2. X-ray Sources 2.1 Electron Impact X-ray Sources - Types of X-ray Source - Bremsstrahlung Emission - Characteristic Emission

Transcription

1 . X-ray Sources.1 Electron Impact X-ray Sources - Types of X-ray Source - Bremsstrahlung Emission - Characteristic Emission. Synchrotron Radiation Sources - Introduction - Characteristics of Bending Magnet Radiation - Characteristics of Undulator Radiation - Undulator Radiation: Undulator Equation, Harmonics, and Radiation Power - Characteristics Wiggler Radiation

2 .1 Electron Impact X-ray Sources Types of X-ray Source Gas-filled tube HV: 30-40kV 4 Gas pressure: ~ 10 torr Anode: Metal Cathode: shaped to focus electrons Modern X-ray tubes: William D. Coolidge(1913) HV: 30-40kV 6 Gas pressure: ~ 10 torr Anode: Metal Cathode: heated filament

3 .1 Electron Impact X-ray Sources Since more than 99% of incident electron beam power is dissipated by heat, the removal of heat without melting or distorting the anode is main consideration to design X-ray tubes.. Most of tubes is operating at up to 1000kV and 3kW. Operating voltage and power are decided by the variety of target metal, electron beam energy density, etc.

4 .1 Electron Impact X-ray Sources X-ray tube for Diffractometer Water Electron irradiated Area: 1mm x 10mm

5 .1 Electron Impact X-ray Sources X-ray tube for Spectroscopy - Forward emission - Characteristic X-ray; change of target metals X-ray tube for Microfocus: -~10μm diameter electron spot - low power high voltage (air cooling) Rotating anode type X-ray tube - power dissipation can be increased by rapidly rotating cooled anode Rigaku: 18kW, 60kW x-ray generator.

6 .1 Electron Impact X-ray Sources X-ray source size; Line focus X-ray source: 0.1mm x 10mm at take off angle ~6 degree - ideal for use with powder diffractometer Point focus X-ray source: 1mm x 1mm at take off angle ~6 degree - ideal for use with single crystal diffractometer

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8 .1 Electron Impact X-ray Sources Bremsstrahlung Emission (from the German bremsen, to brake and Strahlung, radiation, thus, "braking radiation" or "deceleration radiation"), is electromagnetic radiation produced by the acceleration of a charged particle, such as an electron, when deflected by another charged particle, such as an atomic nucleus. Strictly speaking, bremsstrahlung refers to any radiation due to the acceleration of a charged particle, which includes synchrotron radiation; however, it is frequently used (even when not speaking German) in the more literal and narrow sense of radiation from electrons stopping in matter. When the accelerated electrons stop at metal target, the decelerated electrons radiate electron magnetic wave. sin Θ (a) The radiation pattern. (b) 3-D toroidal appearance

9 .1 Electron Impact X-ray Sources E field of the irradiated waves can be obtained from the solution of wave equation. The detailed derivation is beyond this class. Let s use the derivation for electrons, then the electric field associated with the radiated wave becomes; easin Θ ε 0 E( r, t) and H( r, t) k 0 4πε c r μ 0 0 x E( r, t) Radiation power, Poynting vector; S e a sin Θ r, t ) E( r, t) H( r, t) k, where S 3 16π ε c r ( 0 0 I The power per unit solid angle is obtained by noting that, so that da r dω S ( dp / da) k 0, and dp dω e a sin 0 16π ε c 3 Θ

10 .1 Electron Impact X-ray Sources Total power irradiated by an oscillating electron of acceleration a P 8π e a 3 16π ε 0c 3 In relativistic case (Lorentz contraction and relativistic Doppler shift) I e a sin Θ ( 1 β cos ) 6 16π ε 3 0c r Θ where, βv/c; v is the velocity and c is the speed of light in vacuum. Undulator radiation

11 .1 Electron Impact X-ray Sources Total intensity of the whole radiation is integration over the retardation period, I tot 0 e a 1 sin Idt 1 v0 64π ε 0c r β cos Θ 4 ( 1 cosθ) Θ This derivation assumed that, for all electrons, the deceleration is along their initial direction. Many scientists calculated proper radiation model. Kramers (193) s model for frequency distribution; I ν dν where ( 4πε ) I ν v N 1 is is 0 3 the the na, 3π Z 3 3c int ensity speed A is 3 m e e 6 v of the N dν per the unit incident # of atoms frequency electrons per unit area n is the # of electrons/ sec /area

12 .1 Electron Impact X-ray Sources For ν < ν ν max, Iν I0 and for ν > ν max, I This case is a prediction for single collisions, but multiple collision can be derived. The result of intensity is I ν CZ 0. λ λ min ( ν ) max ν or Iλ Cc Z 3 λ λmin Intensitis as functions of λ for thick tungsten target

13 .1 Electron Impact X-ray Sources The total intensity I can be found by integrating over the whole frequency range, I CZ ν 0 max ( ν ν) max dν CZ where ev is the accelerating voltage ν max CZ ev h The wavelength of maximum emission λ m 3 λ min The efficiency ε of X-ray production ε X ray power Electron beam power ZV ( less than CZ 1%) ev h 1 nev

14 .1 Electron Impact X-ray Sources Characteristic Emission:

15 .1 Electron Impact X-ray Sources Characteristic Emission: The hole in an atomic core level due to electron impact has the same quantum state such as spin(s), angular momentum(l), and total angular momentum(j) Labbel nl j where n the principal quantum # l 0, j l + s, 3,... ( n 1)

16 .1 Electron Impact X-ray Sources Energy level diagram

17 .1 Electron Impact X-ray Sources Characteristic emission lines, falling from a higher filled state into the core hole in an outer shell. Principal transitions are governed by the dipole section rules; Δl ± 1 Δj 0, ± 1 but j 0 j 0 ( forbidden) Nomencultures K K K abs. edge, α α 1,, K K β α,...,,..., L abs. edge, L L α α, 1, L β L, α...,...

