Center for X-ray Optics. The Physics of Polycapillary Optics

Transcription

1 Center fr X-ray Optics The Physics f Plycapillary Optics

2 MAXWELL S EQUATIONS FOR A NON-MAGNETIC INSULATOR: E = 0 B = 0 B xe = t xb = µ E t E 1 = E t µ 1 1 v = µ = µ 1 = c n n,index f refractin = S, given an incident plane wave f the frm: E E e iωt = we expect a respnse D = E = E+ P D E E P P E = = + = + P= Nqx

3 Free Electrns: e - E = E csωt F = mx = qe = qe csωt x = x csωt m x = qe x = qe ω mω Nq P = Nqx = E mω Nq = + Nq m = ( 1 ) mω ω = 1 ωp ω

4 n p 1 ωp ε ω = = 1 1 ε ω ω = 1 δ 1 30eV δ= 5 KeV 6

5 Cnsequences fr refractive ptics: n R Lens-maker's rule: f 1 R 1 = n km

6 Cnsequences fr nrmal incidence mirrr: R( θ = 0) = n1 n δ = n1+ n 11

7 POLYCAPILLARY OPTICS AIR n=1- ω ω p Ttal External Reflectin θ < θ c θ Glass

8 θ θ R R+d d cs( ) θ θ θ θ γ θ = + + < = > R R d d R d R d R R d c c

9 Optic Simulatin mm Transmissin 0.0 Single Fiber Data Simulatin : 0.15 mrad waviness, m bend Cllimating Lens Filter 1 cm x 1 cm utput 5 cm input fcal length 1 µm channel ptic Energy, kev

10 Center fr X-Ray Optics EXPERIMENTAL SETUP Lead Bx Irn pwder Capillary Surce lead shielding and 00 µ m pinhle Metal plate Ge detectr FIBER MOTION cunts vertical (mm) hrizntal (mm) Lei Wang and Carlyn MacDnald, July, 1996

11 Nrmalized cunts Center fr X-Ray Optics SOURCE MOTION 30 KeV 40 KeV 50 KeV 59 KeV 68 KeV 75 KeV 80 KeV Surce Psitin (mm) Large angle transmissin (%) Fiber 1 Fiber Fiber 3, pen area 65%, length 5mm, pen area 50%, lengtn 136mm, pen area 6%, length 130mm Energy(KeV) Lei Wang and Carlyn MacDnald, July, 1996

12 Center fr X-Ray Optics data, and mdel, Fiber A data, Fiber B data, and mdel, Fiber C data, and mdel, Fiber D data, and mdel, Fiber E Transmissin(%) Phtn energy (KeV) 0 Lei Wang and Carlyn MacDnald, July, 1996

13 Center fr X-Ray Optics Defect Simulatin Bending: λb > cm parameter: bending radius, R Waviness: λ r< λ < λb parameter: θ θ Mdeled by randm angle shifts f δθ after each bunce: θ = θ + δθ, - θ < δθ < θ (- θ < δθ < θ if θ < θ) Rughness: λ r< 1 µ m parameters: crrelatin length, rms height, z s Rughness 1 L crrelatin assumed g ( x ) = Z ( x ) Z ( x + x ) d x = Z e L 0 expnential: Transmissi n Surce psitin(mm) θ δθ s, µm z, nm x s Lei Wang and Carlyn MacDnald, July, 1996

14 Center fr X-Ray Optics Transmissin(%) Rughness data, Fiber C mdel, perfect capillary, z=0 nm mdel, with rughness z=1 nm mdel, with rughness z=5 nm Phtn energy(kev) Lei Wang and Carlyn MacDnald, July, 1996

15 Center fr X-Ray Optics Nrmalized intensity kev 70 kev data z=0 z=0.5 nm z=1 nm Rughness Nrmalized intensity data z=0 z=1 nm z= nm Surce psitin(mm) Surce psitin(mm) 0 1 Lei Wang and Carlyn MacDnald, July, 1996

16 Center fr X-Ray Optics Transmisisn(%) BENDING data, Fiber C R=1m R=0m R=90m R=80m Phtn energy(kev) Transmissin(%) WAVINESS data, Fiber C θ =1 mrad θ= mrad Phtn energy(kev) Transmissin(%) data, Fiber C R=15m, θ =0.35 mrad R=1m, θ =0.5 mrad R=170m, θ =0.45 mrad Phtn energy(kev) Lei Wang and Carlyn MacDnald, July, 1996

17 Center fr X-Ray Optics Nrmalized transmissin Fiber C data mdel 0 kev 40 kev 60 kev 80 kev Surce psitin(mm) Lei Wang and Carlyn MacDnald, July, 1996

18 Center fr X-Ray Optics 70 Fiber A: OD 0.5 mm, 1 µm, L=5 mm, f=65% R=5m, θ =0.4 mrad, z=0.7 nm Fiber B Lead Glass: OD.5 mm, 1 µm, L=95 mm, f=5% Fiber C: OD 0.75 mm, µm, L=136 mm, f=50% R=15m, θ =0.35 mrad, z=0.5 nm Fiber D: OD 4.0 mm, 1 µm, L=130 mm, f=55% R=1m, θ =0.85 mrad, z=0.8 nm Fiber E: OD 0.3 mm, 4.5 µm, L=5 mm, f=55% R=90m, θ =0.45 mrad, z=0.8 nm Transmissin(%) Phtn energy (KeV) 0 Lei Wang and Carlyn MacDnald, July, 1996

19 Center fr X-Ray Optics Transmissin(%) Applicatin t Radiatin Damage data, UNEXPOSED R=1m, θ =0.85 mrad, z=0.8 nm data, EXPOSED t 1.8 MJ/cm white beam R=90m, θ =0.450 mrad, z=0.8 nm Phtn energy(kev) Lei Wang and Carlyn MacDnald, July, 1996

20 Center fr X-ray Optics Basic Research Scattering Thery Surface Effects Radiatin Effects X-Ray Astrnmy Micrelectrnics Applicatins X-Ray Lithgraphy Tpgraphy Materials Analysis Applicatins X-Ray Diffractin Micr-analysis X-Ray Flurescence Neutrn Analysis and Diffractin Medical Applicatins Mammgraphy Radigraphy Mnchrmatic Imaging X-Ray and Neutrn Therapy

21 SMALL BEAM COLLIMATION f 5 mm 1 ω d D Liuville s Therem: Ω A Ω Ω f A Ω f f Optic A A f

22 Plycapillary cllimating ptic Crssed slits (1.35 x 1.35 mm ) Peak intensity: cps Omega: 14.3 Theta: 8.6 Psi: Intensity (cps) FWHM = 0.5 Peak intensity: cps FWHM: Phi