LIMIT AND ITS FUNDAMENTAL LIMITS
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1 FEL COHERENCE C BELOW THE SHOT-NOISE OS LIMIT AND ITS FUNDAMENTAL LIMITS A.Gor, E.Dyunn Tl-A Unrty Fac. Of Engn., Dpt. of Pycal Elctronc, Tl-A, Iral FEL8 KOREA
2 Nw Concpt: SASE (No Mnmaton I t pol to nanc cornc and rlax dng powr rurmnt for XUV FEL y rducng t nput no? Wat ar t fundamntal lmt of FEL cornc? Not: T locty and currnt ot no trm ar corrlatd at t ntranc to t wgglr! In t art of mcrowa tu, cm for low-no -am tu amplfr wr dlopd. Elctron am no dynamc n t optcal rgm wa ord n SLAC and By.
3 Small Sgnal FEL Modl (Lnar Rpon n(r, t n [ ] t n (r, (r + R [ t ( r, ] ( r, t ( r + R J(r, t J E(r, t R C [ ] t J (r, (r + R (E (r k t
4 ( (H Laplac ( H k E E EE C C ( ( ( ( + + k k k k k j E j j E j E j E j EE j k w w j C C ( ( ( ( ( ( 3 δ j j j ( ( 3 ( ( k k k 3 pr j pr j j + Γ + θ θ δ θ θ δ δ [ ] k j j H( R δ E. Dyunn, A. Gor, NIM A 593, 49 (8
5 P( L C ( L Cornt Start-Up EE E E H ( C ( + H ( ( + H ( ( FEL Amplfr (Sd Radaton Injcton: P( L EE ( C ( H G( θ ( P( Pr-uncd (uprradant FEL*: P( L H E ( ( + H E ( ( *I.Scntr, A.Gor, NIM, A37, 4 (984, M. Arl, A. Gor, PRL, 86, 56 (, A. Gor, PR-ST-AB, 8, 37 (5
6 Incornt Start-Up Spctral Powr: dp( L d nco C ( L T T EM no amplfcaton: dp ( dp( L EE d H ( d T rad no T Spontanou mon & SASE: E H ( dp( L d am no ( + H T E ( ( T
7 SEED-Radaton. Currnt Sot-No (SASE Cornt powr domnat TOTAL SASE powr: P (L > P dp no HG d Δ p ( > I Γ I Δ HG dp d Δ HG ( p dp /d Δ S μ a 3 A m ε γβ w Cornt powr domnat FILTERED SASE powr: dpno P (L > d Δ VISA ΔHG.5 TH dp I /d Δ S TH p P > ( IΔ P Γ ( >.5 W. W
8 SASE Powr Control Ld P tot Wgglr Drft Scton Wgglr dp d I d (tartng from currnt ot-no at, E E. Dyunn, A. Gor, NIM A 593, 49 (8 H E tot a.u. P tot, ( - d Ldλp/ θ p *L d /
9 Dynamc of am plama longtudnal ocllaton n a drft rgon (mong fram 6 n, a.u Z, a.u. θ pr n, a.u Z, a.u. ' ( θ pr pr
10 Dynamc of random am plama longtudnal ocllaton n a drft cton (mong fram θpr
11 E-Bam Plama ocllaton dynamc n t non-radatng Scton: acclraton and drft cton.
12 Bam modulaton tranfr matrx ( L I( M( L ( V L V ( V ( γ ( γ ( ( ( Gnral Non-dpat cton: ( K > W > M( [ m / ] ( V a rlattc Cu kntc oltag K coφ w n φ n φ coφ K w φ Fat Acclraton: Drft Scton: φ prd θ prd L co φ W prd d φ n φ prd n φ co φ prd prd / W d φ L W μ ε ( k θ A φ d pr φ
13 Quartr Prod Plama Ocllaton n a Drft Scton For L θ prd : M W d W d φ If V (, tn : V I ( L ( L φ W I ( d
14 ( ( Lw C ( ( ( ( w H FEL V C C V LL w Acclrator + FEL V ( ( M acc I V ( c ( c C ( dp ( T C Lw d nco T ( ( E EV HTOT c + HTOTV c + H ( ( EE C ( ( H + EV H E H V M + H E E EV H M H M TOT FEL acc FEL TOT FEL acc EV FEL M V acc VV acc
15 Wt drft cton prcdng t FEL ( φ θ L FEL: A H H EV FEL E FEL Γγ I γ m φ p prd d Effct am no nput powr at FEL ntranc: Currnt tranfr Vl Vlocty tranfr << dp ( d n Γ p I co φ p 3 AW d n φ p δe d n p + Γ W d dp V p f 3 ( n φ + AW co d φ p V p δ δe n f Γ ( dp c A d c
