ( ) 1 departing approaching β = v/c

36 S.R. spectral properties (a) t' 1 t' 2 t 1,t 2 Point observer R 1/γ Δt = t 2 t 1 Δt'= t' 2 t' 1 emission time detection time Frequency domain Time domain Short time pulse High frequencies t Δt 4 R 3 cγ 3 ω c 3cγ 3 2R Broad spectrum ω c ω

37 S.R. spectral properties (b) Single emission from circular arc Periodic emission from a circular trajectory Time time time Frequency ω c ω rev ω c

38 S.R. intensity t' 1 t' 2 t 1,t 2 Point observer R 1/γ Δt = t 2 t 1 Δt'= t' 2 t' 1 emission time detection time Δt Δt' ( 1 v /c) Time compression Enhancement of intensity

39 S.R. emission spectra Photons/s/mrad/ 0.1% Δλ/λ F 1 = S.R. universal curve Flux = I γ F I=100 ma, bending magnets Flux (photons / sec / mrad / 0.1% bw) ESRF (E =19.2 kev) c DCI (E = 3.62 kev) c ω/ω c Photon energy (kev)

40 S.R. polarization σ - Horizontal component (in the orbit plane) π - The vertical component: increases with angle decreases with photon energy ± π 2 dephasing Elliptical polarisation SURF MeV γ = 760 Vertical divergence ψ 1 γ for E = E c

41 S.R. time structure Phase-focussing in RF cavities Orbits RF R.F. voltage low-e e - reference e - high-e e - time v c ; ρ = m 0c eb γ time ESRF 20 ps 2.81 µs (1 bunch) 2.82 ns (992 bunches) Bunched structure: - of electron beam - of S.R. emission

42 e ± beam lifetime Collisions with residual gas (photon-stimulated desorption) Occasional large energy losses through S.R. emission Non-linear resonances (anharmonic betatron oscillations) Toushek effect (e-e scattering inside each bunch) τ = I ( t ) di /dt I( t) = I 0 exp[ t /τ] ESRF

43 S. R. from insertion devices

44 Alternating magnetic fields z λ u = period length N S N S x S N S N s g = gap Vertical magnetic field B z (s) = B 0 ( ) cos ( k s u ) = cosh πg/λ u ( ) B cos k u s Gap-period relation ~ B/B0 1 k u = 2π λ u g/λ u

45 Magnetic field effects z B z λ u x s Oscillating vertical magnetic field F = e v B α 0 x s Transverse beam oscillation α 0 = K 1 γ Wiggler/undulator parameter K = ebλ u 2πcm e

46 The K parameter W/U properties SR divergence α 0 = K 1 γ K = ebλ u = B[ T] λ u [ cm] 2πcm e K >1, α 0 > 1 γ High-K devices WIGGLERS K 1, α 0 1 γ Low-K devices UNDULATORS

47 Undulator: interference effect time t 1 λ time t 2 λ u Constructive interference for λ λ u 1+ K 2 2γ γ 2 θ 2

48 Properties of undulator radiation (a) gap λ u mm λ λ u 1+ K 2 2γ γ 2 θ 2 Large N K<1 Interference (monochromatic radiation) tunability: gap B K Angular red-shift

49 Properties of undulator radiation (b) Interference Flux N 2 (in forward direction) N = number of wiggles Electron motion not perfectly sinusoidal higher order harmonics ω 1 4πcγ 2 /λ u 1+ K 2 /2 + γ 2 θ 2 ω n = nω 1 Finite wave-train of radiation emitted by each electron bandwidth ( ) Δω n γ 2 δ θ 2 ω n 1+ K 2 /2 Δω n ω n 1 nn

50 Low-K.vs. high-k devices Low-K Coherent superposition Interference λ λ u 1+ K 2 2γ γ 2 θ 2 Increasing K: λ increases relevance of harmonics interference effects reduced broader spectrum High-K Inoherent superposition Continuous spectrum

51 Undulators.vs. bending magnets (a) Undulator Bending magnet, wiggler θ 1/γ θ v 1/γ Vertical and horizontal collimation Vertical collimation

52 Undulators.vs. bending magnets (b) Flux Undulator Undulator Strong emission at discrete energies (fundamental + harmonics) Tunability by varying the gap Bending magnet Bending magnet, wiggler Photon energy Emission over a continuous spectrum

53 Brilliance of S.R.sources

54 Photon beam properties e-beam size σ x,y ( s) e-beam divergence σ x,y ( s) SR divergence + + = θ 1/γ Photon beam properties ESRF Even I.D. Odd I.D. Horizontal Vertical σ x σ x σ y σ y [ µm] [ µrad] µm [ ] [ µrad] S.R. divergence θ 1/γ 100 µrad

55 Photon beam parameters Brilliance photons s mm 2 mrad 2 bandwidth source size solid angle 0.1% Δλ /λ Integrating over source size + Integrating over vert. angle + Integrating over horiz. angle + Integrating over bandwidth Brightness Spectral flux Total flux photons s mrad 2 bandwidth photons s mrad bandwidth photons s bandwidth photons s

56 Brilliance: comparisons photons s mm 2 mrad 2 bandwidth ESRF Cu K Mo K C K Bremsstrahlung Photon energy (kev)

57 Brilliance: time evolution photons s mm 2 mrad 2 bandwidth

58 Neutron sources

59 Neutron production Radioactive sources Neutrons from nuclear reactors Neutrons from pulsed accelerators - photofission - spallation Most effective for solid state research: Fission (reactors) Spallation (accelerators) n p + p + n n

60 Fission 235 U + n neutron capture thermal neutron kt 25 mev [ 236 U] * radiative capt. fission U + γ Energy ( 200 MeV) X + Y n ( 2 MeV) Moderator 2 MeV 25 mev 1 neutron chain reaction 1.7 neutrons available

61 Spallation Proton accelerator 1 GeV proton interaction with nucleons high-energy particles chain-reactions excitations of nuclei de-excitation (evapor.) neutrons ( 55 MeV) Concentrated source high flux Pulsed source

62 Neutron sources year

63 Largest European Neutron Labs ILL Grenoble, F ESRF(SR) ISIS, Didcot, UK Diamond (SR)

64 ILL reactor source

65 ISIS spallation source

66 Energy of neutrons Moderation: Neutrons are slowed down in moderators, where they are brought to thermal equilibrium through inelastic collisions with light atoms (H, D, Be) The Table refers to the peak values of the Maxwell equilibrium distribution. Ultra-cold Cold Thermal Hot Epi-thermal Energy (mev) Temperature (K) Wavelength (Å) Velocity (m/s)

67 Energy distribution of neutrons K 300K Reactor sources Relative neutron flux K 290K 2000K Spallation sources CONTINUOUS PRODUCTION Energy selection by crystal monochromators (Bragg law) Higher energies available PULSED PRODUCTION Energy selection by time-of-flight techniques Energy (mev)

68 Neutrons and X-rays properties (b) Thermal neutrons X-rays (synchrotron) X-rays (anodes) Energy (ev) 10-1 ev 10 4 ev 10 4 ev Wavelength (Å) Flux (part./cm 2 /s) Sample volume (mm 3 ) Tunability yes yes no Beam divergence 5 mr 10-1 mr 5 mr Δλ/λ Absorption weak medium medium