Electromagnetic Radiation, especially X-rays

1. This presentation will probably involve audience discussion, which will create action items. Use PowerPoint to keep track of these action items during your presentation • In Slide Show, click on the right mouse button • Select “Meeting Minder” • Select the “Action Items” tab • Type in action items as they come up • Click OK to dismiss this box This will automatically create an Action Item slide at the end of your presentation with your points entered. Electromagnetic Radiation, especially X-rays Biology 555 Andrew J. Howard Based in part on notes from T.C. Irving and T.I. Morrison EM radiation, esp. X-rays

2. Electromagnetic Radiation • How do twenty-first-century scientists think about electromagnetic radiation? • The simplest articulation is that of the wave-particle duality: • Light (and other ranges of EM radiation) has both wave-like and particle-like properties • We’ll consider the two sets of properties in turn EM radiation, esp. X-rays

3. Why does this matter? • Many of the techniques we have discussed this semester involve interactions between biological macromolecules and electromagnetic radiation • Often the EM radiation we’ll be using is in the X-ray regime, so we’ll pay special attention to that range of energies or wavelengths EM radiation, esp. X-rays

4. Particle-like properties • We can view light as being composed of discrete packets of energy that we call photons • Photons have zero rest mass, and their velocity in vacuum is c • Their momenta are calculable:p = E/c = h/c EM radiation, esp. X-rays

5. Wavelike properties • When these packets of electromagnetic radiation interact in certain ways with matter and with one another, we observe wavelike phenomena like diffraction and refraction • These properties were known to seventeenth-century physicists, but they were given a mathematical footing in the nineteenth century EM radiation, esp. X-rays

6. The electromagnetic spectrum EM radiation, esp. X-rays

7. Collisions • When EM radiation interacts in other ways with matter, we see scattering phenomena that we can best understand if we view its particle-like nature • EM radiation can transfer momentum to particles of matter in collisions or Compton scattering EM radiation, esp. X-rays

8. Somewhat more exotic phenomena… • Twentieth century physics includes experiments in which a photon or a pair of photons can produce a matter-antimatter pair, e.g. an electron and a positron. e- e+ EM radiation, esp. X-rays

9. Absorption of photons • When photons are absorbed in matter, some or all of the photon energy is transmitted to an electron and potentially to the rest of the atoms in the system. EM radiation, esp. X-rays

10. 3 major forms of absorption • Photoelectric effect: light comes in, electron is liberated from atoms • Compton scattering: photon enters, scatters off an electron (either free or bound) • Pair production (see previous slide) + e- + e- + e- EM radiation, esp. X-rays

11. Which one happens when? • Pair production requires that the incoming photon have at least as much energy as the rest energy of the positron and the electron, i.e., at least 1.022 MeV • At various energies, various processes predominate to differing degrees; it also depends on the kinds of atoms that the photons are interacting with. EM radiation, esp. X-rays

12. Compton Scattering 1. Energy conservation 2. Momentum conservation in x 3. Momentum conservation in y Energy conservation:Ee-,rest + Eg,in = Eg,out + Ee-,out Momentum conservation in x and y: EM radiation, esp. X-rays

13. Compton scattering: equations EM radiation, esp. X-rays

14. Compton scattering: results • And thereforehn’ = hn / {1 + a (1 – cosq)} EM radiation, esp. X-rays

15. Attenuation of EM radiation • Traditionally defined by saying that the fraction lost per unit distance is proportional to the distance traveled through the medium: • dI/I = -µdxwhere µ is the linear attenuation coefficient. • Solving this differential equationwith I = I0 at x = 0 gives I(x) = I0exp(-µx) • So we have derived exponential decay! EM radiation, esp. X-rays

16. Practical uses of X rays • Remember that X-rays are simply electromagnetic radiation in the 1-100 KeV range (corresponds to roughly 0.01 nm - 1 nm) • We have traditionally used them for: • Radiography • X-ray scattering and diffraction • X-ray spectroscopy EM radiation, esp. X-rays

17. Emerging uses • X-ray microscopy • X-ray phase contrast imaging • Diffraction-enhanced imaging (developed significantly at IIT) EM radiation, esp. X-rays

18. How to make X-rays • Traditional method (goes back to Wilhelm Röntgen, 1895) employs a “reverse Compton effect”:a fast electron collides with a metal target, changing the momentum of the electron and thereby liberating a photon from it. photons e- target Filament(voltage ~ kV) EM radiation, esp. X-rays

19. Wavelengths and energies • Typical reverse-Compton wavelengths range from 0.01 nm to 10 nm; • Above 1 nm these are ultraviolet;below that they’re X-rays • RememberE = hc/ ~ 12.398 / if E in keV and  in Ångström, orE = 1.2398 /  if  in nm EM radiation, esp. X-rays

