Summerstudents Lecture 2017 Photon Science

Transcription

1 Summestudents Letue 7 Photon Siene

2 DSY Mahine Histo mloees, Intenational Guests ( aentie, undegaduate, 5 PHD, Postdo) Annual Budget: M DSY founded 959 as an leton Snhoton Failit fo lementa Patile Reseah 964 DSY (Snhoton) e- 7.4 GeV 974 DORIS (Stoage Ring) m e+/e-.5 GeV (late 5 GeV) 98 HASYLAB@DORIS 984 Ugade with 7 Wiggle/Undulato Beamlines 99 Dediated SR Soue at 4.5 GeV 978 PTRA (Stoage Ring).km e+/e- 9 GeV 99 HRA (Stoage Ring) 6.km +/e- 9 GeV / 7.5 GeV (using PTRA as Booste) 997 FLASH (Fee leton Lase) 5 Dediated Use Failit 7 Shutdown of HRA and Reonstution of PTRA PTRA III 9 PTRA III Dediated SR Soue at 6 GeV (esentl most billiant SR soue woldwide) Shutdown of DORIS 4 FLASH II (tension of FLASH) Patiiation in the uoean XFL ojet

3 Snhoton Radiation wiggle / undulatos bending magnet stongl ollimated olaised ulsed Sektum eine time Wolfam Röntgen-Röhe high intensit wide setal ange

4 Snhoton Radiation fom Stoage Rings leton Beam Fousing magnets Insetion Devie Klston HF-Cavities Bending magnet evb mv ρ Bending magnet hoton beam Wiggle/undulato hoton beam

5 Mawell quations Fee sae, SI-units,, Gauss s Law fo -Field div ρ ε Chage is soue of eletial field. letial field lines divege Gauss s Law fo B-Field B divb Magneti field has no soue Magneti field lines do not divege Faada s Law of Indution ot B t Magneti flu densit hanges ause a losed eletial field (ul) Amee s iuital Law B ot B µ J + µ ε t letial uent and flu densit hanges ause a losed magneti field (ul) µ ε ε : feesaeemittivit µ : feesaeemeabilit

6 letomagneti Waves Fee Sae, no hages, no uents: B, t B, B t Identit: ( X) ( X) Leads to: B and B t t X Solution: Plane Waves v sin( ωt + k ) B B sin( ωt + k ) B ˆ n oagation ω π ν and k π λ ˆ n oagation neg flow densit (Pointing Veto) S ( B) 4π

7 t v t v t t t v Satial veto: {,,} Time t Gallilei-Tansfomation Rest fame

8 v t t β β Loent-Tansfomation, i i i v β β Length Contation Time Dilation d d Rest fame ) ( ) ( t t t β β Tansfomation of elativisti motions Sae-Time fou-veto

9 v β β Loent-Tansfomation, i i i v β β neg: m Rest fame Tansfomation of elativisti motions Momentum-neg fou-veto Momentum: v m m

10 Stati field of an eleti hage Unifom motion q Θ Obseve no eneg flow

11 Longitudinal aeleation(aallel to ) qa R sinθ T Θ R otb J + t q Aeleation a B S 4π B neg Flow (Ponting veto) S 4π nˆ

12 Tansvesal aeleation (eendiula to ) qa R osθ T Aeleation a q otb Θ J + B t S R S S neg Flow (Ponting veto) 4π 4π B nˆ

13 Total Radiation Powe 4 os sin 4 da n R a q SdA P Θ Θ Ω Ω π m a & sin Ψ Θ Θ d d R d m q P Lamo Fomula Sheial oodinates

14 Loent Invaiant Reesentation of Lamo Fomula m d d m q P d m q P Loent invaiant Momentum-neg fou-veto,,,

15 Linea (longitudinal aeleation along ) m m v m d v d beause ( m ) d + d, tdeivation:, substitute and ν d v d d d d d P q m d d d d d P linea q m d d amle: Linea eleton aeleato (Tesla) d/d 4 MeV/m ffiien η Plinea d P v d linea d e m 4 e v d d -6

16 Ciula (tansvesal aeleation along ) d d m q P / m R R R v d ω R m q P iula Note: 4. e oton eleton m m P P!

17 Satial Chaateistis of Snhoton Radiation I Deomosition of adiation ulse into lane wave omonents: i( ω t e k hase ) with k π nˆ λ ω nˆ ω [t - n -n -n ] ω[t -n - n - n ] ω [t - n -n -n ] ω[t - n - n -n ] ω[t - β - n -n - n +n β t] t ( ( t β t) β ) ωt ω[ ω[t + n+ n β ] β t] Relativisti Dole ffet

