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 0. April 015

General information Lecture: X-Ray Free Electron Lasers Place: S 17, room 114, Schloßgartenstraße 8, 6489 Darmstadt Time: Monday, 11:40-13:0 (lecture), 13:30-15:10 (exercises) 1. (07.04.14) Introduction. Acceleration of charged particles. (14.04.14) Synchrotron radiation 3. (05.05.14) Low-gain FELs 4. (1.05.14) High-gain FELs 5. (19.05.14) Self-amplified spontaneous emission. FLASH and the European XFEL in Hamburg 6. (0.06.14) Numerical modeling of FELs 7. (3.06.14) New FEL schemes and challenges 8. (30.06.14) Exam PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite

General information Lecture: X-Ray Free Electron Lasers Literature K. Wille, Physik der Teilchenbeschleuniger und Synchrotronstrahlungsquellen, Teubner Verlag, 1996. P. Schmüser, M. Dohlus, J. Rossbach, Ultraviolet and Soft X-Ray Free-Electron Lasers, Springer, 008. 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, 607 Hamburg, Germany phone: +49-40-8998-180 e-mail: Igor.Zagorodnov@desy.de web: www.desy.de/~zagor/lecturesfel PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 3

Contents Motivation. Free electron laser Particle acceleration Betatron. Weak focusing Circular and linear accelerators Strong focusing RF Resonators Bunch compressors Phase space linearization PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 4

Motivation Laser a special light parallel (tightly collimated) monochromatic (small bandwidth) coherent (special phase relations) The laser light allows to make accurate interference images (three dimensional pictures). PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 5

Motivation Free electron laser Quantum Laser gas light accelerator Free electron laser (FEL) undulator laser light energy pump mirrors Light Amplification by Stimulated Emission of Radiation bunch non quantized electron energy the electron bunch is the energy source und the lasing medium John Madey, Appl. Phys. 4, 1906 (1971) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 6

Motivation Why FEL? Reflectivity drops quickly no mirrors under 100 nm no long-term excited states for the population inversion PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 7

Motivation Why FEL? PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 8

Motivation FEL as a source of X-rays peak brilliance [ph/(s mrad mm 0.1% BW)] Photon flux is the number of photons per second within a spectral bandwidth of 0.1% photons Φ = s 0.1 BW Brilliance Φ B = π Σ Σ 4 xy x' y ' photon energy [ev] Σ xy = σ x, eσ y, e Σ = σ σ x' y ' θ, ph θ, ph PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 9 x y

Motivation FEL as a source of X-rays brilliant extremely short pulses (~ fs) ultra short wavelengths (atom details resolution) coherent (holography at atom level) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 10

Motivation Experiment with FEL light H.Chapman et al, Nature Physics,,839 (006) FEL puls 3 nm puls length: 5 fs PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 11

Motivation Experiment with FEL light 1 µm example structure in 0 nm membran diffraction image reconstructed image H.Chapman et al, Nature Physics,,839 (006) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 1

Motivation High-Gain FEL P rad ~ N el P rad ~ N el data from FLASH E[µJ] z[ m ] Exponential growth λ[nm] W. Ackermann et al, Nature Photonics 1, 336 (007) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 13

Motivation FLASH ( Free Electron LASer in Hamburg) RF gun accelerator undulator photon laboratory PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 14

Motivation FLASH ( Free Electron LASer in Hamburg) accelerator PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 15

Particle acceleration Requirements on the beam z L g E( z) ~ e short radiation wavelength λ ~ 1 γ E[µJ] short gain length Lg 5 6 5 4 ε ε σ γ ~ 1+ O 1 I I z[ m] high beam energy high peak current low emittance low energy energy spread PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 16

Particle acceleration Emittance dx px x = = - trajectory slope dz p z ε x = x x xx, ε n x = γε - the normalized emittance is x conserved during acceleration PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 17

Particle acceleration Methods of particle acceleration The energy of relativistic particle 4 0 E = m c + p c with the relativistic momentum p = γ m v 0 ( 1 ) 0.5 γ = β β = v / c Cockroft-Walton generator(1930) can be changed in EM field FL = q( v B + E) r E = F dr = q E dr = qu r L r r 1 1-19 -19 1eV=1.60 10 C 1V=1.60 10 J PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 18

