SASE Wavefront Propagation Calculations Using SRW

Transcription

1 SAS Wavefont Popagation Calculations Using SW O. Chuba F. Polack M.-. Coupie SOI M. abat G. ambet O. Tchebakoff CA DSM/SPAM 99 Gif-su-Yvette Fance

2 Some Compute Codes fo S a-tacing and Wavefont Popagation a-tacing / Geometical Optics Fee: Commecial: Fee: Commecial: SHADOW Univ. Wisconsin XOP b S. del io SF. Dejus APS AY b A. ko et. al. BSSY Impoved a-tacing OSO COD V ZMAX Wavefont Popagation / Phsical Optics PHAS b J. Bahdt BSSY Stationa Phase Method PSTAB 006 SW SF/SOI Fouie Optics ZMAX GAD MICOWAV Studio

3 Self-Amplified Spontaneous mission Descibed b Paaial F quations Appoimation of Slowl Vaing Amplitude of adiation Field Paticles dnamics in undulato and adiation fields aveaged ove man peiods: Paaial wave equation with cuent: dθ = k dz aa γ dγ k fcaau = sin θ φ dz γ dp au v = k foc dz γ d p = dz γ u p k z a a u cos θ φ eε0ifca ep iφ = mc u u ep iθ γ W.B.Colson J.B.Muph C.Pellegini.Saldin.Bessonov et. al. Solving this sstem gives lectic Field at the F eit fo one Slice : slice ~ a z z ep iφ = z= z oop on Slices coping lectic Field to a net slice fom pevious slice stating fom back Popula TD 3D F compute code: GNSIS S.eiche Time-Domain lectic Field in tansvese plane at F eit: z t eit eit eit

4 Thin Optical lement: ~ ~ befoe afte T Fouie Optics Moe Geneall: ~ ] ep[ ~ c i befoe afte G Hugens Hugens-Fesnel Fesnel Pinciple: Pinciple: paaial appoimation Wavefont Wavefont Popagation Popagation Σ Σ ] ep[ ~ ~ d c i c i π lectic Field in lectic Field in Fequenc Fequenc and and Time Time domains domains: dt t i t ep ~ = π d t i t ep ~ and belong to paallel planes pependicula to optical ais Z ] [ z = d d = d Σ Hugens-Fesnel Pinciple is Convolution-tpe integal can be calculated using D FFT Popagation though Fee Space:

5 Analtical Teatment of Analtical Teatment of Quadatic Phase Tem Quadatic Phase Tem: Hugens Hugens-Fesnel Fesnel Pinciple: Pinciple: paaial appoimation An conomic Vesion An conomic Vesion of Fee of Fee-Space Popagato Space Popagato Σ Σ ] ep[ ~ ~ d c i c i π = = Σ Σ ep ep ep ep ep F d d F d d F π π = F ep 0 0 Befoe Popagation: Befoe Popagation: Afte Popagation: Afte Popagation:

6 Stead-State State Simulation amples Wavefonts at F it and afte Popagation in Space = 5 GeV σ = 0. µm σ =.0 µ λ u = 48.5 mm B 0 = 0.93 T λ Å At F it A B C D F d c b a 500 m At 500 m

7 Stead-State State Simulation amples Peculiaities of Satuated / Supeadiant SAS Wavefonts Phase Coection & Focusing fficienc A Intensit at ens Phase Coection Intensit in Image Plane Φ co = ag[ep[ iπ λ iφ0]/ in ] F lens phase co. image plane B c b a S = 500 m S = S = 5 GeV σ = 0. µm σ =.0 µ λ u = 48.5 mm B 0 = 0.93 T λ Å C SPI 000

8 Focusing of Undulato adiation Plana Undulato ven Hamonics = 6 GeV; K =.; 38 4 mm; ε = kev -nd hamonic : imaging; 30 m fom middle of Undulato to Thin ens & Phase Coection NIMA 999

9 Focusing of Undulato adiation Helical Undulato Hamonics n > = 6 GeV; B ma = B z ma = 0.3 T; 8 5 mm; ε = 4.0 kev -nd hamonic : imaging; 30 m fom middle of Undulato to Thin ens & Phase Coection

10 Time-Dependent Wavefont Chaacteization as Measuable Quantities: Intensit in Time and Fequenc domains zobs t ~ o Powe Densit and Spectal Fluence ~ z obs zobs t dt = const ~ Fluence ~ zobs d Powe and Spectal neg ~ zobs t dd ~ zobs dd Simple Optical Schemes: Young s Double-Slit Intefeence Scheme - to test Special Coheence F Two Slits ens M Image Plane Double-Slit Intefeence Scheme with Gating - to test Tempoal Coheence F Gating Image Plane Monochomato efocusing Scheme - often used in VUV / Soft X-a Beamlines F Gating M it Slit M Sample Plane

