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

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

3. Lecture: X-Ray Free Electron Lasers
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, Hamburg, Germany phone:                                    
web:

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

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

7. Reflectivity drops quickly
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 short pulses (~ 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 example structure diffraction
in 20 nm membran
diffraction
image
reconstructed
image
H.Chapman et al,
Nature Physics,
2,839 (2006)

13. Motivation „High-Gain“ FEL data from FLASH Exponential growth
W. Ackermann et al, Nature Photonics 1, 336 (2007)

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

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

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

17. Particle acceleration
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
Betatron
RF resonators B E R

22. Betatron main coils corrector coils yoke 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 Faraday’s law
From Newton’s law
Is equal to the Lorentz force
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, (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? waveguide with irises RF resonators
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.
waveguide with irises
cylindrical waveguide

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
momentum compaction factor

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

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

49. Phase space linearization
FLASH
In compressors the peak current I is increased from 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

51. Phase space linearization
Longitudinal dynamics(exercise 3)
Gun

52. Phase space linearization
Longitudinal dynamics(exercise 3)
Gun

53. Phase space linearization
Longitudinal dynamics(exercise 3)
Gun
Zagorodnov I., Dohlus M., A Semi-Analytical Modelling of Multistage Bunch Compression with Collective Effects, Phys. Rev. ST Accel. Beams, 14, (2011)

54. Outlook FLASH („Free Electron LASer in Hamburg) RF gun accelerator
undulator
laboratory

55. Outlook
FLASH („Free Electron LASer in Hamburg)
undulator
27m