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, ~0MeV PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 19

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) H = J + D t E = B t D = ρ B = 0 generelized Ampere s law Faraday s law Coulomb s law absence of free magnetic poles PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 0

Particle acceleration Acceleration to higher energy? Faraday s law Edr = Bds t Betatron RF resonators E B R PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 1

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. PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite

Betatron Constant orbit condition y E R B Centrifugal force mvϕ Ffug = R Is equal to the Lorentz force F = qv B. L ϕ pɺ = ϕ qrb z z 0 B = 0 B z Edr = π 0 E = E ϕ 0 From Faraday s law Bɺ ds = π ɺ 1 Bɺ zds π R REϕ R Bav Bɺ av = Bav B z = ɺ This 1: relation was found in 198 by Wideröe. PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 3 z R pɺ ϕ From Newton s law pɺ = F ϕ = qe ϕ R pɺ = ϕ q Bɺ x av

Betatron. Weak focusing Betatron oscillations near the reference orbit n = R B z B z r - field index 0 < n < 1 - orbit stability condition Transverse oscillations are called betatron oscillations for all accelerators. PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 4

Betatron. Weak focusing Radial stability ϕ R + r F0 = F ( R) = F ( R) = qv B fug L ϕ z mvϕ mvϕ r r 0 Ffug ( R + r) = 1 = F 1 R + r R R R Bz r FL ( R + r) = qvϕbz ( R + r) qvϕ [ Bz ( R) + r] = F0 (1 n ) r R r Frad ( R + r) = FL + Ffug = F0 ( n 1) R The radial force is pointed to the design orbit if R n < 1 n = B PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 5 z B z r

Betatron. Weak focusing Radial stability (exercises 1,) field index orbit 1 1.5 1 0.5 0 0 0. 0.4 0.6 t[mks] relative radius 1. y[m] 0.5 0-0.5-1 -1 0 1 x[m] relative moment 1. 1.1 1 0.9 0 0. 0.4 0.6 t[mks] 1.15 1.1 1.05 1 0 0. 0.4 0.6 t[mks] PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 6

Betatron. Weak focusing Vertical stability B = µ J + D t FL = q( v B + E) B = B r z z r z = 0 Br Bz z Fz ( z) = qvϕ Br ( z) qvϕ z = qvϕ z = F0 n z r R The vertical force is pointed to the design orbit if r Frad ( R + r) = F0 ( n 1) n < 1 R z F ( z) = F n n > 0 R z 0 n > 0 The orbit is stable in all directions if 0 < n < 1 PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 7

Betatron PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 8

Circular and linear accelerators Circular accelerators: many runs through small number of cavities. Linear accelerators: one run through many cavities PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 9

Strong focusing BESSY II, Berlin PETRA III, Hamburg S. Kahn, Free-electron lasers. (a tutorial review) Journal of Modern Optics 55, 3469-351 (008) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 30

Strong focusing dipole qudrupole sextupole multipolar expansion equations of motion transfer matrix (quadrupole) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 31

Strong focusing PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 3

RF Resonators Waveguides Maxwell equations in vacuum E = µ 0 H ɺ H = ε 0 E ɺ E = 0 From F = F F follows wave equations 1 E = c E ɺɺ 0 H = H = 0 We separate the periodical time dependance und use the representation (traveling wave) z E( r, t) = E( r ) i ( t k z ) e ω z H( r, t) = H( r ) i ( t k z ) e ω 1 c H ɺɺ x r = y z 0 r x = y PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 33

RF Resonators For the space field distribution in transverse plane we obtain ( ) k c ( ) 0 E r + E r = H( r ) + H( r ) = 0 k = k k k = ω / c c z Waveguides k c The smallest wave number (cut frequency) k c Wave propagation in the waveguide is possible only if k>k c. If k<k c then the solution exponentially decays along z. k k = kz + kc k c Phase velocity is larger than the light velocity ω ck k vph = = = c + > c k k k c 1 z z z k z PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 34

