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

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Presentation on theme: "Lecture 1. Introduction. Acceleration of charged particles X-Ray Free Electron Lasers Igor Zagorodnov Deutsches Elektronen Synchrotron TU Darmstadt, Fachbereich."— Presentation transcript:

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

2 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 2 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 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 3 General information Lecture: X-Ray Free Electron Lasers Literature  K. Wille, Physik der Teilchenbeschleuniger und Synchrotron- strahlungsquellen, Teubner Verlag,  P. Schmüser, M. Dohlus, J. Rossbach, Ultraviolet and Soft X-Ray Free-Electron Lasers, Springer,  E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov, The Physics of Free Electron Lasers, Springer, Lecturer: PD Dr. Igor Zagorodnov Deutsches Elektronen Synchrotron (MPY) Notkestraße. 85, Hamburg, Germany phone: web:

4 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 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 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 5 Motivation Laser – a special light monochromatic (small bandwidth) parallel (tightly collimated) coherent (special phase relations) The laser light allows to make accurate interference images (three dimensional pictures).

6 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 6 gas mirrors energy pump light accelerator undulator bunch Motivation  non quantized electron energy  the electron bunch is the energy source und the lasing medium Quantum Laser Free electron laser (FEL) Free electron laser laser light John Madey, Appl. Phys. 42, 1906 (1971) „Light Amplification by Stimulated Emission of Radiation“

7 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 7 Motivation  no mirrors under 100 nm  no long-term excited states for the population inversion Why FEL? Reflectivity drops quickly

8 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 8 Motivation Why FEL?

9 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 9 Motivation FEL as a source of X-rays photon energy [eV] peak brilliance [ph/(s mrad 2 mm 2 0.1% BW)] Photon flux is the number of photons per second within a spectral bandwidth of 0.1% Brilliance

10 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 10 Motivation  brilliant  extremely short pulses (~ fs)  ultra short wavelengths (atom details resolution)  coherent (holography at atom level) FEL as a source of X-rays

11 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 11 Motivation H.Chapman et al, Nature Physics, 2,839 (2006) Experiment with FEL light FEL puls  32 nm  puls length: 25 fs

12 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 12 Motivation reconstructed image example structure in 20 nm membran 1 μm Experiment with FEL light diffraction image H.Chapman et al, Nature Physics, 2,839 (2006)

13 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 13 Motivation data from FLASH „High-Gain“ FEL W. Ackermann et al, Nature Photonics 1, 336 (2007) Exponential growth

14 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 14 Motivation FLASH („Free Electron LASer in Hamburg) RF gunacceleratorundulatorphoton laboratory

15 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 15 Motivation FLASH („Free Electron LASer in Hamburg) accelerator

16 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 16 Particle acceleration short gain length short radiation wavelength Requirements on the beam  high beam energy  high peak current  low emittance  low energy energy spread

17 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 17 Particle acceleration - the normalized emittance is conserved during acceleration Emittance - trajectory slope

18 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 18 Particle acceleration Methods of particle acceleration The energy of relativistic particle with the relativistic momentum can be changed in EM field Cockroft-Walton generator(1930)

19 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 19 Particle acceleration Daresbury, ~20MeV 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.

20 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 20 Particle acceleration 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) The particles are sent repeatedly through the electrostatic field. Acceleration to higher energy? Faraday‘s law Coulomb‘s law absence of free magnetic poles generelized Ampere‘s law

21 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 21 Particle acceleration Betatron RF resonators Acceleration to higher energy? Faraday‘s law B E R

22 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 22 Betatron main coils corrector coils yoke vacuum chamberbeam 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 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 23 B E R Betatron This 1:2 relation was found in 1928 by Wideröe. Constant orbit condition Centrifugal force Is equal to the Lorentz force From Faraday’s law From Newton’s law

24 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 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 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 25 Betatron. Weak focusing The radial force is pointed to the design orbit if Radial stability

26 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 26 Betatron. Weak focusing Radial stability (exercises 1,2)

27 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 27 Betatron. Weak focusing The vertical force is pointed to the design orbit if The orbit is stable in all directions if Vertical stability

28 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 28 Betatron

29 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 29 Circular and linear accelerators Circular accelerators: many runs through small number of cavities. Linear accelerators: one run through many cavities

30 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 30 Strong focusing BESSY II, Berlin PETRA III, Hamburg S. Kahn, Free-electron lasers. (a tutorial review) Journal of Modern Optics 55, (2008)

31 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 31 Strong focusing multipolar expansion equations of motiontransfer matrix (quadrupole) dipole qudrupole sextupole

32 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 32 Strong focusing

33 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 33 RF Resonators Maxwell equations in vacuum Fromfollows wave equations We separate the periodical time dependance und use the representation (traveling wave) Waveguides

34 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 34 RF Resonators For the space field distribution in transverse plane we obtain The smallest wave number (cut frequency) k c Wave propagation in the waveguide is possible only if k>k c. If k

35 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 35 RF Resonators Unlike free space plane wave the waves in waveguides have longitudinal components TM waves TE waves Waveguides

36 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 36 RF Resonators Waveguides

37 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 37 RF Resonators The cylindrical waveguide were an ideal accelerator structure, if it were possible to use E z component of TM wave. However the velocity of the particle is always smaller than the wave phase velocity v ph. waveguide with irises (traveling waves) RF resonators (standing waves) Acceleration?

38 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 38 RF Resonators 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 (traveling wave) waveguide with irises cylindrical waveguide

39 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 39 RF Resonators Acceleration with standing and traveling waves

40 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 40 RF Resonators We separate only the periodic time dependence and take the represantation (standing wave) For the space field distribution we obtain

41 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 41 RF Resonators TM 010 -Welle Pillbox

42 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 42 RF Resonators The electron beam energy is converted in RF energy. Klystron

43 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 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 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 44 RF Resonators the concept of wake fields is used to describe the integrated kick (caused by a source particle, seen by an observer particle) self field of cavity (driven by bunches) 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 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 45 Bunch compressors

46 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 46 Bunch compressors momentum compaction factor

47 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 47 Bunch compressors M. Dohlus et al.,Electron Bunch Length Compression, ICFA Beam Dynamics Newsletter, No. 38 (2005) p.15

48 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 48 Phase space linearization In accelerator modules the energy of the electrons is increased from 5 MeV (gun) to 1200 MeV (undulator). FLASH

49 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 49 Phase space linearization In compressors the peak current I is increased from A (gun) to 2500 A (undulator). FLASH

50 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 50 Phase space linearization rollover compression vs. linearized compression ~ 1.5 kA ~2.5 kA Q=1 nC Q=0.5 nC

51 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 51 Phase space linearization Gun Longitudinal dynamics(exercise 3)

52 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 52 Phase space linearization Gun Longitudinal dynamics(exercise 3)

53 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 53 Phase space linearization Gun Zagorodnov I., Dohlus M., A Semi-Analytical Modelling of Multistage Bunch Compression with Collective Effects, Phys. Rev. ST Accel. Beams, 14, (2011) Longitudinal dynamics(exercise 3)

54 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 54 Outlook FLASH („Free Electron LASer in Hamburg) RF gunaccelerator undulatorlaboratory

55 PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 1 | 07. April 2014 | Seite 55 Outlook FLASH („Free Electron LASer in Hamburg) undulator 27m


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