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**X-Ray Free Electron Lasers**

Lecture 1. Introduction Acceleration of charged particles Igor Zagorodnov Deutsches Elektronen Synchrotron TU Darmstadt, Fachbereich 18 07. April 2014

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**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

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**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:

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**Contents Motivation. Free electron laser Particle acceleration**

Betatron. Weak focusing Circular and linear accelerators Strong focusing RF Resonators Bunch compressors Phase space linearization

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**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).

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**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)

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**Reflectivity drops quickly**

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

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Motivation Why FEL?

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**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]

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**Motivation FEL as a source of X-rays brilliant**

extremely short pulses (~ fs) ultra short wavelengths (atom details resolution) coherent (holography at atom level)

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**Motivation Experiment with FEL light H.Chapman et al, Nature Physics,**

2,839 (2006) FEL puls 32 nm puls length: 25 fs

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**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)

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**Motivation „High-Gain“ FEL data from FLASH Exponential growth**

W. Ackermann et al, Nature Photonics 1, 336 (2007)

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**Motivation FLASH („Free Electron LASer in Hamburg) RF gun accelerator**

undulator photon laboratory

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Motivation FLASH („Free Electron LASer in Hamburg) accelerator

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**Particle acceleration**

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

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**Particle acceleration**

Emittance - trajectory slope - the normalized emittance is conserved during acceleration

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**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

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**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

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**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

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**Particle acceleration**

Acceleration to higher energy? Faraday‘s law Betatron RF resonators B E R

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**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.

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**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.

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**Betatron. Weak focusing**

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

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**Betatron. Weak focusing**

Radial stability The radial force is pointed to the design orbit if

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**Betatron. Weak focusing**

Radial stability (exercises 1,2)

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**Betatron. Weak focusing**

Vertical stability The vertical force is pointed to the design orbit if The orbit is stable in all directions if

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Betatron

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**Circular and linear accelerators**

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

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**Strong focusing BESSY II, Berlin PETRA III, Hamburg**

S. Kahn, Free-electron lasers. (a tutorial review) Journal of Modern Optics 55, (2008)

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**Strong focusing dipole qudrupole sextupole multipolar expansion**

equations of motion transfer matrix (quadrupole)

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Strong focusing

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**RF Resonators Waveguides Maxwell equations in vacuum From**

follows wave equations We separate the periodical time dependance und use the representation (traveling wave)

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**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

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**RF Resonators Waveguides**

Unlike free space plane wave the waves in waveguides have longitudinal components TM waves TE waves

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RF Resonators Waveguides

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**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)

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**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

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RF Resonators Acceleration with standing and traveling waves

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

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RF Resonators Pillbox TM010 -Welle

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**RF Resonators Klystron**

The electron beam energy is converted in RF energy.

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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.

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**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

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Bunch compressors

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Bunch compressors momentum compaction factor

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

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**Phase space linearization**

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

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**Phase space linearization**

FLASH In compressors the peak current I is increased from A (gun) to 2500 A (undulator).

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**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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**Phase space linearization**

Longitudinal dynamics(exercise 3) Gun

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**Phase space linearization**

Longitudinal dynamics(exercise 3) Gun

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**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)

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**Outlook FLASH („Free Electron LASer in Hamburg) RF gun accelerator**

undulator laboratory

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

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