SLAC Summer School on Electron and Photon Beams. Tor Raubenheimer Lecture #3: High Gain FEL s

Transcription

1 SLAC Summer School o Electro ad Photo Beams Tor Raubeheimer Lecture #3: High Gai FEL s

2 Outlie Sychrotro radiatio Bedig magets Wigglers ad udulators Iverse Compto scatterig Free Electro Lasers FEL Oscillators High gai X-ray FEL s Coherece ad Seedig Lecture #1 Lecture # Lecture #3 SSSEPB, July -6, 013

3 Types of FEL s SSSEPB, July -6, 013 3

4 High Gai Free Electro Laser Priciple Electros slip behid EM wave by 1 per udulator period ( u ) x K / e u v x E x < 0 v x E x > x-ray z Due to sustaied iteractio, some electros lose eergy, while others gai eergy modulatio at 1 e losig eergy slow dow, ad e gaiig eergy catch up desity modulatio at 1 (microbuchig) Microbuched beam radiates coheretly at 1, ehacig the process expoetial growth of radiatio power SSSEPB, July -6, 013 4

5 Early LCLS Gai Measuremets SSSEPB, July -6, 013 5

6 6 1-D Wave Equatio Allowig the field to chage slowly (>> u ) alog the udulator, the wave equatio i 1-D is where ad I the 1-D approximatio, we igored the self-fields (space charge) from the beam ad diffractio effects of the radiatio as well as the matchig of the beam ad radiatio fields. To solve this, we drop the d derivatives because the field is assumed to be chagig slowly where J 1 is the compoet of the curret at the radiatio wavelegth t J t z E t c z x x 0 ), ( 1 )] ( )exp[, ( ), ( t kz i t z E t z E x ) cos( ), ( z k K J t z J u z x 1 ~ 0 ~ 4 ), ( 1 J K c t z E t c z r

7 1-D FEL Equatios Now we have the pedulum equatios for the motio of the particles withi the radiatio bucket which depeds o a varyig electric field but the field ad curret equatios deped o the particle distributio N+ equatios d dz d dz ~ J 1 _ J k z k z u N u N 1 ~ ek E mc r exp( i ~ E where exp( i 1... N ) r ) 0cK 4 ~ J 1 #, p. 3 SSSEPB, July -6, 013 7

8 1-D Solutio (I) Itroduce dimesioless variables: zˆ a k u 1 4 z ek[ JJ] mc I I A the eglect ad liearize i terms of collective variables b P a ad k r ~ E exp( i ˆ exp( i ˆ / K[ JJ] 1 K / ) ) 1/3 Compex field Buchig parameter Collective mometum d dzˆ dˆ dzˆ zˆ ˆ a exp( i 1 ) cc a da dzˆ db dzˆ b ip exp( i ad ) dp a dzˆ SSSEPB, July -6, 013 R. Boifacio, C. Pellegrii, ad L.M. Narducci, Collective istabilities ad high-gai regime i a free-electro laser, Opt. Commu., 50, 373 (1984). 8

9 1-D Solutio (II) This has a geeral solutio of the form a~ exp( zˆ) i with 3 1 has three roots: oe oscillatory, oe damped ad oe growig. The equatio ca be futher geeralized to iclude the detuig ad eergy spread where is the fractioal detuig (- r )/ r ad is the width of a uiform eergy spread i uits of The high gai FEL differs from the small sigal gai i that the highest gai occurs o resoace SSSEPB, July -6, 013 9

10 Evolutio of the FEL Microbuchig FEL bucket grows rapidly as the beam begis to buch ad radiate coheretly. After a ¼ sychrotro oscillatio the buchig begis to decrease agai ad the FEL saturates SSSEPB, July -6, 013 From P. Schmuser et al. 10

11 Gai Legth ad Lethargy After some iitial mode competitio, the expoetially mode will grow. The 1-D power gai legth is give i terms of u LG0 4 3 At the begiig, the growig mode is competig with the oscillatory ad the damped modes field is roughly divided betwee modes ad it takes 1 ~ gai legths to get started SSSEPB, July -6,

