Accelerator Physics Xray Sources and FELs. A. Bogacz, G. A. Krafft, and T. Zolkin Jefferson Lab Old Dominion University Lecture 12

Transcription

1 Acclato Physics Xay Soucs a FELs A. Bogac G. A. Kafft a T. Zolki Jffso Lab Ol Domiio Uivsity Lctu

2 High Fil Spctal Distibutio ; si φ π pp c E Γ Ω ; cos * si si cos si cos θ β θ θ θ θ θ π pa S S c E Ω.6 I th bam fam wh / si / si ; ; ; π π π N f f N

3 I th lab fam E pa Ω E pp Ω f c γ * N c γ * S + S / β * cosθ si β * cosθ ; θ si si φf S S N γ * ; θ γ * γ * β * cosθ si θ cos cosθ β * siθ β * cosθ siθ cosθ + φ f N πn β * cosθ / β * π β * cosθ / β * ; θ

4 [ ] θ φ θ φ f S S c E N pp ; cos si si / + Ω θ θ θ θ θ β β θ f S S c E N pa ; cos si si cos * * cos + Ω f N is highly pak with pak valu N aou agula fqucy as / * * cos * * + θ γ β γ θ β β θ K

5 Egy Distibutio i Lab Fam E pp Ω c si φ si θ cos [ S + S / ] f ; θ S cosθ β * β * cosθ si E θ pa fn Ω c S + siθ cosθ Th agumts of th Bssl Fuctios a ow ξ ξ siθ cosφ β * + cosθ / c / c φ siθ cosφ N β * cosθ cosθ ; θ K γ β * K β * cosθ 8γ β.7

6 F I th Fowa Dictio I th fowa ictio v hamoics vaish +k tm vaishs wh Bssl fuctio o-o at o agumt a all oth tms i sum vaish with a pow high tha as th agumt gos to o a fo o hamoics oly +k - cotibut to th sum K E pp Ω E pa Ω γ c γ c K F F K K si cos φ f φ f N N ; θ ; θ J J γ 4 + β * γ 4 + K / 4 + K / K K

7 Numb Spctal Agula Dsity Covtig th gy sity ito a umb sity by iviig by th photo gy o t fogt both sigs of fqucy! N pp / Ω F αγ K si φ f N ; θ N pa / Ω F αγ K cos Pak valu i th fowa ictio φ f N ; θ N / Ω αγ N tot F K

8 Raiatio Patt: Qualitativly No-o Agula Dsity Emissio at a Giv Fqucy θ y Ctal Co θ l l θ Doppl Dowshift Hamoic Raiatio Ctal co: high agula sity gio aou fowa ictio

9 Hamoic bas at Dimsio Estimats θ l l + γ K / Ctal co si stimat by quiig Gaussia istibutio with coct pak valu itgat ov soli agl to th sam umb of total photos as itgatig f + K / λ λ c / θ γ N L Much aow tha typical opig agl fo b

10 Numb Spctal Dsity Flu Th flu i th ctal co is obtai by stimatig soli agl itgal by th pak agula sity multipli by th Gaussia itgal F N tot Ω θ π F I παn Δ g K g K + K / F K /

11 Pow Agula Dsity E pp Ω si φ αnh θ [ S + S / ] si θ cos φ E pa Ω αnh θ S cosθ β * β * cosθ si + S siθ cosθ θ Do t fogt both sigs of fqucy!

12 φ θ β β θ θ β γ α φ θ β γ α cos cos * * cos cos * 4 si cos * 4 Ω Ω pa pp K NF N K NF N / 4 / 4 / K K J K K J K K K F Fo K lss tha o of o o Compa with.

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14 ERL light souc ia Thi gatio light soucs a stoag ig bas facilitis optimi fo pouctio of high billiac -ays though spotaous sychoto aiatio. Th tchology is matu a whil som impovmt i th futu is likly o ought to ask whth a altativ appoach ists. Two othogoal ias both liac bas a XFEL a ERL. XFEL will ot b spotaous sychoto aiatio souc but will liv GW pak pows of tasvsly coht aiatio at vy low uty facto. Th souc paamts a vy itstig a at th sam tim vy ifft fom ay istig light souc. ERL aspis to o btt what stoag igs a vy goo at: to povi aiatio i quasi-cotiuous fashio with supio billiac moochomaticity a shot pulss.

