WAKEFIELD UNDULATOR RADIATION

Transcription

1 WKEFIELD UNDULTOR RDITION. Opanasnko NSC KIPT, UKRINE MECHNISM OF WFU RDITION SPECTRL -NGULR CHRCTERISTICS MODEL OF WF UNDULTOR WKEFIELD DISTRIBUTION HRD X-RY GENERTING POSSIBILITY of EXPERIMENTL STUDY

2 MECHNISM OF WFU RDITION 2 bunch of N lcons WF Undulao Radaon n D n 2 2γ Wakflds (Cohn Paamc-Chnko-Radaon) 2π ( h) ω h = n D

3 MECHNISM OF WFU RDITION 3 Wak foc n fom of Floqu s ss ()()()2z,,pzpDFFzπ = p=- lnang anss wak foc (p ) can g s o undulang h pacls wh anss locy ()()()2,,2pzpDcKπττγ = p γ >> 1 Undulao paam ()()()(),,ppzfdkpmcττπ =

4 MECHNISM OF WFU RDITION 4 Cohn wffn WF WFU RDITION 23phwfPNFN No cohn 224phwfPNFN Cohn

5 Mhod Radaon acon foc h chag of pacl s dsbud, ρ=_f[-()] h quaon of moon flds a found fom by Hamlon mhod (V.Hal) Bass V.L.Gnzbug, V.Ya.Edman (1959).I.khz, Ya.B.Fanbg, G.Ya.Lubask (1955) () x z y ( ) ( ) ( ) ( ) [ ] + = - H, E, 3 d 1 d d f c m γ H E o c = Φ =, 1 + = Δ c c c ρ π ( ) ( ) ( ) = q, R ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ).. d d 4,, * * 2 2 c ñ o o V c c o = < ω ω ω ω ω ω ω F f[-()] δ[-()] 5

6 Slf-wak foc 6 f spac ang dffacon ang ω ω cu off ω=ck ω= k Egnfuncons ω > ω cu off k ( ) = π a, l c 4, l ω << ω cu off g n= ( n ( ) = ) ( ) h n z Zoh od appoxmaon = = + F ( ) = 2 p= w ( ) = z,, ( p) pω h ph hamonc of wakfuncon + c h n, k ( p w ) D 2 4c V ( n g ) z, j cll n= j dω dh = j ( n+ p) ( n+ p) Ωp ( gz, g z, j g j ω ω n+ p, j

7 Th fs od appoxmaon ()()(),pppcγ Ω =+=+ K ()()(),,2pppcpδ Ω =++=++Ω K ()()()()22p-pppmc +ΩKww ( ).. d d ) ( 2 c c m m p p p + = Ω w γ γ F h small paam fom h quaon of moon h cocd law of moon Radaon pow ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) lm,, 1 lm * * 2 2 c ñ d d V c d d P c o + + = < ω ω ω ω ω F 7

8 Radaon pow n h fs od appoxmaon ()()()()()()()()(){} sn1sncos,,161snsn,,Rsn2sn,,cos1cos1pp 8 ω > ω cu off f spac ang ()lm pppupppmcγ<<= dffacon ang R ( ω θ, p) ω < ω cu off ()()()()22,,11222jjjjpnnpnpzznpcllDDPggdVpdhβωγπ+ ++ = = =+ Infnc of Chnko and Undulao-yp adaon Rsonan condon, ω 2 ω 1 cos β θ β Ωp Ωp ω 2 h = 2 nω

9 WFUR SPECTRL -NGULR CHRCTERISTICS 9 Sngl- Pacl Radaon ()1pK<< Th spcal-angula pow dnsy of had UR md sponanously by a sngl pacl of h bunch ()(){()()()()()()}()() sncos,,1snsn,,8sn1cosRsn2sn,,1cosppuxypuuzuppuxyuzuudPNKR H dω=snθ dθdϕ 2uzDωπ=

