1. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 1 Accelerator Physics Topic IX Wigglers, Undulators, and FELs Joseph Bisognano Engineering Physics & Synchrotron Radiation Center University of Wisconsin

2. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 2 Bending Magnet Radiation CERN School 1998

3. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 3 Wiggler or Undulator (Insertion Devices) CERN School 1998 More flux or higher brightness Wigglers: high field, broad spectrum Undulators: low field, interference peaked spectrum

4. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 4 Insertion Devices CERN School 1998

5. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 5 Light Source CERN School 1998

6. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 6 Ideal ID Field Pattern (infinite pole tips in x) Gap and period go hand in hand

7. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 7 Gap Dependence of Magnetic Field CERN School 1998

8. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 8 Equation of Motion of Electrons in IDs Neglecting vertical motion, we have

9. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 9 First Order Solution Since there is a B s, one can get a vertical force; i.e., focusing

10. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 10 Basic Parameters

11. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 11 Second Order Energy Conservation says that if x is moving it’s at the expense of longitudinal energy

12. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 12 In Beam Frame Beam frame coordinates t and frequency

13. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 13 Lorentz Transforms and Radiating

14. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 14

15. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 15 Photon Frequency in Lab Expect a “blue” shift since waves get pushed together as beam is moving toward observer Use fact that energy of photon is hf, momentum is hf/c

16. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 16 Undulator Spectrum Since train is of finite length (N cycles), there is a width to spectrum, but it is very narrow, order 1/N If one includes that motion is really not perfectly sinusoidal (remember the figure 8 and energy modulation) but that it does repeat in time, there is harmonic generation

17. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 17 Cern School Higher harmonics add to reach of an undulator Require care in phase errors of undulator periodic fields

18. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 18 Fundamental power/total power=1/(1+K 2 /2) 1/2 Cern School R Walker

19. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 19

20. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 20 Spontaneous Emission Note that for higher frequency, you need higher energy or shorter undulator period Shorter undulator period implies smaller gap

21. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 21 R Walker, CERN School

22. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 22 Brightness/Brilliance

23. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 23 Physics of FELs An electron beam moving on a linear trajectory will have no net energy coupling to a co-moving E&M wave, just “jiggled” In a wiggler (really undulator), an electron beam develops a transverse oscillation, as we’ve just seen If the oscillation stays in phase with the fields, there can be a net exchange of beam energy to the wave; i.e., the electron beam acts to amplify the electromagnetic wave

24. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 24 Oscillators and SASEs If one puts beam/wiggler into optical resonantor, there is a feedback loop that generates an oscillator and a laser If the wiggler is long enough, the energy modulation of the electron beam can generate “microbunches” which can radiate coherently, generation self-amplified spontaneous emission (SASE) from the Schottky noise on the beam, lasing without mirrors from a beam instability Or one can “seed” the beam with an energy modulation induced by an external laser Sources are tunable (beam energy or wiggler field) and coherent

25. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 25 Basic FEL Configuration

26. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 26 Jlab FEL

27. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 27 Spontaneous Emission

28. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 28 FEL Dynamics I

29. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 29 FEL Dynamics II

30. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 30 FEL Dynamics III

31. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 31 Another Pendulum Equation

32. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 32 CERN School Gain only when energy of beam doesn’t quite match “ideal” energy If wiggler is two long, process reverses, unless wiggler is “tapered” η φ

33. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 33 FEL parameters Need high beam density

34. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 34 SYLee Text

35. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 35 SYLee Text

36. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 36 SYLee Text Looks like derivative of undulator power spectrum: fluctuation- dissipation or Madey’s theorem

37. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 37 High Gain Regime So far, we haven’t included how the increasing electromagnetic wave affects the continued electron motion Also, there is a density variation developing Also, at high enough frequencies there are no good mirrors to make an optical resonator “High Gain” regime, really an instability saves the day, and points to X-ray lasers

38. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 38 Basic Principle: Coherent Synchrotron Radiation If we can get “microbunching” of electron beam, strong enhancement over incoherent synchrotron radiation

39. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 39 High Gain FEL to the Rescue: Basic Feedback Loop Electron beam responds to co-traveling electromagnetic wave in a wiggler/undulator –Electrons radiate by stimulated emission in wiggler –Electrons move relative to each other: density variations at wavelength of radiation Density variations radiate coherently in wiggler/undulator Electromagnetic field is enhanced, with changes to both its amplitude and phase Electron move relative to each other in response to to co-traveling electromagnetic other: density variations grow at wavelength of radiation Genuine instability with exponential growth of both the density variation and the electromagnetic radiation

40. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 40 Further Details Can send beam through a dispersive compressor where the microbunching through energy variation is enhanced, “optical klystron” Generates higher harmonics Since Schottky (shot) noise is “noisy,” can instead seed with laser

41. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 41 Zhirong Huang, SLAC

42. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 42

43. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 43

44. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 44

45. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 45

46. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 46  (fs)  The SASE radiation is powerful, but noisy! Solution: Impose a strong coherent modulation with an external laser source A SASE FEL amplifies random electron density modulations Spectrum From a SASE FEL Graves

47. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 47 Bill Graves

48. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 48 Brookhaven Laser Seeding Demonstration Buncher e-e- Laser 800 nm Modulator 266 nm outpu t Radiator Suppressed SASE noise Amplified coherent signal Narrowed bandwidth Shifted wavelength High Gain Harmonic Generation (HGHG) SASE x10 5 HGHG L.H. Yu et al., Phys. Rev. Lett. 91, 74801 (2003).

49. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 49 To Produce Transform-Limited Hard X-ray Pulses Use “cascaded” High Gain Harmonic Generation methods Input seed  0 1 st stage2 nd stage …N th stage Stage 1 output at 5  0 seeds 2 nd stage Stage 2 output at 25  0 seeds 3 rd stage …N th stage output at 5 N  0 W. Graves, MIT

50. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 50 Key facility elements Photoinjector SRF linac Bunch compresso r Ebeam switch Undulators Photocathode laser Bunch compresso r Seed laser W. Graves, MIT

51. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 51

52. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 52 High Harmonic Generation (HHG) Seeding Courtesy of B. Sheehy

53. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 53 HHG laser seeds at 100 eV Mod 1 100 eV 200 eV Rad 1 Buncher magnets 1.Initial seed is 3 nJ at 100 eV. 2.Radiator 1 amplifies the seed laser. 3.Buncher magnets control the power in each succeeding section by changing the magnitude of harmonic bunching. 1240 eV FEL seeded by 100 kW at 100 eV 2.5 GeV ebeam 1.2 GW @ 1200 eV 3 m 1.5 m 2 m22 m Spent ebeam is dumped Fiber link synchronization 1200 eV600 eV 3 m Rad 2Rad 3Rad 4 Graves, MIT

54. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 54 Transform-limited output – longitudinal and transverse Many beamlines operating simultaneously Complete tunability from 6 – 1200 eV Fully tunable polarization Peak power and brilliance much larger than current XUV sources Average flux and brilliance much larger than best synchrotrons and ERLs Synchronization of ~10 fs to user lasers Performance Goals

55. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 55 Three Standard Operating Modes Single-shot—Experiments that require the highest available peak brilliance/flux and cannot be cycled rapidly. kHz-class experiments—often driven by pump lasers and operate from 10-1000 Hz. Requires CW SC linac. MHz-class experiments—includes experiments which can cycle rapidly, where time constants of interest are less than a micro-second. Also includes experiments in the energy domain needing high energy resolution and high flux. Requires CW SC linac and gun. All available at the same time

56. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 56 Breakthrough Science SRF Electron Injectors Superconducting Electron Accelerator FEL Undulatorss Experimental Areas Jacobs and Moore, SRC Monochromators RF Separation Time Resolved Imaging and Coherent Scattering Taking advantage of the short duration and variable polarization of the FEL x-ray pulse, this technique is particularly suited to study magnetization dynamics. Examples include new materials for high- speed high-density magnetic storage devices. Resonant Inelastic X-ray Scattering This is a powerful technique for studies of low energy electronic and magnetic excitations in materials. Femtochemistry Allows chemists to follow the dynamics of chemical reactions over extremely short time scales. This may enable chemists to better control reactions to create new products. Biological Systems Complex biological processes (for example, photosynthesis, or the transport of information from the eye to the brain) can be studied in snap shot experiments utilizing the precise time pattern and tunability of the FEL. Exotic Materials, Clusters and Nanostructures The FEL can be used to the selectively fabricate of atomic clusters and other nanostructures (a billionth of a meter in scale) with specifically tailored medical or material properties.The FEL can also be used to characterize the properties of these new nanoscale materials. Ultrahigh Resolution Spectroscopy Photoemission spectroscopy is the tool of choice to study highly correlated systems such as high Tc superconductors, now done with energy resolution in the meV range. With a pulsed FEL source energy resolution of several 10 μeV should be possible. Bunch compressors

57. Topic Nine: Wiggler to FELs UW Spring 2008 Accelerator Physics J. J. Bisognano 57 Homework Problems In the text, the vertical focusing in an undulator is derived from a hamiltonian. From a more newtonian approach in an expansion in 1/γ show that there is vertical focusing when the expansion is carried out to second order. Starting at equation 5.17 of Lee, fill in the details to get to equation 5.32. Lee 5.1.1