15 Coht o icoht? Raiatio fil fom a sigl k th lcto i a buch: Ek E p itk Raiatio fil fom th whol buch buchig facto b.f. Raiatio Itsity: I I N b. f. p it N b. f. N k log buch : > icoht covtioal SR sigl lcto shot buch o b μ-buchig:. f. ~ / I > coht FELs SR N I N b. f. I ~ IN ERL ha -ay souc is visio to us covtioal SR k

16 Dma fo X-ays Io chal poti ~85% stuctus by -ay cystallogaphy CHESS 3 Nobl Pi i Chmisty: Roick MacKio Rockfll Uiv. st K + chal stuctu by -ay cystallogaphy bas o CHESS ata 998

17 X-ay chaactistics fo poply tu uulato: X-ay phas spac is a plica fom lcto buch + covolutio with th iffactio limit ially o wats th phas spac to b iffactio limit i.. full tasvs cohc.g. ε ms λ/4π o. Å fo 8 kv X-ays Cu K α o. μm omali at 5 GV Flu Bightss Billiac ph/s/.%bw ph/s/ma /.%bw ph/s/mm /ma /.%bw

18 Itouctio Lt s viw why ERL is a goo ia fo a light souc Citical lcto bam paamts fo X-ay pouctio: 6D Phas Spac Aa: Hoiotal Emittac { } Vtical Emittac {y y } Egy Spa & Buch lgth {ΔE t} Numb of Elctos / Buch Buch Rp Rat: I pak I avag

19 Itouctio: aiabatic ampig p p p p θ p liac θ p lcto buch ε p ε ε p gomtic { θ } ε ε βγ omali p { } mc ε is ivaiat sic {; p mc βγ θ } fom caoically cojugat vaiabls

20 Itouctio: stoag igs I Equilibium Quatum Ecitatio vs. Raiativ Dampig E ph ρ p B t E & ~ N phe ph Emittac ho. Egy Spa Buch Lgth

21 Itouctio: stoag igs II Touschk Effct p i p out p out p i Bam Liftim vs. Spac Chag Dsity

22 Why a ERL? ESRF 6 ma ε 4 m ma ε y. m ma B ~ ph/s/mm /ma /.%BW L ID 5 m ERL 5 - ma ε ε y. m ma B ~ 3 ph/s/mm /ma /.%BW L ID 5 m ERL o compssio ERL w/ compssio ESRF t

23 Compaig pst a futu soucs I lcto bam billiac / ε + λ / 4π ε y + λ / 4π lcto bam moochomaticity / 5 / E E A/m-a ma N u A/m-a compas billiac fom two shot itical K N u uulatos A/m-a ma N u compas maimum achivabl billiac

24 Agstom billiac compaiso ERL btt by ERL mittac is tak to b PRSTAB ε [mm-ma].73+.5/ [mm].3 q[c] plus a facto of mittac gowth fo hoiotal

25 Coll visio of ERL light souc To cotiu th log-staig taitio of pioig sach i sychoto aiatio Coll Uivsity is cafully lookig ito costuctig a fist ERL ha -ay light souc. But fist SASE?

26 N fo th ERL pototyp Issus iclu: CW ijcto: pouc i avg ma q buch ~ 8 3 MH ε < mm m low halo with vy goo photo-catho logvity. Maitai high Q a E acc i high cut bam coitios. Etact HOM s with vy high fficicy P HOM ~ pvious. Cotol BBU by impov HOM ampig paamti i th. How to opat with hi Q L cotol micophoics & Lot tuig. Pouc + mas. t ~ fs with q buch ~.3.4 C i avg < ma usta / cotol CSR usta limits o simultaous billiac a shot pulss. Chck impov bam cos. Ivstigat multipass schms. Ou coclusio: A ERL Pototyp is to solv outstaig tchology a acclato physics issus bfo a lag ERL is built

27 Coll ERL Pototyp Egy MV Ma Avg. Cut ma Chag / buch 4 pc Emittac om. mm m@77 pc Ijctio Egy 5 5 MV E Q Buch Lgth. ps

28 Coll ERL Phas I: Ijcto Ijcto Paamts: Bam Egy Rag 5 5 a MV Ma Avag Bam Cut ma Ma Buch Rp. 77 pc.3 GH Tasvs Emittac ms om. < b μm Buch Lgth ms. ps Egy Spa ms. % a at uc avag cut b cospos to 77 pc/buch

