X線散乱と放射光科学
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- このか たかひ
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1 8 X II (a) (b) (c) Photon Factory PF-AR SPring SASE SACLA
2
3 8 X II 7 I ) ) 7 X I z x y x y σ x σ y (FWHM) σ x 2.35σ y x σ x σ y σ x σ x σ y σ y (8.33) (8.35) σ p convolution x y Σ x = σp 2 + σx 2, Σ y = σp 2 + σy 2 (8.1) σ p x y Σ x = σ 2p + σ2x, Σ y = σ 2 p + σ2 y (8.2) (photon flux) F (photon flux density) D (brilliance ) B
4 306 8 X II F : photons/sec/0.1% bandwidth D : photons/sec/mrad 2 /0.1% bandwidth B : photons/sec/mm 2 /mrad 2 /0.1% bandwidth (brightness) D D nat z (ψ = 0) (7.32) (7.58) F N F D nat d2 N dtdw/w = d 3 N dtdωdw/w D nat dω (8.3) θ σ p z (ψ = 0) (8.4) F θ 2πσ p D nat,ψ=0 (8.5) 2πσ z (ψ = 0) F 2πσ 2 p D nat,ψ=0 (8.6) D eff z (ψ = 0) D eff,ψ=0 = σ p F D nat,ψ=0 = Σ y 2π θσy D eff,ψ=0 = σ2 p D nat,ψ=0 = Σ x Σ y F 2πΣ x Σ y (8.7) (8.8) (8.1) (8.2) B = D eff,ψ=0 2πΣ x Σ y = F (2π) 2 Σ x Σ y Σ x Σ y 1 d 2 N = (2π) 2 Σ x Σ y Σ x Σ y dtdw/w (8.9) 1 mm 2 1 mrad % 1 ma
5 µm 2 1 µrad , 6) (linear accelerator, ) ( 8.1) 3 v p v e MeV v p S (2.8 GHz) 1 m MeV 10 MeV S 2 C (5.7 GHz), 4 X (11.4 GHz) x, y
6 308 8 X II 8.2 (synchrotron) (microtron) (bending magnet) ( ) 8.2 C SPring π/88 (quadrupole magnet) ( 8.3) (sextupole magnet) (radiation loss) RF cavity klystron 8.4 TM 010
7 revolution time L, v c T 0 = L/c (8.10) revolution frequency f rev = 1/T 0 (8.11) RF f RF f RF = hf rev (8.12) h harmonic number) T 0 /h 1 (, bunch ) bucket, 1/f RF SOR-RING 7) SOR-RING SPring-8 ) 380 MeV 8 B 1 B 8 R 1 R 4 S 2 S 4 S 6 S 8 4 S 1 S 3 S 5 S 7
8 310 8 X II 8.5 (a) a-1 r m(d 2 r/dt 2 r(dθ/dt) 2 ) = evb rdθ/dt = v ( d 2 ) r m dt 2 v2 = evb (8.13) r 8.5 R x, y s (= vt) x(s) y(s) s z (8.13) 7.13 r = R + x (x R) d 2 x dt 2 = v2 ( 1 R + x 1 ) v 2 x R R 2 (8.14) t s(= vt) dx/dt = vdx/ds, d 2 x/dt 2 = v 2 d 2 x/ds 2 d 2 x ds 2 = x R 2 (8.15) d 2 y ds 2 = 0 (8.16) a-2 quadrupole magnet) 8.3 N S 2 xy xy = ±r0 2 ±x2 y 2 = K 2 B(ay, ax, 0) F ( ev ax, ev ay, 0)
