8 X II 305 8.1..................................... 305 8.1.1................. 305 8.1.2.................................... 307................................... 307............................ 308......................... 310 (a)................................... 310 (b)................................. 314 (c).............................. 316............................... 320 8.1.3.............................. 321............................... 321........................... 322 Photon Factory PF-AR...................... 324 SPring-8................................ 326 8.1.4.............................. 329 8.2......................... 330 8.2.1................................. 330............................ 330 SASE....................... 333 SACLA................... 335 8.2.2............................. 336 8.3.................................. 338 8.3.1.............................. 338.................................... 338............................... 338............................ 339 8.3.2............................. 340 343 345
8 X II 7 I 8.1 1 3) 8.1.1 4) 7 X I z x y x y σ x σ y (FWHM) 2.35 2.35σ 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
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 7.2.2 7.2.3 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 2 0.1 % 1 ma
8.1 307 8.1 1 µm 2 1 µrad 2 8.1.2 5, 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
308 8 X II 8.2 (synchrotron) (microtron) (bending magnet) ( ) 8.2 C SPring-8 88 1 2π/88 (quadrupole magnet) ( 8.3) (sextupole magnet) (radiation loss) RF cavity klystron 8.4 TM 010
8.1 309 8.3 8.4 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 1977 1997 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
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)
8.1 311 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)
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 2 2 + 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
8.1 313 8.7 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 ( ) 8.7 2 η x a-6 ( ) closed orbit distortion COD steering magnet pf x + qf y = r (p, q, r: ) (8.29)
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
8.1 315 8.9 8.10 E ϕ radiation loss RF cavity U 0 8.9 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
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)
8.1 317 8.12 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 0.1 0.01 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-8 44 36 8 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
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 10 100 ps c-4 SPring-8 2436(= 2 2 3 7 29) 4.79 µs 1.97 ns σ 13 ps, FWHM 31 ps 10 mm 8.1 8.13 bunch impurity 10 10
8.1 319 (b)-1 (b)-2 (c) 8.13 8.1 (b)-1 12 (b)-2 3 4 (c) 4 + 1/6 8.14 SPring-8 (a) (b) 10) c-5 1/e ( 1/2.7) H 2 CO RF (Touschek) RF c-6 (top-up: ) SPring-8 12 24 1 0.1% ( 8.14) 10)
320 8 X II 8.15 8.16 11) 8.15 X 8.16 X X
8.1 321 8.17 X 12) X +, ( 8.17) X X (311) [011] [011] (311) (111), (511), (711) MOSTAB ( monochromator stabilization) 12) SPring-8 300 W/mm 2 mm 2, 50 8.1.3 8.2 (7.22) R 3 (7.55) λ 0
322 8 X II 8.2 2 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 1974 1997 X 1970 1 SPEAR CHESS DESY KEK 1997 X X Photon Factory (PF 1982 2 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) 2001 1
8.1 323 8.3 8.4 MR 1995 8.3 1993 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-8 2005 JASRI JASRI 3 SPring-8 8.4 1.5 GeV NewSUBARU 2000 SPring-8 1 GeV 1984 UVSOR 2003