RF Resonators Waveguides Unlike free space plane wave the waves in waveguides have longitudinal components mπ x mπ y Ez = E e a b H = 0. z ( ) 0 sin sin i ω t k z z, π m π n kc = +, m = 1,,...; n = 1,,... a b TM waves TE waves mπ x mπ y ( z ) 0 cos cos i ω t H k z z = H e, a b Ez = 0. π m π n kc = +, m = 0,1,,...; n = 0,1,,... a b E E J k r m e H i( ωt kz z) z = 0 m ( c )cos( ϕ), z = 0. xmn kc =, m = 0,1,,...; n = 1,,... a H H J k r m e i( ωt kz z) z = 0 m ( c )cos( ϕ), Ez = 0. x mn kc =, m = 0,1,,...; n = 0,1,,... a PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 35 J ( x ) = 0 m mn J ( x ) = 0 m mn

RF Resonators Waveguides PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 36

RF Resonators Acceleration? 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) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 37

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. k cylindrical waveguide vph = c waveguide with irises vph < c π L k z L PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 38

RF Resonators Acceleration with standing and traveling waves π mode PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 39

RF Resonators π mode We separate only the periodic time dependence and take the represantation (standing wave) E( r, t) = E( r) e iωt H( r, t) = H( r) e iωt For the space field distribution we obtain ( ) k E( r) 0 E r + = ( ) k H( r) 0 H r + = PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 40

RF Resonators Pillbox TM 010 -Welle 0 E( r) = 0 E z H( r) 0 = H ϕ 0 r E 0 z + Ez + k Ez = z r r 0 0 ( ) E = E J kr E ( ) 0 H = ϕ J1 kr c k =.405. R PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 41

RF Resonators Klystron P Klzstron =ηui Strahl The electron beam energy is converted in RF energy. η klystron efficiency (45-65%) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 4

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 λ/4 from the wall. PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 43

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 PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 44

Bunch compressors PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 45

Bunch compressors δ s 0 momentum compaction factor ( 3 δ δ δ ) s = s + s = s R + T + U 1 0 0 56 566 5666 PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 46

Bunch compressors M. Dohlus et al.,electron Bunch Length Compression, ICFA Beam Dynamics Newsletter, No. 38 (005) p.15 PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 47

Phase space linearization FLASH In accelerator modules the energy of the electrons is increased from 5 MeV (gun) to 100 MeV (undulator). E = ev cos( ks + ϕ ) 1,1 1,1 1,1 E = ev cos(3 ks + ϕ ) 1,3 1,3 1,3 E = ev cos( ks1 + ϕ) E = ev cos( ks + ϕ ) 3 3 3 PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 48

Phase space linearization FLASH In compressors the peak current I is increased from 1.5-50 A (gun) to 500 A (undulator). i ( 3 ) 56δ 566δ 5666δ s = R + T + U PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 49

Phase space linearization rollover compression vs. linearized compression Q=0.5 nc ~ 1.5 ka Q=1 nc ~.5 ka PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 50

Phase space linearization Gun Longitudinal dynamics(exercise 3) B C 1 B C M 1,1 M 1,n M M 3 V ( s) maxv 1,1 1. 1 0.8 0.6 0.4 0. V = V cos( ks) + V cos(3 ks + ϕ ) V + V cosϕ 1,1 1,3 1,3 1,1 1,3 1,3 ( 1,3 ϕ1,3 ) ( 1,1 1,3 ϕ1,3 ) 3 3V sin ks 0.5 V + 9V cos( ) k s + O( s ) ϕ V 1,3 = π 1 = V 9 1,3 1,1 V V V + O( s ) 1,1 1,3 3 0-0. -1.5-1 -0.5 0 0.5 1 1.5 ks PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 51

Phase space linearization Gun Longitudinal dynamics(exercise 3) B C 1 B C M 1,1 M 1,n M M 3 PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 5

Phase space linearization Gun Longitudinal dynamics(exercise 3) B C 1 B C M 1,1 M 1,n M M 3 Zagorodnov I., Dohlus M., A Semi-Analytical Modelling of Multistage Bunch Compression with Collective Effects, Phys. Rev. ST Accel. Beams, 14, 014403 (011) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 53

Outlook FLASH ( Free Electron LASer in Hamburg) RF gun accelerator undulator laboratory PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 54

Outlook FLASH ( Free Electron LASer in Hamburg) undulator 7m PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 1 0. April 015 Seite 55