9 d 2 x ds 2 = ea m x, d 2 y ds 2 = ea m y (8.17) a 0 N S a 0 x Focusing x Defocusing) F D 2 FDFD a-3 (x y ) d 2 x ds 2 + K x(s)x = 0, d 2 y ds 2 + K y(s)y = 0 (8.18) K x (s) K y (s) x, y K x (s) (8.15) (8.18) (betatron oscillation) x β (s) = W x β x (s) sin{ϕ x (s) + ϕ x0 } y β (s) = W y β y (s) sin{ϕ y (s) + ϕ y0 } (8.19) β x,y (s) (x, y ) 1, x, y β W x,y s ϕ x,y (s) β x,y (s) ϕ x0,y0 ϕ x,y (s) = s 0 ds β x,y (s) (8.20) 1 tune 2π f x,y = 1 ds 2π β x,y (s) (8.21) f x,y 1 (8.18) x y x x dx/ds x x W x β = β x (s) [ α x(s) sin{ϕ x (s) + ϕ x0 } + cos{ϕ x (s) + ϕ x0 }] (8.22) x β = W x γ x (s) sin{ϕ x (s) + ϕ x 0} (8.23)
10 312 8 X II 8.6 x, x α x (s) = 1 2 β x(s) γ x (s) = { 1 + α 2 x(s) } /β x (s) (8.24) α x, β x γ x Twiss) (8.19), (8.22) W x = γ x (s)x 2 + 2α x (s)xx + β x (s)x 2 { = 1 ( ) } β x x (s) x β x (s)x β x (s) 2 (8.25) (8.25) x, x 8.6 πw x s (Liouville) s πw x π W x s ϕ x0 x(s) ± W x β x x (s) ± W x γ x a-4 x E (s) x β (s) x(s) = x β (s) + x E (s) (8.26) x E (s) = η x (s) E E (8.27) η x (s) 1 energy dispersion function) η x (s) L E
11 B: QF QD: D O L L = α E E (8.28) α momentum compaction factor (dilation factor) α (7.4) E pc, p/p E/E (8.28) α > 0 a-5 (lattice) (Chasman-Green) 3 Double Bend Achromat ( ) η x a-6 ( ) closed orbit distortion COD steering magnet pf x + qf y = r (p, q, r: ) (8.29)
12 314 8 X II 8.8 (a) ( ) p i : p ph : p RF RF p f RF (b) ( ) 9) a-7 8) radiation damping radiation excitation ) ( 8.8(a)) ( 8.8(b)) 9) ε x (b) (x, y ) z
13 E ϕ radiation loss RF cavity U V RF U 0 = ev RF sin ϕ s (8.30) ϕ s ( ) π/2 < ϕ s < π p U 0 ϕ s ϕ s q U 0 ϕ s (synchrotron oscillation) 0 < ϕ s < π/2 E ϕ 8.10 E separatrix
14 316 8 X II 8.11 RF (bucket) ε max ε max /E RF RF bucket height (ϕ s ) a bunch ϕ (c) c-1 (8.25) W x W x < W x > 1/2, ε x 8.11 s (x, x ) x x σ βx = ε x β x, σ β x = ε x γ x = ε x /β x 1 + β 2 x /4 (8.31) σ E η x σ ηx = η x σ E /E, σ η x = η xσ E /E (8.32) σ x = ε x β x + η 2 x(σ E /E) 2, σ x = ε x γ x + η 2 x (σ E /E) 2 (8.33)
15 SPring-8 β x, β y η x ID/(Q/S/Q/S/Q)/BM/(Q/S/Q/S/Q/S/Q)/BM/(Q/S/Q/S/Q)/ID s = 0, 30 ε y ( ) ε x0 coupling constant κ (0 κ 1) ε x = ε x0 /(1 + κ), ε y = κε x0 /(1 + κ) = κε x (8.34) κ ε y ε x η x σ y = ε y β y, σ y = ε y γ y = ε y /β y 1 + β 2 y /4 (8.35) c-2 SPring β x, β y η x 8.12 (ID) 2 (BM) (Q) 10 (S) 7 6 nm rad 3 nm rad η x η x β x c-3