20. Two ways to make EM from electrons • Bremsstrahlung (braking) radiation:Maxwell’s equations say that any charged particle that changes momentum (speed or direction) must radiate, even if it’s just bending or slowing a little • Characteristic radiation:electron interacts with atom, causing a bound electron to be promoted to a higher energy level. As it falls back to a lower level, it emits a photon with a very specific energy. EM radiation, esp. X-rays

21. How does characteristic radiation work? • An electron is promoted from a K or L shell into a higher shell • After a brief interval it decays back to the shell it starts in • As it does so it emits a photon whose energy is exactly the difference between the energies of the two energy levels h e- EM radiation, esp. X-rays

22. Characteristic X-ray Emission Lines:Atomic Energy Level Transitions http://xdb.lbl.gov/Section1/Sec_1-2.html EM radiation, esp. X-rays

23. Energetics of characteristic radiation • Most common transitions are kl, km • kl : (K) = hc/El- hc/Ek • km : (K) = hc/Em- hc/ Ek • Copper K has  = 1.5418Å; energy is about 8 keV • Molybdenum is ~ 0.71Å, 15.7 keV • These are popular because these metals are fairly easy to cool with water EM radiation, esp. X-rays

24. How X-rays are produced But it isn’t quite this simple. EM radiation, esp. X-rays

25. An ideal X-ray source • The source should be: • Intense • Spatially small • Non-dispersive • Monochromatic (for most applications) EM radiation, esp. X-rays

26. Intensity • More photons on the sample allow for shorter data acquisition times and might help cut down on radiation damage per unit information • But! X-ray production from target metals is inefficient • Total input power = acclerating potential * input beam current • 99% of input power goes into heat EM radiation, esp. X-rays

27. Wait! It gets worse! • X-rays are produced nearly isotropically from conventional sources, for which the electrons are nonrelativisitic: relatively few go in the direction you want them to go. Electron beam Your experiment EM radiation, esp. X-rays

28. How bad is it? An example: 3 kW X-ray source 1.54 Å radiation (8.05 keV) 107 photons/sec (107 *8.05 *103 *1.6 *10-19)/(3*103) ~ 0realistic efficiency: 4* 10-12. EM radiation, esp. X-rays

29. Power supplies Virtually always the anode floatsat 20-80KV; the cathode is grounded or held at a small bias EM radiation, esp. X-rays

30. Traditional rotating anodes This has typically meant big, heavy supplies with big, heavy transformers(e.g., 18kW = 60 kV * 300 mA) http://www.rigaku.com/protein/ruh3r.html EM radiation, esp. X-rays

31. Compact, high-brilliance sources • Net power lower but comparable number of photons on sample http://www.voltronics.com/products/index.html EM radiation, esp. X-rays

32. How to cool the target • Spread the electron beam out • Shape the target: • so the beam comes off at a glancing angle: • Projected source is: Actual source x sin(takeoff angle) • Active cooling:Water flows through and past metal target • Move electron beam along the target(or move the target along the beam):The rotating anode EM radiation, esp. X-rays

33. We usually want monochromatic radiation • We can use diffraction from a highly ordered crystal to select out a single angle and therefore a single wavelength, to within the acceptance of the crystal • Graphite traditionally used with conventional sources • Silicon or germanium more common with storage ring sources • Or we can filter out unwanted wavelengths with an absorber that preferentially absorbs away from the primary energy(Z = Ztarget-1) EM radiation, esp. X-rays

34. Can we focus X-rays? • Yes, but: • X-ray lenses per se are difficult because the refractive index of most materials is extremely close to 1 for high energies • But there are ways to use total internal reflection to get the same effect • We can also use diffraction to accomplish focusing EM radiation, esp. X-rays

35. What do X-rays do to biological samples? • Three things can happen to a forward pass: two of them are bad. -Bart Starr • Similarly, Xrays can: • Go through the sample unaffected • Get scattered or diffracted • Get absorbed • Absorption leads to sample damage • Two kinds of damage: • Direct: photon displaces atom in the polymer • Indirect: photon produces free radicals that diffuse to the polymer and mess it up EM radiation, esp. X-rays

36. How can we mitigate damage? • Not much you can do about direct damage: it’s zeroth-order • Free radical scavengers (ascorbate, glutathione): occasionally work • Cooling! • 110K reduces radical mobility enough that the polymer survives • Good & bad: atoms don’t move as much, but cooling itself causes some disorder, and the experiment is less representative of biological system • Cryoprotection techniques thoroughly developed; Cryocrystallography and CryoEM trade ideas with one another. EM radiation, esp. X-rays

37. Special Relativity • Einstein modified galilean relativity, under which velocities are additive. • Galileo: automobile velocity with respect to ground = u =v + w • Einstein says: u < c so we need new rules! EM radiation, esp. X-rays

38. Special Relativity: Energy • Einstein’s new rules require that time & distance formulae depend on velocity • Corrections are significant in nuclear reactions, radiation scattering, and accelerators, so we study them here a little • They also give riseto the concept of relativistic energy Hendrick Lorentz EM radiation, esp. X-rays