12 Gai versus Detuig I the low gai FEL the maximum gai arises whe the FEL is slightly detued ad the beam eergy is higher tha the amplified sigal. Low Gai High Gai I the high gai case, this differs ad maximum gai arises o resoace however it takes some legth for this expoetial mode to domiate Growig mode Damped mode SSSEPB, July -6, 013 1

13 Small Gai Limit of High Gai FEL SSSEPB, July -6, 013 From P. Schmuser et al. 13

14 Eergy Spread ad Emittace Effects Eergy spread eeds to be small compared to the width of the gai curve Traverse emittace has two effects: 1. Icrease the logitudial slipage. 1K / J J x y z 1 x y eff where x ad y are the accelerator optical fuctios NOT velocity ad J x ad J y are the particle trasverse amplitudes. Match the beam to the radiatio size ad miimize diffractio 4 (1 x, y K ) SSSEPB, July -6,

15 3-D Parametrizatio May effects icrease the 1-D gai legth: eergy spread, emittace, diffractio, fiite buch legth, These effects ca be approximated as L G = L G0 (1 + ) where: ad Fially, the saturatio power is estimated to scale as: Xie, M.: Exact ad variatioal solutios of 3D eigemodes i high gai FELs. Nucl. Istr. Meth. A 445, 59 (000) 9, 93 SSSEPB, July -6,

16 SASE FEL Micro-Buchig Alog Udulator electro beam photo beam udulator beam dump SASE* FEL starts up from oise S. Reiche * Self-Amplified Spotaeous Emissio log (radiatio power) UCLA Power comes from last gai legth L g distace SSSEPB, July -6,

17 SASE Pulse Evolutio Starts from oise but as the beam propagates, the spectrum arrows. However, the light is still temporally chaotic uless the correlatio legth is comparable to the buch legth LCLS Simulatio SCSS spectrum 17

18 Iitial measuremets of e-beam ad x-ray temporal profiles usig the XTCAV FEL Off FEL O Data take o Jue 4 th, 013. Beam eergy 3.5GeV, 150pC. Temporal resolutio is about 1.7fs rms i this test. Prelimiary results. SSSEPB, July -6, 013

19 SASE Temporal Coherece SIMULATED FEL PULSES Sigle pass SASE FEL starts from oise 1.5 Å, photos I pk = 4.8 ka 0.4 µm Y. Dig Z. Huag Slippage legth is ~ (L g * u ) No phase correlatio betwee portios Would like to have trasform limited pulses for may experimets SASE Simulatio at 1.5 Å based o measured ijector & liac beam & Elegat trackig, with CSR, at 0 pc. 15 Å, photos, I pk =.6 ka, 0.4 µm Y. Dig Z. Huag 1. fs Seeded SSSEPB, July -6, 013 Simulatio at 15 Å based o measured ijector & liac beam & Elegat trackig, with CSR & 0 pc.

20 Trasverse Coherece Radiatio ca be decomposed ito trasverse modes. The TEM 00 has the highest itesity o axis while other modes exted out radially. The fudemetal TEM 00 mode grows fastest ad rapidly domiates although the other modes ca catch up oce ito saturatio I the LCLS SSSEPB, July -6, 013 0

21 Liac Coheret Light Source Facility First Light April 009, CD-4 Jue 010 Ijector at -km poit Existig Liac (1 km) (with modificatios) New e Trasfer Lie (340 m) UCLA Udulator (130 m) Near Experimet Hall X-ray Trasport Lie (00 m) SSSEPB, July -6, 013 Far Experimet Hall Slide 1

22 LCLS Cocept: Fourth Geeratio Workshop 1 Years Ago C. Pellegrii, A 4 to 0.1 m FEL Based o the SLAC Liac, Workshop o Fourth Geeratio Light Sources, February, 199 Claudio Pellegrii Herma Wiick Herma Wiick s Study Group SSSEPB, July -6, 013 Egaged Bjor Wiik ad Gerd Materlik durig sabbaticals at SLAC