Presentation on theme: "X-Ray Free Electron Lasers"— Presentation transcript:
1X-Ray Free Electron Lasers Lecture 1. Introduction Acceleration of charged particlesIgor ZagorodnovDeutsches Elektronen SynchrotronTU Darmstadt, Fachbereich 1807. April 2014
2Lecture: X-Ray Free Electron Lasers General informationLecture: X-Ray Free Electron LasersPlace: S2|17, room 114, Schloßgartenstraße 8, DarmstadtTime: Monday, 11:40-13:20 (lecture), 13:30-15:10 (exercises)1. ( ) Introduction. Acceleration of charged particles2. ( ) Synchrotron radiation3. ( ) Low-gain FELs4. ( ) High-gain FELs5. ( ) Self-amplified spontaneous emission.FLASH and the European XFEL in Hamburg6. ( ) Numerical modeling of FELs7. ( ) New FEL schemes and challenges8. ( ) Exam
3Lecture: X-Ray Free Electron Lasers General informationLecture: X-Ray Free Electron LasersLiterature 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:
4Contents Motivation. Free electron laser Particle acceleration Betatron. Weak focusingCircular and linear acceleratorsStrong focusingRF ResonatorsBunch compressorsPhase space linearization
5Motivation 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 makeaccurate interference images(three dimensional pictures).
6Motivation Free electron laser Quantum Laser Free electron laser (FEL) gasmirrorsenergy pumplightundulatoracceleratorlaser lightbunchnon quantized electron energythe electron bunch is the energy source und the lasing medium„Light Amplification by Stimulated Emission of Radiation“John Madey, Appl. Phys. 42, 1906 (1971)
7Reflectivity drops quickly MotivationWhy FEL?Reflectivity drops quicklyno mirrors under 100 nmno long-term excited states for the population inversion
9Motivation 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%Brilliancephoton energy [eV]
10Motivation FEL as a source of X-rays brilliant extremely short pulses (~ fs)ultra short wavelengths (atom details resolution)coherent (holography at atom level)
11Motivation Experiment with FEL light H.Chapman et al, Nature Physics, 2,839 (2006)FEL puls32 nmpuls length: 25 fs
12Motivation Experiment with FEL light example structure diffraction in 20 nm membrandiffractionimagereconstructedimageH.Chapman et al,Nature Physics,2,839 (2006)
13Motivation „High-Gain“ FEL data from FLASH Exponential growth W. Ackermann et al, Nature Photonics 1, 336 (2007)
14Motivation FLASH („Free Electron LASer in Hamburg) RF gun accelerator undulatorphoton laboratory
15MotivationFLASH („Free Electron LASer in Hamburg)accelerator
16Particle acceleration Requirements on the beamshort radiation wavelengthshort gain lengthhigh beam energyhigh peak currentlow emittancelow energy energy spread
17Particle acceleration Emittance- trajectory slope- the normalized emittance is conserved during acceleration
18Particle acceleration Methods of particle accelerationCockroft-Waltongenerator(1930)The energy of relativistic particlewith the relativistic momentumcan be changed in EM field
19Particle acceleration Acceleration in electrostatic fieldVan de GraffacceleratorThe 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
20Particle 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 lawFaraday‘s lawCoulomb‘s lawabsence of free magnetic poles
21Particle acceleration Acceleration to higher energy?Faraday‘s lawBetatronRF resonatorsBER
22Betatron 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.
23Betatron Constant orbit condition Centrifugal force From Faraday’s law From Newton’s lawIs equal to the Lorentz forceThis 1:2 relation was found in 1928 by Wideröe.
24Betatron. Weak focusing Betatron oscillations near the reference orbit- field index- orbit stability conditionTransverse oscillations are called betatron oscillations for all accelerators.
25Betatron. Weak focusing Radial stabilityThe radial force is pointed to the design orbit if
33RF Resonators Waveguides Maxwell equations in vacuum From follows wave equationsWe separate the periodical time dependance und use the representation (traveling wave)
34RF Resonators Waveguides For the space field distribution in transverse plane we obtainThe smallest wave number (cut frequency) kcWave 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
35RF Resonators Waveguides Unlike free space plane wave the waves in waveguides have longitudinal componentsTM wavesTE waves
37RF 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)
38RF 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 irisescylindrical waveguide
39RF ResonatorsAcceleration with standing and traveling waves
40RF ResonatorsWe separate only the periodic time dependence and take the represantation (standing wave)For the space field distribution we obtain
42RF Resonators Klystron The electron beam energy is converted in RF energy.
43RF ResonatorsThe 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.
44RF 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 interactionsimportant for FELs: longitudinal single bunch wakes change the energy chirp and interfere with bunch compression
48Phase space linearization FLASHIn accelerator modules the energy of the electrons is increased from 5 MeV (gun) to 1200 MeV (undulator).
49Phase space linearization FLASHIn compressors the peak current I is increased from A (gun) to 2500 A (undulator).
50Phase space linearization rollover compression vs. linearized compressionQ=0.5 nC~ 1.5 kAQ=1 nC~2.5 kA
51Phase space linearization Longitudinal dynamics(exercise 3)Gun
52Phase space linearization Longitudinal dynamics(exercise 3)Gun
53Phase space linearization Longitudinal dynamics(exercise 3)GunZagorodnov I., Dohlus M., A Semi-Analytical Modelling of Multistage Bunch Compression with Collective Effects, Phys. Rev. ST Accel. Beams, 14, (2011)
54Outlook FLASH („Free Electron LASer in Hamburg) RF gun accelerator undulatorlaboratory
55OutlookFLASH („Free Electron LASer in Hamburg)undulator27m