10 WFUR SPECTRL -NGULR CHRCTERISTICS 1 Sngl-Pacl Radaon ()1pK<< Rsonan fquncs of h WFUR _ h hamoncs ()()()()()()12221,,,21,2qpuqKpτωθτωγγτθ = =++ Th spcal-angula phoon flux dnsy of h _ h hamoncs n h fowad dcon ()()()()()()2222sn,1,1372puppuuuppNNdpKddpNθωπωγτωτωωωππω =

11 1/f f WFUR SPECTRL -NGULR CHRCTERISTICS bunch of N pacls Bam Radaon 11 pulsponttη= Tpuls Tpon Puls duy faco Th spcal-angula dsbuon of phoon flux dnsy of ()()()()()()()()()() ,sn,,,137ppbamufbuSuppufbSupdNdfNddfddddpNDNNfddfupNθθπητ h _ h hamonc fom a h fowad dcon ()()()()2,,ppFuNττ = Th _ h hamonc of wak funcon

12 FORMULS FOR QUNTITTIVE ESTIMTIONS WF chaacscs of wakly cougad wagud 12 Radus of wagud ()()211xppppbzbzbzDπεε = =+=+ ()1, zbdε WF undulao paam ()()()()()(),,,,,,,,,,1,,,,,sn2sn2cos,,8xpxp22221mmspmsppmspmspbpmsmsmsmspmspmmKNBbbωτωτωτωτϕϕτεωτωτδ == ΔΔ ()()(),,,mmsmsmmsjbbjµµ ()()()2,,22,,mmsmsmmsmsJbbmBbJmµµµ

13 XILLY SYMMETRICL MODEL OF WKEFIELD UNDULTOR Th WFU and lcon bunch paams fo poducng 792 kv phoons Pod D 3 µm ag adus b 3 µm Engy of lcons W 5 GV Bunch lngh σ z 3,3 µm Rla amplud of cougaons Δ 3 µm Numb of pods N u 1 Bunch dsanc fom axs b 26 µm ag bam cun I 1 m Th bam paams a ypcal fo concpual pojcs of synchoon X-ay soucs basd on Engy ERL.

14 14 WKEFIELD DISTRIBUTION INDUCED BY UNIFORM CHRGED BUNCH Th la ngy losss p bunch chag along h bunch 3 µm bunch lngh 3 µm bunch lngh Th dsbuons of ()()()(),,ppzfsdkspmcπ = h undulao paam K p bunch chag

15 HRD X-RY GENERTING 15 ( y s n d x u l F Bunch lngh 3 µm Bunch lngh 3 µm Chag of h bunch ( nc ) Th.8 MV phoon flux dnsy.s. bunch chag.

16 WF UNDULTOR S ULTR-FST X-RY SOURSE 16 Pod D 397 µm ag adus b 115 µm Rla cougaon ε 1.65 Bunch dsanc fom axs b 54 µm Bunch dam 2ρ b 4µm o o h P f o b m u N SR XFEL, Eγ=2 kv Chag of a bunch ( nc ) bunch duaon - 1 fs bunch duaon - 3 fs 1 fs 3 fs WFU, Eγ=26.5 MV

17 FORMULS FOR QUNTITTIVE ESTIMTIONS 17 WFU adaon Spcal flux (phoons/s) no a small Δω of h _ h hamoncs ()()()222ppuapdNNfKdωαγωΔ=ΩF Full flux n h cnal con ()()22ppfullaNfKπα=F 22uNπγΔΩ= no FWHM bandwdh ()punωωδ ()2...,...bSddfττ = Bunch aagng

18 FORMULS FOR QUNTITTIVE ESTIMTIONS 18 D 2a 2b x d Loss faco ()()2,121,1sn222qqqdJabDcZdkdbDJDθ z cll cll 1 cll 2 WF undulao paam ()()()()()()()()()()21,1,2,,,,sn2sn22222,22sn222qqqqpqppqqqpqpqpqqpqdddppIkIkNkDDDKdddmcIkaIk