29 To la mo about Coll ERL Two wb-sits a availabl Ifomatio about Coll ERL X-ay scic applicatios oth lat pojcts wolwi ERL tchical mmoaum sis

30 B Uulato Wiggl h h h h whit souc patially coht souc powful whit souc Flu [ph/s/.%bw] Bightss [ph/s/mm /m /.%bw] Flu [ph/s/.%bw] h h

31 y Uulato Raiatio fom Sigl S N S K /γ θ Elcto λ N S N B y B si k K 93.4B[T] λ p[m] Halbach pmat magt uulato: B[T] 3.33p[ κ κ ] fo SmCo 5 h κ gap / λ p p λ p Appoachs:. Solv quatio of motio tivial gab Jackso a calculat ta pottials ot so tivial usually o i th fa fil appoimatio. Foui Tasfom th fil s by th obsv to gt th spctum. Mo ituitivly i th lcto st fam:. Doppl shift to th lab fam aly simpl hamoic oscillato aiatio. 3. Doppl shift Thomso back-scatt uulato fil photos. O simply 4. Wit itfc coitio of wavfot mitt by th lcto.

32 Ituitiv ustaig of uulato aiatio P Ω ~ γ P Ω off-ais o ais Δ ~ N λ λ / γ p p Θ i fam si Θ P Ω Δ h N back to lab fam aft pi-hol aptu λ p λ + K + γ θ γ Δλ ~ λ N p fo fi θ oly!

33 High Hamoics / Wiggl K K << > motio i fam K uulato K > wiggl 3K K 4 7 c citical hamoic umb fo 6wiggl 548 i aalogy to c of big magt K c 4 P Ω log spiks cotiuum b v N 3Bγ c m ~ γ wiggl o wiggl a b spcta aft pi-hol aptu log

34 Total Raiatio Pow I P tot π E[GV] K α h K + K N o P [W] 76 L[m] I[ 3 [cm] A] tot λ.g. about photo fom ach lcto i a -pol uulato o kw c.w. pow fom m istio vic fo bam cut of 5 GV K.5 λ p cm Not: th aiat pow is ipt fom lcto bam gy if o ca kp B λ p cost whil λ p ~ γ to povi th sam aiatio wavlgth..g. low gy sychoto a Thomso scattig light soucs Howv most of this pow is isca bw ~. Oly a small factio is us. p Raiatio N wavlgth. Å if a ha -ay souc bw - -4 small souc si & ivgc tmpoal cohc spatial cohc

35 Uulato Ctal Co Slct with a pi-hol aptu th co: to gt bw: + K θ c γ N Δ ~ N Flu i th ctal co fom th hamoic i bw Δ / : λ L N& ph Δ I παn gk I g K πα Not: th umb of photos i bw ~ /N is about % ma of th umb of fo ay-lgth uulato Uulato fficicy : P P c tot 3g K K + K N p Fuctio K g K + [ JJ ] K

36 A Wo o Cohc of Uulato Raiatio cotai i th ctal co is tasvsly coht o bam mittac! appat souc isk L θ c R Youg s oubl-slit itfc coitio: R ~ λ i Fauhof limit: ~ θcl θ c ~ λ / L θ c ~ / R sam as ctal co Spatial cohc ms: θ c λ 4π Tmpoal cohc: l λ /Δλ Photo gacy: c Δ c & N ph c t c tc lc / c -ay souc Δ c Rigs < ERLs > XFEL >> Nt w will stuy th ffct of fiit bam 6D mittac o uulato aiatio.