16 318 8 X II 8.1 SPring-8 (a) (b)-1 (b)-2 (c) σ E E E α f rev t = α E f rev E (8.36) t ϕ = 2πf RF t = 2πhf rev t = 2πhα E E (8.37) 8.10 Ω Ω 2 = 2πf RFαeV RF T 0 E cos ϕ s = αe V RF T 0 E (8.38) V RF V RF = V RF cos ϕ s T 0 σ t = α σ E (8.39) Ω E 8.10 σ E ϕ c σ t σ t ps c-4 SPring (= ) 4.79 µs 1.97 ns σ 13 ps, FWHM 31 ps 10 mm bunch impurity 10 10
17 (b)-1 (b)-2 (c) (b)-1 12 (b) (c) 4 + 1/ SPring-8 (a) (b) 10) c-5 1/e ( 1/2.7) H 2 CO RF (Touschek) RF c-6 (top-up: ) SPring % ( 8.14) 10)
18 320 8 X II ) 8.15 X 8.16 X X
19 X 12) X +, ( 8.17) X X (311) [011] [011] (311) (111), (511), (711) MOSTAB ( monochromator stabilization) 12) SPring W/mm 2 mm 2, (7.22) R 3 (7.55) λ 0
20 322 8 X II λ 0 ( ) (7.22) R ε 2 θ 3 ε γ 2 θ 3 (8.40) parasitic dedicated 100 nm rad 10 nm rad 1960 X (1.3 GeV) SOR-RING X SPEAR CHESS DESY KEK 1997 X X Photon Factory (PF X SRS ( ) NSLS ( ) KEK ( ) 3 km MR (Main Ring, 30 GeV) AR (Accumulation Ring, 6.5 GeV) 1987 AR PF-AR (Photon Factory Advanced Ring)
21 MR ESRF European Synchrotron Radiation Facility, 6 GeV APS Advanced Photon Source, 7 GeV SPring-8 Super-Photon ring-8 GeV 1997 Japan Synchrotron Radiation Research Institute, JASRI SPring JASRI JASRI 3 SPring GeV NewSUBARU 2000 SPring-8 1 GeV 1984 UVSOR 2003
22 324 8 X II UVSOR-II UVSOR-III 165 nm rad 27 nm rad 15 nm rad UVSOR-III 2 HiSOR HiSOR-II Rits SR 2006 X SAGA LS (1.4 GeV) NUSR 1.2 GeV ( 72 m) GeV GeV Swiss Light Source SOLEIL, DIAMOND Light Source, Australian Synchrotron SSRF, ALBA 2.3 km PETRA (12 GeV) PETRA III ( 6 GeV 1 nm rad) NSLS II 791 m ESRF 3 GeV (1.8 T, 50 m ) 0.55 nm rad MAX-IV Siam Photon Source, SORTEC SESAME BESSY SESAME Synchrotron-light for Experimental Science and Applications in the Middle East! Photon Factory PF-AR 1) Photon Factory 2.5 GeV Photon Factory (PF) 14, 15) 400 nm rad 36 nm rad 3 Photon Factory 8.6 KEK 68 m 50 m L = 187 m E = 2.5 GeV 3 GeV 2.5 GeV I = 450 ma
23 (1 GeV ) 13) ε x = 36 nm rad ε y 0.4 nm rad R = 8.66 m B = 1 T E c = 4.0 kev, λ c = 0.31 nm RF f RF = MHz f rev = c/l = 1.6 MHz /f RF = 2.00 ns σ 33 ps (rms) 10 mm
24 326 8 X II 8.18 PF PF-AR 16) PF-AR PF EMPW: MPW: VW: U: SGU: Bend: NE: NE NW: NW 17) 8.18 Photon Factory 2) PF-AR PF-AR 6.5 GeV Photon Factory 8.6 PF-AR 2.5 GeV 6.5 GeV L = 377 m f rev = 794 khz RF f RF = MHz 640 1/f rev = 1.30 µs, 62 ps (rms) ma 8.18 PF-AR (4) SPring ) SPring SPring m 1 GeV 396 m 8 GeV 1436 m 8 GeV 4.79 µs 100 ma 3.4 nm rad 0.2 %