19 s g n a ( n o a d a R U F W1.1 5 RDITION BY HIGH ENERGY ELECTRON BUNCH p Und-smaon of phoon flux DLW mod D (mm) d(mm) a(mm) b(mm) L(m) STRUM-9 4π/ l a n C1.1 5 SLC-yp 2π/ ) s / h ( n o C f o h g 1 n 1 l 1 a.1 W Elcon Engy (MV) STRUM9 (4p/3) (KIPT) 2p/3 (SLC) 77 nm - upp lm of sbl spcum n x u l 1 F l l u F Chag of a bunch ( nc ) STRUM9 (4p/3) (KIPT) 2p/3 (SLC)

20 Upp-smaon of anss manc 2 D N u D u ()2,max4bnuaNDεγ = d b ρb θ bunch axs a b 2,222bbnuaNDθθρσσεγσσγσθσ= ==== n a 5 4 m 3. m o n adus (mm) STRUM9 (KIPT) SLC scon 4baσ =

21 RDITION BY LOW ENERGY ELECTRON BUNCH Und-smaon of phoon flux 21 U F W 9 f o 8 h g n l a W Pod of Sucu (mm) Elcon ngy, 1 MV Elcon ngy, 8 MV upp lm of sbl lg und lm of sbl lg TU/ Phoo-njco Engy: Pak Cun: Emanc: Lngh: Chag: lcon ngs 8 1 MV 1 MV 1 k 1 mm mad 1 fs 1 pc Pods mm

22 RDITION BY LOW ENERGY ELECTRON BUNCH Und-smaon of phoon flux K Opmzaon Th opmal dmnsons of a S-band wagud mod D mm d mm a mm b mm 4π/ Phas Shf ( p ) p=1 (numb of wakfld spaal hamonc) p=2 p=3 mod 4π/3 Th opmal dmnsons of a S-band wagud Rducon ao, n D' mm d' mm a' mm b' mm

23 RDITION BY LOW ENERGY ELECTRON BUNCH Und-smaon of phoon flux 23 ()()22ppfullNKπα=F n o o h P f o b m u N Chag of a bunch ( nc ) Scalng - n=2 Scalng - n=15

24 Upp-smaon of anss manc 24 Rducon D' d' a' b' ao, n mm mm mm mm ε m m m m ( n adus (mcon) n=15, h opmal 4p/3 n=2, h opmal 4p/3

25 RDITION BY LOW ENERGY ELECTRON BUNCH WFU adaon fom wakly cougad wagud 25 Wagud Pod D.4 mm ag adus b.1 mm mplud of cougaons ε 1.65 Numb of pods N u 3 Bam Engy W 1 MV Duaon Δτ 1 fs Dsanc fom axs b 75 µm

26 RDITION BY LOW ENERGY ELECTRON BUNCH WFU adaon fom wakly cougad wagud 26 h p ( x u l F k a P Chag of a bunch ( nc ) b/rmn=.75 n o o h P f o b m u 1 N Chag of a bunch ( nc ) b/rmn=.75

27 CONCLUSION Fo xpmnal sudy WFU adaon ph/sc n S-band sucus, h lcon bams a qud wh h paams : : bunch chag 1 nc, lcon ngy 1 _V bam adus 1 mm nomalzd manc (fo 3 m scons ) 15 µm SLC -12 nc

28 2. Fo obsaon WFU adaon 1 2 ph/bunch wh TU/ Phoo-njco, I s qud h paams sub-mm cougad wagud wh : pod.3.6 mm anss szs.1-.2 mm bam adus 1 mm nomalzd manc 1 µm adus bam 8 µm 28

29 29 3. Fo xpmnal sudy WFU adaon ph/sc by sho pulsd bams n S-band sucus (2π/3, 4π/3) h lcon bams a qud wh duaon 1-8 ns chag of puls 1 nc, lcon ngy 1 _V bam adus 1 mm nomalzd manc (fo 3 m scons ) 15 µm