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X-Ray Free Electron Lasers

X-Ray Free Electron Lasers. Lecture 1. Introduction. Acceleration of charged particles. Igor Zagorodnov Deutsches Elektronen Synchrotron TU Darmstadt, Fachbereich 18 07 . April 2014. General information. Lecture: X-Ray Free Electron Lasers

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X-Ray Free Electron Lasers

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  1. X-Ray Free Electron Lasers Lecture 1. Introduction. Acceleration of charged particles Igor Zagorodnov DeutschesElektronen Synchrotron TU Darmstadt, Fachbereich 18 07. April 2014

  2. General information Lecture: X-Ray Free Electron Lasers Place: S2|17, room 114, Schloßgartenstraße 8, 64289 Darmstadt Time: Monday, 11:40-13:20 (lecture), 13:30-15:10 (exercises) 1. (07.04.14) Introduction. Acceleration of charged particles 2. (14.04.14) Synchrotron radiation 3. (05.05.14) Low-gain FELs 4. (12.05.14) High-gain FELs 5. (19.05.14) Self-amplified spontaneous emission. FLASH and the European XFEL in Hamburg 6. (02.06.14) Numerical modeling of FELs 7. (23.06.14) New FEL schemes and challenges 8. (30.06.14) Exam

  3. General information • Lecture: X-Ray Free Electron Lasers • Literature • K. Wille, Physik der Teilchenbeschleuniger und Synchrotron- strahlungsquellen, Teubner Verlag, 1996. • P. Schmüser, M. Dohlus, J. Rossbach, Ultraviolet and Soft X-Ray Free-Electron Lasers, Springer, 2008. • E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov, The Physics of Free Electron Lasers, Springer, 1999. • Lecturer: PD Dr. Igor Zagorodnov • Deutsches Elektronen Synchrotron (MPY)Notkestraße. 85, 22607 Hamburg, Germanyphone:  +49-40-8998-1802                                  e-mail: Igor.Zagorodnov@desy.de • web: www.desy.de/~zagor/lecturesFEL

  4. Contents • Motivation. Free electron laser • Particle acceleration • Betatron. Weak focusing • Circular and linear accelerators • Strong focusing • RF Resonators • Bunch compressors • Phase space linearization

  5. Motivation Laser – a special light monochromatic (small bandwidth) coherent (special phase relations) parallel (tightly collimated) The laser light allows to make accurate interference images (three dimensional pictures).

  6. Motivation Free electron laser Quantum Laser Free electron laser (FEL) light gas undulator accelerator laser light bunch energy pump • non quantized electron energy • the electron bunch is the energy source und the lasing medium mirrors „Light Amplification by Stimulated Emission of Radiation“ John Madey, Appl. Phys. 42, 1906 (1971)

  7. Motivation Why FEL? Reflectivity drops quickly • no mirrors under 100 nm • no long-term excited states for the population inversion

  8. Motivation Why FEL?

  9. Motivation FEL as a source of X-rays peak brilliance [ph/(s mrad2 mm2 0.1% BW)] Photon flux is the number of photons per second within a spectral bandwidth of 0.1% Brilliance photon energy [eV]

  10. Motivation FEL as a source of X-rays • brilliant • extremely shortpulses (~ fs) • ultra short wavelengths (atom details resolution) • coherent (holography at atom level)

  11. Motivation Experiment with FEL light H.Chapman et al, Nature Physics, 2,839 (2006) • FEL puls • 32 nm • puls length: 25 fs

  12. Motivation Experiment with FEL light 1 μm example structure in 20 nm membran diffraction image reconstructed image H.Chapman et al, Nature Physics, 2,839 (2006)

  13. Motivation „High-Gain“ FEL datafrom FLASH Exponential growth W. Ackermann et al, Nature Photonics1, 336 (2007)

  14. Motivation FLASH („Free Electron LASer in Hamburg) photon laboratory accelerator RF gun undulator

  15. Motivation FLASH („Free Electron LASer in Hamburg) accelerator

  16. Particleacceleration Requirements on the beam short radiation wavelength short gain length • high beam energy • high peak current • low emittance • low energy energy spread

  17. Particleacceleration Emittance - trajectory slope - the normalized emittance is conserved during acceleration

  18. Particle acceleration Methods of particle acceleration Cockroft-Walton generator(1930) The energy of relativistic particle with the relativistic momentum can be changed in EM field