18 .1 Electron Impact X-ray Sources The sum of the intensities of all lines a multiplet which belong to the same initial or final state is proportional to the statistical weight ratio of j+1 of the initial or final state respectively. For Kα1 and Kα, j13/ and j1/ and thus the intensity ratio; I α / I ( j1 + 1) /( j + 1) 1 α For triplet Lα, L, 1 α and L β comparing the α1, α pair, which originates 1 from the LIII, with the β1 line, form LII, ( I + I ) α 1 I β 1 α ( I + I ) 1 The pair α, β1 has final state MIV whilst that the α1 line has the final state MV and thus α 1 I α β 3

19 .1 Electron Impact X-ray Sources From these two equations, I α : I : 1 α I β 1 9 :1: 5

20 .1 Electron Impact X-ray Sources Absolute Intensities of characteristic X-rays; Empirical relationship I where ( V V ) V K K 1.7 is the energy required to produce a hole Line widths of characteristic X-rays; quantum mechanical calculations ΔE h ( 4 A + BZ ) where A, B are cons tan t, ans Z atomic number.

21 .1 Electron Impact X-ray Sources Fluorescence Yield; Once a hole state has been formed it can relax by i) X-ray fluorescence or ii) Auger electron emission. For a K hole the fluorescence yield ωk is defined as the ratio; ω K Intensity of K x - ray photons Intensity of K x - ray photons + Auger electrons The probability of radiative decay is proportional to 4 Z, but the probability of Auger electron emission is a constant independent of Z, i.e. ω K 4 Z Z 4 + a a where, for K-shell emission,. Thus for low Z elements x-ray fluorescence will be week due to competition from the Auger process. 6

22 . Synchrotron Radiation Sources Advance Light Source(ALS) Beam lines I. Bending Magnet II. Undulator III. Wiggler

23 . Synchrotron Radiation Sources Structure of Synchrotron I. Injection system - Linear accelerator + Booster ring (ALS, APS, Spring-8 etc) - Linear accelerator (PLS, Photon factory) II. Storage Ring III. Beam Lines Electron injection RF Cavity Bending magnet Storage Ring Undulator Or Wiggler Structure of undulator

24 1. Synchrotron Accelerator Components of Synchrotron Accelerator Linac Accelerator Tunnel Energy Doubler Storage ring Quadrupole of PAL

25 1. Synchrotron Accelerator Beamline Designs X-ray Microprobe Beamline High-Resolution Powder Diffraction Beamline

26 . Synchrotron Radiation Sources Bending Magnet Radiation occurs when a relativistic electron travels in a uniform magnetic field, executing a circular motion with acceleration directed toward the center. The radiation is directed tangentially outward in a narrow radiation cone, giving the appearance of sweeping searchlight. The radiation spectrum is very broad, analogous to a white light x-ray light bulb. The emission angle is typically 1/ γ, where γ Lorentz contraction factor. v electron γ 1/ 1 c Bending Magnet Radiation

27 . Synchrotron Radiation Sources Undulator Radiation is generated as highly relativistic electron travels a periodic magnetic field. In the undulator limit, the magnetic field is relatively weak and resultant angular excursions of electron are smaller than the angular width of natural radiation cone, 1/ γ, normally associated with synchrotron radiation. The frequency spread of undulator radiation can be very narrow, and the radiation can be extremely bright and partially coherent, under certain circumstances. The characteristic emission angle is narrowed by a factor 1/ N, where N is the number of magnetic periods. Typically N is of order 100. Depending on the magnet strength, harmonic radiation may be generated. Undulator Radiation

28 . Synchrotron Radiation Sources Wiggler Radiation is generated from periodic magnetic structure, but in the strong magnetic field limit where in at least one plane the angle excursions are significantly greater than the natural(1/γ) radiation cone. Because accelerations are stronger in this limit, the radiation generated peaks at higher photon energies and is more abundant (high photon flux and more power is radiated, wiggler radiation is less bright because of the substantially increased radiation cone. Wiggler Radiation

29 . Synchrotron Radiation Sources Comparison of X-ray Photons; Intensity(Log scale) λ(linear scale)

30 . Synchrotron Radiation Sources Comparison of Old Synchrotron and Modern Synchrotron Early synchrotron radiation facilities were basically circular rings for bending magnet radiation. Modern storage rings are dedicated to broad scientific use and optimized for high spectral brightness through the inclusion of many long straight sections for undulators and wigglers as well as tightly confined electron beams.