25 Photon-Factory PF-AR 16) 8.7 < µm (RF) f RF = MHz f rev = MHz /f RF = 1.97 ns σ 13 ps, FWHM 31 ps (10 mm ) (3) c-4 ) (3) c-6 R = 39.3 m E c 28.9 kev m m 4 X 4.5 m ( 32 mm, 140) 25 m ( 32 mm 780) kev X 4.5 m photons/sec/mm 2 /mrad 2 /0.1% bandwidth 25 m kev 100 kev 120 kev 300 kev 0.3 kev GeV γ
26 328 8 X II 8.7 SPring-8 22) m m m 1 km 200 m RI (250 ev 2 kev) SPring Hz 0.3 µm (1436m 0.1/( ))
27 SPring-8 23) , 24) (Ultimate storage ring, USR) 25) λ/(4π) 100 % 2 3 SPring-8 SPring-8 II SPring-8 6 GeV 300 ma SPring-8 Double Bend Achromat (3) a θ /(2 44) 6 6-Bend Achromat 67 pm rad SPring nm rad 1/ kev 10 23
28 330 8 X II 8.20 (a) (b) SASE 8.2 X (1) 26) free electron laser, FEL 1977 Madey 3.4 µm 27) 8.20(a)
29 (a) (b) dp/dt F dε/dt F v dp dt = F, dε dt = F v (8.41) z B 0 y z x z z ( ) E r B r x F = e {E r + v (B 0 + B r )} (8.42) dε dt = ee r v (8.43) 8.21 A 0 B 0 ee r v A 0 E rx > 0, v x > 0 B 0 E rx < 0, v x > 0 E r x v x (λ 0 /2) (λ/2) A 0 A 1 B 0 B 1 ee r v A 1
30 332 8 X II 8.22 B 1 (λ 0 ) (λ) A 2 B 2 v z λ 0 /2 v z (7.51) (c v z ) λ 0 2 v z = λ 2 (8.44) λ = λ 0 K2 (1 + 2γ2 2 ) (8.45) λ γ ( K ) γ γ r (8.43) dε/dt γ γ r (γ γ r ) /γ r 8.22 γ γ r 1/4N N γ γ r optical klystron ( 8.20(a))
31 SASE (2) SASE 28) 50 nm 1 1 ( ) Self-Amplified Spontaneous Emission, SASE SASE (X-ray Free-electron Laser, XFEL) (1) p p x ε x p x /p 1/p 1/(γv) ε = ε n /(βγ) (8.46) ε n, 8.20(b) 8.23
32 334 8 X II XFEL/SPring-8 (EUV FEL) (a) SASE (b) (a) (b) 1/10, (buncher) 8.24 (chicane) ( 8.20(b)) SASE SASE 3) SASE ( ) XFEL/SPring-8 (EUV FEL) 800 nm nm
33 SACLA 30) 160 nm 8.25 SASE-FEL nm 2, 29) SACLA (SLAC) LCLS (Linac Coherent Light Source) 4 km 2 km 14.3 GeV 0.15 nm (DESY) European XFEL km, GeV nm FLASH 109 nm SPring-8 XFEL / SPring-8 (SACLA, SPring-8 Angstrom Compact Free Electron Laser) 31) 8.26 SACLA 8 GeV, 710 m CeB kev C (5.7 GHz) 40 MV/m S m 18 X 18 mm SASE Å X 3, 32, 33) 0.63 Å 8.8 SACLA
34 336 8 X II 8.8 SACLA X 32) 1 2 XFEL (EUV FEL) 250 MeV 1/32 15 mm nm 10 nm FEL X X XFEL,, 10 10,,, (Energy-Recovery Linac, ERL) ε (8.46) RF x, y 1 ps 100 fs ERL 8.27 RF