37 Bightss Dfiitio: Gomtic Optics Bightss is a masu of spatial tasvs cohc of aiatio. Spctal bightss p. % BW is usually quot as a figu of mit which also flcts tmpoal cohc of th bam. Th wo spctal is oft omitt. Pak spctal bightss is popotioal to photo gacy. Fo th most pats w will follow K-J Kim s agumts gaig bightss fiitios. A ay cooiat i 4D phas spac is fi as Bightss is ivaiat i losslss lia optics as wll as flu: whil flu sitis a ot: ψ y 4 ; F B ; B F iv B F B F ; ;

38 Bightss Dfiitio: Wav Optics h lctic fil i fqucy omai is giv i ith cooiat o agula pstatio. Fa-fil agula patt is quivalt to th Foui tasfom of th a-fil cooiat patt: A wo of cautio: bightss as fi i wav optics may hav gativ valus wh iffactio bcoms impotat. O way to al with that is to valuat bightss wh iffactio is ot impotat.g. a us optics tasfom thaft. ik E E T c B h + ξ ξ ξ ξ ε ; / ; / ; * y ik y E y E y T c h + λ ε ; / ; / * λ ; ; E E E E ik ik

39 Diffactio Limit Gaussia las bam quatio: With cospoig bightss: cot p R ik w k i w w E E R / R w w + λ π / w R / R R + + p ; B B / / kw w R π λ / 4 / λ / B F coh F B π

40 Effct of Elcto Distibutio Pvious sult fom uulato tatmt: Th fil i tms of fc lcto tajctoy fo i th -lcto is giv by: Fo bightss w to valuat th followig smbl avag fo all lctos: tm is th FEL tm. Typically so oly th st tm is impotat. / h 4 ; β π λ πε t t c E t t i / i i i ; ; c t i E E N E E E E i i i ; ; ; ; + j i j i ; ; E E N k N N << k N phas of i th -lcto

41 Effct of Elcto Distibutio ; ; ; ; i i i ik E E N E E v ; ; i i B N B f B N ; ; lcto istibutio Bightss u to sigl lcto has b alay itouc. Total bightss bcoms a covolutio of sigl lcto bightss with lcto istibutio fuctio. Bightss o ais u to sigl lcto: / ; λ F B flu i th ctal co

42 Fiit Bam Emittac Effct Ofttims bightss fom a sigl lcto is appoimat by Gaussia: B ; F λ / p + Icluig th lcto bam ffcts amplitu a sigma s of bightss bcom: λl / 4π λ / L B; F π T T Ty Ty T + + a + L + 36 L T + Ty + y + y L + 36 ψ L T y + y

43 Matchig Elcto Bam Match β-fuctio is giv by bam waist at th ct of uulato: opt β / / π y L Bightss o ais bcoms: B ; F λ / ε ε + + y λ / 4π λ / 4π tasvsly coht factio of th ctal co flu Match β-fuctio has a boa miimum fo ε / λ / 4π << o ε / λ / 4π >> mi fo β Lε / λ also if ε ~ λ / 4π T T mi fo β L / π opt β 6β L is still accptabl mi fo β λl /8π ε

44 Egy Spa of th Bam Egy spa of th bam ca ga bightss of uulatos with may pios. If th umb of uulato pios is much gat tha Nδ. / δ bightss will ot gow with th umb of pios. Maimal spctal bightss o ais bcoms B; F λ / ε ε + + y λ / 4π λ / 4π + N N δ

45 Photo Dgacy Numb of photos i a sigl quatum mo: Pak bightss is a masu of photo gacy E.g. maimum photo gacy that is availabl fom uulato o-fel h h h h h t E y k k ψ c B pak c 3 λ λ Δλ Δ K g N K g N N y c c : howv mo typically 3 3 ma ε ε ε λ α λ α Δ Δ iffactio-limit mittac omiat

46 Mo aig o sychoto aiatio. K.J. Kim Chaactistics of Sychoto Raiatio AIP Cofc Pocigs pp R.P. Walk Istio Dvics: Uulatos a Wiggls CERN Acclato School pp.9-9 a fcs thi. Availabl o th Itt at 3. B. Lgl Cohc i X-ay physics Natuwissschaft 88 pp a fcs thi. 4. D. Attwoo Soft X-ays a Etm UV Raiatio: Picipls a Applicatios Cambig Uivsity Pss 999. Chapts 5 Sychoto Raiatio a 8 Cohc at Shot Wavlgth a fcs thi.

47 Oscillato FEL

48 Egy Rcov FEL

49 Jffso Lab IR DEMO FEL Wiggl assmbly Nil G. R. t. al Physical Rviw Ltts 84 6

50 IR FEL Upga 5 PowkW PowkW 3 Gai 3 Gai Wavlgthµm

51 SASE FEL

52 XFEL.3 GH Cavitis

53 XFEL Uulato

54 LCLS Uulato