18 Satial Chaateistis of Snhoton Radiation II ω [t - n -n -n ] ω[t -n - n - n ] ω [t - n -n -n ] ω[t -n - n -n ] ω [t - β - n - n -n + n β t] n n n n n (+ β n n (+ β n β + n (+ β n ) ) ) n n n n + n osθ + n osθ sin sin Z: dietion of motion X: dietion of aeleation Θ: angle between given dietion and dietion of motion(z) Θ Θ ň Θ sinθ sin Θ (+ osθ ) Θ n β Θ 9 o n

19 Angula distibution of emitted adiation π π + + L (Rest sstem) L (Laboato sstem) 957 [GeV] amle PTRA III: 6. GeV 74 Θ.85 mad.5 o m

20 Angula distibution of emitted adiation π π + + L (Rest sstem) L (Laboato sstem) 957 [GeV] amle PTRA III: 6. GeV 74 Θ.85 mad.5 o m

21 Time stutue of adiation emitted b a single atile ρ t t t sin ρ Talo: 6 t d ρ sin s t s v ρ,v t P P / d / P ρ / / ρ amle: DORIS III 886 ρ. m t - s

22 Fouie Comosition Signal I(t) t I i ( ) ( ω) e ω t t A dω π Time, t Fouie Comonents A(ω) A π iωt ( ω) I( t) e ω ½ ω ω t - Fequen, ω ω 6 6 ε h t ρ ( ) m ρ

23 A onvenient fomula fo the itial eneg Citial neg ε h 6 ( ) m ρ with gives ρ ε [ m]. 5 BT [ ].665 [ GeV] [ GeV] BT [ ] Cental Foe Loent Foe evb mv ρ ρ eb v ρ amle PTRA III Patile neg Cuvatueadiusofbendingmagnets Magnetifieldofbendingmagnets Citial hoton eneg fom bending magnets 6. GeV ρ.9 m B.87 T.9 kev.6 nm

24 Setal hoton densit of a bending magnet dn& I dε ε ξ : ω ω P ω 9 S ; S( ξ) ξ K ( ξ dξ beam ω ω 8π ) 5 h ξ Bessel Funtion. S(ω/ω )..ξ /.777 ξ / /e ξ S( ξ) dξ ξω/ω

25 Summa: Tansvesel aeleated elativisti hage. mitted adiation owe 4 m R 4. Obseved setum shifted to highe fequenies due to Loent Tansfomation (Relativisti Dole ffet). Wide fequen setum due to shot ulse duation 4. Radiation mainl obseved in the fowad dietion due to Loent Tansfomation

26 PTRA III Paametes Positon eneg() 6 GeV Maimum ositonbeam uent(i) ma Ciumfeene 4 m Numbe of bunhes 4 / 96 Bunh Length se Revolution time 7.6 µse Bunh Seaation 9 / 8 nse Maimum beam lifetime / 4 h Hoiontal ositonbeam emittane(ε ) nmad Couling fato % Vetialositonbeam emittane(ε ). nmad Positon beam eneg sead(ms). % Cuvatueadiusofbendingmagnets.9 m Magnetifieldofbendingmagnets.87 T Citial hoton eneg fom bending magnets.9 kev Radiation Powe at Diole 5. kw

27 Diol (Bending magnet) Quaduoles, Setuoles(Fousing) mittane ε i andβ-funtion letonbeam sie σ i anddivegene σ i σ ε σ σ ε σ β ε σ β ε σ σ σ ε σ σ ε / ', / ', ', ',,, h i eleton i hoton i σ σ σ + HF Cavities leton Bunhes Pulsed time stutue leton neg, Diole Field B, Bending adius R Photon Intensit I(Θ,Ψ,ω) Beam Cuent I b ms-values nsemble of letons in a Stoage Ring Hoiontal divegene defined b aetue slits

28 mittane, Beta Funtion, Beam Sie & Divegene Beta Funtions β andβ Peta III segment ( m long) PTRA III mittane: ε nm ad ε. nm ad Position along stoage ing /m β m β m

29 Diffeent quantities to desibe hoton intensit Total Flu F numbe of hotons e time [ ] F tot Numbe of s hotons Setal Flu numbe of hotons e time and eneg [ F] Numbe of hotons s.% BW Billiane B numbe of hotons e time, eneg, solid angle and soue aea [ B] Numbe of smm mad hotons.% BW Peak billiane B eak billiane saled to total ulse duation B B eak τ f τ - ulse duation f - ulse fequen