35 RF RF ERL (CW) ERL XFEL 34) α-al 2 O 3, ( ) 14.3 kev, 0.2 mm 0.07 mm 100 m ERL RF Cornell KEK 1983 PF ERL 35, 36) ERL (cerl : MeV) KEK ERL 5 GeV 10 pm rad 1 10 kev X ERL 5 GeV 3 GeV 5/3 17 pm rad VUV- 3 GeV
36 338 8 X II X X SASE-FEL SASE-FEL 100 Hz ERL 1.3 GHz 500 MHz SASE-FEL ERL,,. XFEL XFEL ) x, y z x = dx/dz, y = dy/dz x, y x, y rms (σ) x x, y y x x λ 4π, y y λ 4π (8.47) ( diffraction limit ) 4 (x, x, y, y ) V 4 V 4,min (λ/2) 2 V 4 = (2π) 2 x x y y (8.47) x = k x /k, y = k y /k ( ) 2 λ (8.48) 2 x k x 1 2, y k y 1 2 (8.49) ħ x p x ħ 2, y p y ħ 2 (8.50) (1) ( ω) t rms (σ) t ω
37 t ω ω λ 4πc (8.51) ( Fourier transform limit ) (x, x, y, y, t, ω) V 6 V 6 = (2π) 3 x x y y t w/w 1 c ( ) 3 λ (8.52) 2 V 6,min (λ/2) 3 /c (8.51) t ω 1 2 (8.53) ħ t E ħ 2 (8.54) (8.53) z = c t, ω = c k c k z z k z 1 2 (8.55) B (8.9) B = F (2π) 2 x x y y (8.56) Σ x x B V 4 F V 4,min F c F c = V 4,min B = ( ) 2 λ B (8.57) 2 F c F coherent fraction 1 ˆB V 6 N V 6,min photon degeneracy δ (8.59) δ = V 6,min ˆB = 1 c ( ) 3 λ ˆB (8.58) 2 3 X
38 340 8 X II (photons/sec/mm 2 /mrad 2 /0.1% band width) (ps) 8.28 SPring-8 (FEL) (ERL) X ERL FEL δ 1 FEL δ FEL ERL 38) FEL 3 10 FEL ps 100 fs FEL 100 Hz ˆB = N (2π) 3 x y x y t w/w (8.59) ESRF, APS, SPring-8 Swiss LS, SOLEIL, DIAMOND LS 10
39 (USR ) 2 3 SPring-8 II KEK KEKB X XFEL SPring-8 XFEL 3 XFEL XFEL ERL KEK ERL 3 XFEL XFEL ERL
40 342 8 X II X VUV
41 1) 20 (2007) ) 24 (2011) ) 24 (2011) ) : 17 (2004) ) : p.1, ) ( ): (1996). 7) T. Miyahara, H. Kitamura, S. Sato et al.: Particle Accelerators 7 (1976) ) : 16 (2003) ) :. 10) H. Tanaka, M. Adachi, T. Aoki et al.: J. Synchrotron Rad. 13 (2006) ) : 7 (2010) ) : 9 (1996) ) 14) No.243, 9 (1983). 15) PF KEK, ) Photon Factory Activity Report 2010, KEK. 17) 25 (2012) ) 2 (1989) ) 3 (1990) ) 9 (1996) ) 14 (2001) 3. 22) SPring-8 Research Frontiers ) SPring-8 JASRI. 24) 89 JASRI. 25) 24 (2011) ) 37 (1982) 906 ; 57 (1988) ) D. A. G. Deacon, L. R. Elias, J. M. J. Madey et al.: Phys. Rev. Lett. 38 (1997) ) (,(1989) p ) SPring ) SACLA ) 64 (2009) ) 25 (2012) ) 24 (2011) 312.
42 344 34) K- J. Kim, Y. Shvyd ko and S. Reiche: Phys. Rev. Lett. 100 (2008) ), KEK ) ERL 24 (2011) ) ) 14 (2001) 323.