  19. Particle acceleration Acceleration in electrostatic field Van de Graff accelerator The energy capability of this sort of devices is limited by voltage breakdown, and for higher energies one is forced to turn to other approaches. Daresbury, ~20MeV

  20. Particle acceleration Acceleration to higher energy? The particles are sent repeatedly through the electrostatic field. No pure acceleration is obtained. The electric field exists outside the plates. This field decelerates the particle. Time dependent electromagnetic field! Maxwell‘s equations (1865) generelized Ampere‘s law Faraday‘s law Coulomb‘s law absence of free magnetic poles

  21. Particle acceleration Acceleration to higher energy? Faraday‘s law RF resonators Betatron E B R

  22. Betatron yoke main coils corrector coils vacuum chamber beam The magnetic field is changed in a way, that the particle circle orbit remains constant. The accelerating electric field appears according to the Faraday’s law from the changing of the magnetic field.

  23. Betatron Constant orbit condition Centrifugal force From Newton’s law From Faraday’s law E Is equal to the Lorentz force B R This 1:2 relation was found in 1928 by Wideröe.

  24. Betatron. Weak focusing Betatron oscillations near the reference orbit - field index - orbit stability condition Transverse oscillations are called betatron oscillations for all accelerators.

  25. Betatron. Weak focusing Radial stability The radial force is pointed to the design orbit if

  26. Betatron. Weak focusing Radial stability (exercises 1,2)

  27. Betatron. Weak focusing Vertical stability The vertical force is pointed to the design orbit if The orbit is stable in all directions if

  28. Betatron

  29. Circular and linear accelerators Circular accelerators: many runs through small number of cavities. Linear accelerators: one run through many cavities

  30. Strong focusing BESSY II, Berlin PETRA III, Hamburg S. Kahn, Free-electron lasers. (a tutorial review) Journal of Modern Optics 55, 3469-3512 (2008)

  31. Strong focusing dipole qudrupole sextupole multipolar expansion equations of motion transfer matrix (quadrupole)

  32. Strong focusing

  33. RF Resonators Waveguides Maxwell equations in vacuum From follows wave equations We separate the periodical time dependance und use the representation (traveling wave)

  34. RF Resonators Waveguides For the space field distribution in transverse plane we obtain The smallest wave number (cut frequency) kc Wave propagation in the waveguide is possible only if k>kc. If k<kc then the solution exponentially decays along z. Phase velocity is larger than the light velocity

  35. RF Resonators Waveguides Unlike free space plane wave the waves in waveguides have longitudinal components TM waves TE waves

  36. RF Resonators Waveguides

  37. RF Resonators Acceleration? The cylindrical waveguide were an ideal accelerator structure, if it were possible to use Ez component of TM wave. However the velocity of the particle is always smaller than the wave phase velocity vph. waveguide with irises (traveling waves) RF resonators (standing waves)

  38. RF Resonators Waveguide with irises (traveling wave) Through tuning of phase velocity according to the particle velocity it is possible to obtain, that the bunches synchronously with TM wave fly and obtain the maximal acceleration. cylindrical waveguide waveguide with irises

  39. RF Resonators Acceleration with standing and traveling waves

  40. RF Resonators We separate only the periodic time dependence and take the represantation (standing wave) For the space field distribution we obtain

  41. RF Resonators Pillbox TM010 -Welle

  42. RF Resonators Klystron The electron beam energy is converted in RF energy.

  43. RF Resonators The exact resonance frequency could be tuned. The resonator is exited through an inductive chain. The waveguide from klystron is at the end closed in such way, that a standing wave exists with its maximum at distance /4 from the wall.

  44. RF Resonators self field of cavity (driven by bunches) the concept of wake fields is used to describe the integrated kick (caused by a source particle, seen by an observer particle) short range wakes describe interaction of particles in same bunch long range wakes describe multi bunch interactions important for FELs: longitudinal single bunch wakes change the energy chirp and interfere with bunch compression

  45. Bunch compressors

  46. Bunch compressors momentumcompaction factor

  47. Bunch compressors M. Dohlus et al.,ElectronBunchLengthCompression, ICFA Beam Dynamics Newsletter, No. 38 (2005) p.15

  48. Phase space linearization FLASH In accelerator modules the energyof the electrons is increased from 5 MeV (gun) to 1200 MeV (undulator).

  49. Phase space linearization FLASH In compressors the peak currentI is increased from 1.5-50 A (gun) to 2500 A (undulator).

  50. Phase space linearization rollover compression vs. linearized compression Q=0.5 nC ~ 1.5 kA Q=1 nC ~2.5 kA

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