Undulator radiation from electrons randomly distributed in a bunch

Transcription

1 Undulator radiation from electrons randomly distributed in a bunch Normally z el >> N u 1 Chaotic light Spectral property is the same as that of a single electron /=1/N u Temporal phase space area z ~(/ z el 1

2 A monochromator increases temporal coherence A monochromator extends a wavetrain: M <<, / M =N M M A collection of randomly distributed N e wavetrains becomes coherent 1 if z el N M << D Periodic & coherent tm, 1 N z 1 N 1 el 2 However, the intensity add incoherently, ~ N e The amplitudes add, therefore intensity~ N e2 if z el << or if electrons are concentrated at positions z =n, n=1,2,.. This is what FELs can achieve! FEL Theory Tutorial Aug 2011 KJK 2

3 Amplification in the presence of e-beam When the EM wavelength satisfies the undulator condition, an electron sees the same EM field in the successive period sustained energy exchange A 0 A 1 A 2 A 3 An e - arriving at A 0 loses energy to the field (ev E <0). Similarly the e - at distance n n=1,2, also loses energy. However, those at /2 +n) away gain energy. The electron beam develops energy modulation (period length ). Higher energy electrons are faster density modulation develops Coherent EM of wavelength is generated Free electron laser 3

4 Low gain FEL from quantum mechanics (J.M.J. Madey, 1971) Transition amplitudes for emission and absorption aa, 1 n1a n n1; n1an n n1; p aj a J n; p n1 p J p e n1; p aj a J n; p n p J p a a e Variation on Madey Theorems December

5 Electron-photon interaction in the presence of external potential 2-momenta; Conservation: 2 m p E, E, k (, ), q(0, Q) 2E, p q p k p q k p Emission case: 2 2 m m E Ee, E Q Ee 2E 2E m m 2E ku Q Q; Q 2 2 2E 2( E) m (1 K /2) Absorption case is similar: E a 2 k E; Variation on Madey Theorems December 2013 e e 2 U 2 1 K /2 a 5

6 Probability of spont. emission Probability of absorption 2 * 2 2 Gain in photon energy=emission-absorption Gain NeΔW n1g Ne Γ( E,, Q) Γ( E,, Q) n Γ NW e s Eg Ne E E N e W s =radiation energy produced by the e-beam 2 p J p Γ( E,, Q) p J p p J p = p J p =Γ( E,, Q) a a a a ΔW n Γ( E,, Q) Γ( E,, Q) + Γ( E,, Q) e Variation on Madey Theorems December

7 Gain via Madey s Theorem The classical gain formula when g 2 dws j q m dd 0 E Variation on Madey Theorems December

8 Several routes to x-ray FEL High-gain amplifiers With extreme high-gain, initial noise is amplified to highintensity, radiation self-amplified spontaneous emission do not need coherent seed input but is temporally chaotic With coherent, low frequency input, high-gain harmonic generation coherent soft x-ray may be reached Terawatt pulses with femtosecond duration will permit single shot imaging Low-gain Need repeated amplification in an x-ray cavity oscillator Do not need seed input but can achieve high coherence Need CW accelerator and x-ray cavity Ultra-fine spectral purity and,in principle, even pulse-topulse coherence 8

9 SASE: Initial undulator radiation is amplified to intense, quasi-coherent radiation Saturation Transverse mode z = 25 m z = 37.5 m Exponential Gain Regime Undulator Regime z = 50 m z = 90 m Electron Bunch Micro-Bunching 9

10 Temporal characteristics of SASE Random bunching in SASE: N ~N e N lc N lc = # of electrons in one coherent region

11 An FEL for x-rays requires high e-beam qualities not achievable from storage rings photo-cathode gun & a linear acc BNL type LCLS S band RF Photocathode KEK/JAERI DC gun LBNL 180 MHz RF Photocathode 11

12 Hard X-Ray FELs in Operation & Under Construction LCLS I, II 2009, GeV, 120 Hz NC SACLA GeV, 60 Hz NC XFEL GeV, 3000 x 10 Hz SC PAL XFEL GeV, 100 Hz NC SWISS FEL GeV, 100 Hz NC 12