43 309, A ALBA 324 APS 323 AR 322 Australian Synchrotron 324 C CHESS 322 D DESY 322 DIAMOND Light Source 324 D 311 E ERL 336 ESRF 323 European XFEL 335 EUV FEL 336 F F 311 H HiSOR 324 HiSOR-II 324 J JASRI 323 L LCLS 335 M MR 322 N NewSUBARU 323 NSLS 322 NUSR 324 P PETRA III 324 PF-AR 323, 324 Photon Factory 322, 324 R RF 316 Rits SR 324 S SACLA 335 SAGA LS 324 SASE 333 SASE 333 SESAME 324 Siam Photon Source 324 SOLEIL 324 SOR-RING 309, 322 SPEAR 322 SPring-8 308, 309, 323, 326 SRS 322 SSRF 324 Swiss Light Source 324 T TM U UVSOR 323 X , , 314, , , ( ) ,
44 , , , 312, , , (Liouville)
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1906 R n m 1 = =1 1 R R= 8h ICP s p s HeNeArXe 1 ns 1 1 1 1 1 17 NaCl 1.3 nm 10nm 3s CuAuAg NaCl CaF - - HeNeAr 1.7(b) 2 2 2d = a + a = 2a d = 2a 2 1 1 N = 8 + 6 = 4 8 2 4 4 2a 3 4 π N πr 3 3 4 ρ = = =
(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x
![(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x](/thumbs/104/162595168.jpg "(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x")
Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k
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大学加速器施設一覧 大学加速器連携協議会 305-0801 1-1 029-864-5214 e-mail uac@kek.jp URL http://www2.kek.jp/accl/kek_university/index.html 1 YU-AMS 2 3 CYRIC 4 5 6 1.3 GeV BST 7 t-acts 8 9 UTTAC 10 GHMC 11 FEL-TUS 12 LEBRA
量子力学 問題
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) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)
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SO(3) 7 = = 1 ( r ) + 1 r r r r ( l ) (5.17) l = 1 ( sin θ ) + sin θ θ θ ϕ (5.18) χ(r)ψ(θ, ϕ) l ψ = αψ (5.19) l 1 = i(sin ϕ θ l = i( cos ϕ θ l 3 = i ϕ
SO(3) 71 5.7 5.7.1 1 ħ L k l k l k = iϵ kij x i j (5.117) l k SO(3) l z l ± = l 1 ± il = i(y z z y ) ± (z x x z ) = ( x iy) z ± z( x ± i y ) = X ± z ± z (5.118) l z = i(x y y x ) = 1 [(x + iy)( x i y )
磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論
email: takahash@sci.u-hyogo.ac.jp May 14, 2009 Outline 1. 2. 3. 4. 5. 6. 2 / 262 Today s Lecture: Mode-mode Coupling Theory 100 / 262 Part I Effects of Non-linear Mode-Mode Coupling Effects of Non-linear
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128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds = 0 (3.4) S 1, S 2 { B( r) n( r)}ds
127 3 II 3.1 3.1.1 Φ(t) ϕ em = dφ dt (3.1) B( r) Φ = { B( r) n( r)}ds (3.2) S S n( r) Φ 128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds
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7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±
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7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α
50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq
49 2 I II 2.1 3 e e = 1.602 10 19 A s (2.1 50 2 I SI MKSA 2.1.1 r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = 3 10 8 m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq F = k r
19 σ = P/A o σ B Maximum tensile strength σ % 0.2% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional
19 σ = P/A o σ B Maximum tensile strength σ 0. 0.% 0.% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional limit ε p = 0.% ε e = σ 0. /E plastic strain ε = ε e
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BELLE TOP 12 1 3 2 BELLE 4 2.1 BELLE........................... 4 2.1.1......................... 4 2.1.2 B B........................ 7 2.1.3 B CP............... 8 2.2 BELLE...................... 9 2.3
q π =0 Ez,t =ε σ {e ikz ωt e ikz ωt } i/ = ε σ sinkz ωt 5.6 x σ σ *105 q π =1 Ez,t = 1 ε σ + ε π {e ikz ωt e ikz ωt } i/ = 1 ε σ + ε π sinkz ωt 5.7 σ
H k r,t= η 5 Stokes X k, k, ε, ε σ π X Stokes 5.1 5.1.1 Maxwell H = A A *10 A = 1 c A t 5.1 A kη r,t=ε η e ik r ωt 5. k ω ε η k η = σ, π ε σ, ε π σ π A k r,t= q η A kη r,t+qηa kηr,t 5.3 η q η E = 1 c A
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Junji OHTSUBO 2012 FFT FFT SN sin cos x v ψ(x,t) = f (x vt) (1.1) t=0 (1.1) ψ(x,t) = A 0 cos{k(x vt) + φ} = A 0 cos(kx ωt + φ) (1.2) A 0 v=ω/k φ ω k 1.3 (1.2) (1.2) (1.2) (1.1) 1.1 c c = a + ib, a = Re[c],
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9 AR (i) (ii) MA (iii) (iv) (v) 9.1 2 1 AR 1 9.1.1 S S y j = (α i + β i j) D ij + η j, η j = ρ S η j S + ε j (j =1,,T) (1) i=1 {ε j } i.i.d(,σ 2 ) η j (j ) D ij j i S 1 S =1 D ij =1 S>1 S =4 (1) y j =