39. Rest energy and mass • If v = 0, E = E0= m0c2; this is rest energyif m0 is the rest mass, i.e. the mass as it is ordinarily defined. • We can summarize the results by defining a relativistic mass m so that we can sayE = mc2 = gm0c2 where m = gm0 • For v = 0.1c, m = 1.05m0 for v = 0.98c, m = 5m0. • Why do we care about SR here? EM radiation travels with v = c? • Answer: because the electrons that produce it are relativistic! EM radiation, esp. X-rays

40. Atomic Structure • JJ Thomson (1897): heavy nucleus with electrons surrounding it. • Rutherford showed that the nucleus had to be very small relative to the atomic size EM radiation, esp. X-rays

41. The Bohr Model • Bohr model: quantized angular momentum so that radiation is emitted in quanta equal to difference between energy levels of the atom. Used classical energy calculations! EM radiation, esp. X-rays

42. Bohr model: radius • Quantized angular momentummvr = nh/2p • But this is associated with coulombic attraction for which the centripetal force must equal the coulombic force:F = mv2/r = kZe2/r2, so r = kZe2/mv2 • Thus v = nh/(2pmr)= 2pkZe2/nh so r = n2h2/(4p2kZe2m) • For n=Z=1,r = 0.529*10-10 m = Bohr radius EM radiation, esp. X-rays

43. Bohr model: Electron Energies • Velocity = v = 2pkZe2/(nh) • Kinetic energy = 1/2mv2 = 2p2k2Z2e4m/(n2h2) • Potential energy = -kZe2/r = -4p2k2Z2e4m/(n2h2) • Total energy = KE + PE = -2p2k2Z2e4m/(n2h2) • Photons emerge from transitions from one value of n to another. • Transition from n = 3 to n = 2 gives photon energy = -2p2k2Z2e4m / [(1/9 - 1/4) h2]= 1.89 eV EM radiation, esp. X-rays

44. DeBroglie Wave Theory • So: we’ve allowed electromagnetic radiation to behave as a wave and a particle. We can express momentum of light asP = E/c = hn/c = h/l • Can we also talk about matter behaving both as a wave and a particle? Yes. • Particles can exhibit interference effects associated with wave behavior. • Wavelength l = h/P = h / mv EM radiation, esp. X-rays

45. Nonrelativistic approximation:KE = (1/2)mv2 so l = h/(mv) = h(2(KE)m)-1/2 Further, since the angular momentum mvr is quantized (mvr = nh/(2p)), we can say 2pr = nl So we can say that the circumference of the electron’s orbit is an integer multiple of the electron’s wavelength! Standing waves! Wave Behavior in electrons EM radiation, esp. X-rays

46. Synchrotron radiation • Accelerating any charged particle will give rise to electromagnetic radiation • Accelerating electrons that are traveling at close to the speed of light produces radiation in the ultraviolet or X-ray range • A simple way to do this is to accelerate the electrons on a straight path and then squirt them into a roughly circular ring • If acceleration is roughly perpendicular to the direction of motion, we describe the resulting radiation as synchrotron radiation • Since v = c – d, SR applies to these electrons! EM radiation, esp. X-rays

47. A very brief history of synchrotron facilities • 1960-1980: Roughly-circular electron colliders enabled high-energy physics experiments in which electrons collided with each other or with positrons, producing showers of exotic particles • Synchrotron radiation was an unavoidable byproduct of these setups; researchers realized that they could capture the radiation as sources • 1980’s: Synchrotron experiments became so popular that dedicated storage-rings began to be built (SSRL, NSLS, several in Europe, Asia) • 1990’s: High-brilliance facilities containing wigglers or undulators (below) built and instrumented EM radiation, esp. X-rays

48. Curves and straight sections • In the curved sections of a storage ring, the X-rays are produced by bending the e-beam with dipole magnets so it curves along the path; this produces a “dipole” source • In the straight sections the beam can be wiggled or undulated through a series of tetrapole or hexapole magnets. If the magnet array exploits resonance between the radiation emitted from one segment and the next, we describe the source as an undulator; if not, it’s a wiggler EM radiation, esp. X-rays

49. Bandpass • Bending magnets and wigglers produce a broad spectral distribution; so if you want one wavelength, you need to select it with a monochromator • Undulators can be tuned to produce a narrow bandpass (DE/E~0.01-0.1); can be further monochromatized if necessary EM radiation, esp. X-rays

50. Time-resolved studies • Each electron requires 2pr/c ~ 3.7*10-6 sec to make a full circuit • Storage ring electrons aren’t circulating at a constant rate; there’s a time-structure to their emission (ps-scale “buckets” repeated every few ns) • We can capture X-ray photons emitted during parts of that cycle • Not enough photons for monochromatic studies, but for white-beam or pink-beam studies this time-structure can be used. EM radiation, esp. X-rays