13 Self-seeding demonstration at LCLS SASE FEL spectrum Seeded FEL spectrum SASE Seeded Pulse energy (mj) ~ 20 ev ~ 0.5 ev Near Fourier Transform limit Single shot pulse energy from the gas detectors with 40pC charge Concept developed by Geloni, Kocharyan and Saldin, DESY (2010). The mean seeded FEL power is 8 GW with a 2.5 GW SASE background at 8 kev for 40 pc bunch charge. Peak seeded power is in excess of 15 GW, comparable to SASE but with a spectral bandwidth reduction by the factor of 40. Pulse energy jitter : SASE e beam energy jitter SASE and Seeded spectra recorded on single shots. The left panels are SASE with 150 pc, 3kA peak current, un-seeded. The FWHM of the SASE spectrum is 0.2 % Bandwidth. The right panels are the seeded beam with the same electron beam parameters. The FWHM of the seeded beam is 0.5 ev (5x10-5 bandwidth) Slide 13

14 Various R&D programs are in progress to enhance the performance of high-gain XFEL SASE is temporally incoherent fluctuation in spectrum and intensity Coherent soft x-rays (< 1 nm) via seeding Laser HHG, Cascaded HGHG, EEHG, self-seeding Self-seeding for hard x-rays Other spectrum enhancing schemes isase, psase, two color generation LCLS-II will incorporate CW capability by a super-conducting linac 14

15 Free Electron Laser Oscillator A low-gain device with high Q optical cavity Optical pulse formed over many electron passes Difficult for x-rays Electron beam qualities High-reflectivity normal incidence mirror Science Outlook and R&D Issues for an XFELO Feb 14 15,

16 X-Ray FEL Oscillator (XFEL-O) An FEL oscillator is feasible in hard x-ray region by using Bragg mirrors R. Collela and A. Luccio, 1983; KJK, Y. Shvyd ko, and S. Reiche, 2008 Tuning is possible with a four mirror configuration R. M.J.Cotterill, (1968) KJK & Y. Shvyd ko (2009) Ultra-high spectral resolution ( mev) with storage ring like stability 16 Science Outlook and R&D Issues for an XFELO 16 Feb 14 15, 2013

17 Example Parameters Electron beam: Energy t 6 GeV, Bunch charge ~ pc low intensity, Bunch length (rms) d 1 (0.1 ps) Peak current 20 (100) A, Normalized rms emittance d 0.2 (0.3) mm-mr, rms energy spread ~ 2â10-4, Constant bunch rep ~1 MHz Undulator: L u = 60 (30) m, u 2.0 cm, K= Optical cavity: 2- or 4- diamond crystals and focusing mirrors Total round trip reflectivity > 85 (50) % XFELO output: 5 kev dñ d 25 kev Bandwidth: ~ 1 (5) 10-7 ; rms pulse length = 500 (80) fs # photons/pulse ~ Rep rate ~ a few MHz(limited by crystal heat load and damage) 8 17

18 Diamond is the best material. The tolerance on optical element placement (10 nr), and R. & fig. errors for focusing mirrors appear feasible. Null feedback on HRM to 50 nr High heat diffusivity at < 100K Yamauch, JTEC, R~ 99%, fig error< 1 r 18

19 Damage issue of diamond crystals for XFELO cavity Power density on XFELO crystal 1 kw/mm2 Power density for APS HHL crystal Power density of focused beam for ESRF experiment in

20 XFELO Applications High resolution spectroscopy Inelastic x-ray scattering Mössbauer spectroscopy 103/pulse, 109/sec Moessbauer s (14.4 kev, 5 nev BW) X-ray photoemission spectroscopy Bulk-sensitive Fermi surface study with HX-TR-AR PES X-ray imaging with nm resolution Smaller focal spot with the absence of chromatic aberration picosecond time resolution A second user WS was held at POSTECH in Feb

21 Nuclear-resonance-stabilized XFELO(B.W. Adams and K.-J. Kim, to be published) The XFEL-O output pulses are copies of the same circulating intra-cavity pulse By stabilizing cavity RT time to less than 0.01/c, the spectrum of XFELO output becomes a comb The extreme-stabilized XFEL-O will establish an x-ray-based length standard and have applications in fundamental physics such as x-ray Ramsey interferometer to probe quantum gravity, etc. 21

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23 Possible Accelerator system Injector for XFELO is available from ERL research The 17GeV pulsed Euro XFEL can be operated 7GeV CW The KEK ERL project, if built, will incorporate an XFELO as an upgrade 4 GeV SCRF linac for LCLS II can drive XFELO at 3 rd or 5 th harmonics 23