11 Time-Dependent Simulation amples SAS Pulse Pofiles and Specta at F it -Beam: = GeV I peak =.5 ka A: Seeded F opeation Peak Powe vs ong. Position σ t e ~ 00 fs ε = ε =. π mm-mad P ma ssed ~ 50 kw σ t seed ~ 5 fs Undulato: Powe vs Time K ~.06 λ u = 30 mm tot ~ 5 m h 0 = 00.5 ev AcnCiel phase neg Spectum GNSIS B: SAS not satuated

12 Time-Dependent Simulation amples Intensit Distibutions at F it A: Seeded F opeation Powe Densit Cuts at Pulse Cente Peak Spectal Fluence Tansvese Cuts Fluence B: SAS not satuated

13 Time-Dependent Simulation amples Wavefont Chaacteistics in Image Plane of Young s -Slit Intefeomete Two Slits A: Seeded Spectal Fluence vs Photon neg and Vetical Position at = 0 Powe Densit vs Time and Vetical Position at = 0 F d = mm ens f = 8 m f =.6 m ~0 m ~3 m Image Plane Fluence /Time-Integated Intensit vs Hoiz. and Vet. Positions vs Vet. Position at = 0 B: Stated fom noise

14 Time-Dependent Simulation amples ffect of Gating: Seeded F Wavefont Befoe and Immediatel Afte Gating Fluence in Tansvese Planes Pependicula to Optical Ais Befoe Gating Afte Gating Plane Gating Powe Densit Afte Gating at Diffeent Vetical Positions Powe vs Time 90 - θ i ~.5 ~ 50 l/mm mλ = d[sinθ sin θ ] m i

15 Time-Dependent Simulation amples Wavefont Chaacteistics in the Image Plane of a -Slit Intefeomete with Gating A: Seeded Spectal Fluence vs Photon neg and Vetical Position at = 0 Powe Densit vs Time and Vet. Pos. at = 0 F Gating Slits M Image Plane Fluence /Time-Integated Intensit vs Hoiz. and Vet. Positions vs Vet. Position at = 0 Powe vs Time B: Stated fom noise

16 Time-Dependent Simulation amples SAS Wavefont Chaacteistics in Image Plane of a -Slit Intefeomete with Gating B-: SAS pulse Spectal Fluence vs Photon neg and Vetical Position at = 0 Powe Densit vs Time and Vet. Pos. at = 0 Fluence /Time-Integated Intensit vs Hoiz. and Vet. Positions vs Vet. Position at = 0 B-: SAS aveage of 0 pulses

17 Time-Dependent Simulation amples Wavefont Cases fo Simulation of Popagation though a Monochomato A: : Seeded F opeation Peak Powe vs ong. Position F Gating M it Slit 30 µm M ~ 0 m ~ 4 m ~ m ~ m neg Spectum Sample Plane B-: : SAS: Two cases with slightl shifted Specta

18 Time-Dependent Simulation amples Wavefont Popagation though a Monochomato F Gating M it M Slit Sample Plane A Spectal Fluence Befoe it Slit vet. cuts at = 0 Fluence Afte it Slit Spectal Fluence at Sample vet. cuts at = 0 Fluence at Sample B- B-

19 Time-Dependent Simulation amples Wavefont Chaacteistics at Sample Plane of a Monochomato F Gating M it M Slit Sample Plane A Spectal Fluence vs photon eneg at = 0 neg Spectum Powe B- B-

20 Pactical Aspects of Time-Dependent Wavefont Popagation Calculations All eamples wee calculated on a egula PC with GB of AM 3-bit Windows An entie wavefont sampled vs Photon neg /Time Hoizontal and Vetical Positions /Angles was kept in memo duing popagation - tpical sampling: ~300 phot. en. 400 h. pos. 400 v. pos - use of wavefont esizing / esampling - popagation simulations took much less CPU time than calculation of oiginal SAS wavefonts To facilitate data echange and automation of simulations GNSIS.3 has been integated into mission pat of SW afte convesion b FC Font-nd used b SW: IGO Po - poweful scipting envionment eas to sequence / automate simulations - instant gaphics / visualization

21 Possible Applications Paticipation in F mission Simulations: - tanspot of seeding photon beam - wavefont popagation in F oscillatos - use of optical elements e.g. gatings / cstals in single-pass Fs lecton Beam Diagnostics and Intepetation of F peiments data Optimization of Optical Beamlines fo 4 th geneation S Souces peseving coheence keeping tack of wave-optics phenomena in fequenc and time domains Towads Simulation of Use peiments - imaging on the limits of phsical optics phase-contast diffaction-enhanced with magnetic effects time-esolved - diffaction: fom cstals to molecules? - time-esolved spectoscopies? -

22 Acknowledgements J.-. aclae P. lleaume A. Snigiev SF P. Dumas P. o SOI G. Williams Jab M. Bowle 4GS N. Vinokuov O. Shevchenko BINP. Saldin DSY UOF