16 out Wt drft cton prcdng t FEL ( φ θ L φ p prd d FEL: A EV H E FEL I HFEL Γγ γ m Effct am no nput powr at FEL ntranc: Γ ( dp p d n I dp V p ( d n I δ Γ Γ ( δ δ dp V p c d n I Γ Γ c
17 Mnmum am - no: o For AW Mnmum no at: φ d p d + 3AWd / AW dp d dp ( ( d n d φ n φ p ( dp V ( K dp d n φ p d n φp p ( dp d n φ p K r p γ γ γ β δe 3 / ( A kγ 3 dγ d β d μ ε I
18 Fundamntal Cornc Lmt A Conrat of moton n a non- dpat -am tranport cton: ( ( c ( V c δe c Mnmum nput no: dpn δec + d + mn kt Mcrowa/TH rgm: dp n δ Ec δ E + k BT d mn c Optcal rgm: dpn d mn δec +
19 CONCLUSION It pol to adjut t -am currnt ot- no ll y controllng t longtudnal plama ocllaton dynamc. T can ud to nanc FEL cornc and rlax dng powr rurmnt. Aftr lmnaton of ot no, IR/XUV FEL cornc ultmatly lmtd y t uantum nput no dp / d. Warnng: Cornc nancmnt lmtd y tranr Coulom cattrng (Borc ffct
20
21 Conntonal Tory: ( M I c C V ( Lw ( ( ( Lw H FEL ( ( V Lw C V ( I ( c M ( acc ( V c C ( dp ( T C Lw d nco T ( ( E EV HTOT c + HTOTV c + H ( ( EE C ( H E TOT H E FEL EV EV H TOT H FEL (
22 Conntonal o Tory: M I ( c c Γ dp p ( I d n δ Γ ( dp V ( dp d n d n δ δ Γ dp V c ( dp d n ( d n ( dp E d n k B c T Currnt ot-no Vlocty ot-no Kntc powr no Spontanou/lack-odyody
23 At t catod or Vrtual catod Currnt ot no: I V ( mc δγ Vlocty octyno: o Kntc powr: δ ( ( V ( mc γ f ( δ / E ff γ cγccδcmc c c ( k T c c j j ( δc ( j c j
24 Effct Input no ( dp ff dp w EE d n d H nco FEL ( ( ( L EE dp d Cornc condton: [ P ( ] >> Δ co ff n
25 Laplac Tranform: f ( d L{ f (} f ( C ( C ( ( + k + k H ( ( w ( + k + k w ( H ( Δ ( θ + θ ( θ pr ( θ I k p Q / I I p p Q I ( θ / I ( θ Q p k k p θ k k Δ ( θ ε a w 3 γβ A m w Q γ ( + θ Q μ 3 ( 3 a γ 3 w β 5 I I A k A m pr A JJ Γ k w ρ
26 Hg Gan Tnuou Bam Rgm ( ( ( ( 3 L 3 ( H HG + Γ Δ + p p k k I / 6 / 6 4 p k Q Q k I I Q /3 / 6 /3 / p k I Q I Q /3 / 6 4
27 Exprmntal Vrfcaton of Spac Carg and Trant Tm Rducton of No n Elctron Bam* db *C. C. Cutlr, C. F. Quat, Py. R. 8, 875 Dc. 95
28 Currnt Pr-uncng. Sot-No (SASE E μ-pr-uncng: Pp ( L, H ( n ( H Sot no: dp no ( L, d 9 3ΓL S p I Γ P p dpno > ΔHG d ( n > λ w Γ I L (VISA: >.% from am currnt I
29 Rlattc at tcextnton to of Cu ukntc tcvoltag otag mc V (, t [ γ (, t ] t V + R V ( ( ( mc V γ dv ( ( V ( dv ( [ ( ] γ [ ( ( ( ] γ m / (
30 Non Dpat cton φ V d d ( I ( ( φ ( U( ( d' / ( ' U I d ε A ( I ( d pr ( ε A θ ( ( ' θ pr ( pr ( ( [ ] ' pr rp n εmγ γ U d U ( θ ( U ( d pr
31 Poyntng Tm. For flowng carg ( + E H V J ê ρ μ H ε E V m γ γ ( (,V ( ( A ( ( L,V ( L { E,H } L
32 Non Dpat cton Extndd Cu Kntc powr tm: R [ ( L ( L ] R ( ( V [ ] V ( (,V ( ( A ( ( L,V ( L L
33 E-Bam Plama Dynamc n t non-radatng Scton: acclraton and drft cton Rlattc Extnon of Cu Kntc Voltag: mc V (, t γ (, t t V + R V ( ( [ ] ( ( γ ( ( ( γ / [ m / ] ( V
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