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) 2011 3 3 GeV 50 8.5 1GeV 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
8.1 325 8.5 (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 = 500.1 MHz f rev = c/l = 1.6 MHz 312 312 1/f RF = 2.00 ns σ 33 ps (rms) 10 mm
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 = 508.6 MHz 640 1/f rev = 1.30 µs, 62 ps (rms) 10 8 60 ma 8.18 PF-AR (4) SPring-8 18 21) SPring-8 8.7 SPring-8 140 m 1 GeV 396 m 8 GeV 1436 m 8 GeV 4.79 µs 100 ma 3.4 nm rad 0.2 %
8.1 327 8.6 Photon-Factory PF-AR 16) 8.7 < µm (RF) f RF = 508.58 MHz f rev = 0.2088 MHz 2436 2436 1/f RF = 1.97 ns σ 13 ps, FWHM 31 ps (10 mm ) 8.1.2 (3) c-4 ) 8.1.2 (3) c-6 R = 39.3 m E c 28.9 kev m 34 30 m 4 X 4.5 m ( 32 mm, 140) 25 m ( 32 mm 780) 8.19 10 kev X 4.5 m 2 10 20 photons/sec/mm 2 /mrad 2 /0.1% bandwidth 25 m 9 10 20 10 30 kev 100 kev 120 kev 300 kev 0.3 kev GeV γ
328 8 X II 8.7 SPring-8 22) 62 38 6 m 34 30 m 4 24 1 80 m 1 km 200 m RI (250 ev 2 kev) SPring-8 0.1 Hz 0.3 µm (1436m 0.1/(508 10 6 ))
8.1 329 8.19 SPring-8 23) 10 10 2004, 24) 8.1.4 8.1.3 (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 8.1.2 (3) a-5 8.38 θ 4 360 /(2 44) 6 6-Bend Achromat 67 pm rad SPring-8 3.4 nm rad 1/50 10 10 kev 10 23
330 8 X II 8.20 (a) (b) SASE 8.2 X 8.2.1 (1) 26) free electron laser, FEL 1977 Madey 3.4 µm 27) 8.20(a) 7.2.3 1
8.2 331 8.21 (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
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))
8.2 333 8.23 SASE (2) SASE 28) 50 nm 1 1 ( ) Self-Amplified Spontaneous Emission, SASE 3 10 10 SASE (X-ray Free-electron Laser, XFEL) 8.1.2 (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
334 8 X II 8.24 8.25 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 5 160 nm
8.2 335 8.26 SACLA 30) 160 nm 8.25 SASE-FEL 13 61 nm 2, 29) SACLA (SLAC) LCLS (Linac Coherent Light Source) 4 km 2 km 14.3 GeV 0.15 nm 2009 4 (DESY) European XFEL 12 3.3 km, 10 20 GeV 0.085 nm 2014 2000 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 6 500 kev C (5.7 GHz) 40 MV/m S 2 2 5 m 18 X 18 mm SASE 2011 6 1.24 Å X 3, 32, 33) 0.63 Å 8.8 SACLA
336 8 X II 8.8 SACLA X 32) 1 2 XFEL (EUV FEL) 250 MeV 1/32 15 mm 51 61 nm 10 nm FEL X X XFEL,, 10 10,,,. 8.2.2 (Energy-Recovery Linac, ERL) ε (8.46) RF x, y 1 ps 100 fs ERL 8.27 RF
8.2 337 8.27 180 RF RF ERL (CW) ERL XFEL 34) α-al 2 O 3, (0 0 0 30) 14.3 kev, 0.2 mm 0.07 mm 100 m ERL RF Cornell KEK 1983 PF ERL 35, 36) ERL (cerl : 35 245 MeV) KEK ERL 5 GeV 10 pm rad 1 10 kev X ERL 5 GeV 3 GeV 5/3 17 pm rad 10 22 1 VUV- 3 GeV 3 2 3 2 3
338 8 X II X X SASE-FEL SASE-FEL 100 Hz ERL 1.3 GHz 500 MHz SASE-FEL 10 33 ERL,,. XFEL XFEL-0 8.3 8.3.1 37) 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
8.3 339 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
340 8 X II 10 36 (photons/sec/mm 2 /mrad 2 /0.1% band width) 10 32 10 28 10 24 10 20 10 16 0.01 0.1 1 10 100 1000 (ps) 8.28 SPring-8 (FEL) (ERL) X ERL FEL δ 1 FEL δ 1 8.28 2 3 FEL ERL 38) FEL 3 10 FEL 30 100 ps 100 fs FEL 100 Hz 8.3.2 8.29 ˆB = N (2π) 3 x y x y t w/w (8.59) ESRF, APS, SPring-8 Swiss LS, SOLEIL, DIAMOND LS 10
8.3 341 8.29 (USR 8.1.4 ) 2 3 SPring-8 II KEK KEKB X XFEL SPring-8 XFEL 3 XFEL XFEL ERL KEK ERL 3 XFEL XFEL ERL
342 8 X II X VUV
1) 20 (2007) 266. 2) 24 (2011) 312. 3) 24 (2011) 210. 4) : 17 (2004) 228. 5) : p.1, 1989 10. 6) ( ): (1996). 7) T. Miyahara, H. Kitamura, S. Sato et al.: Particle Accelerators 7 (1976) 163. 8) : 16 (2003) 245. 9) :. 10) H. Tanaka, M. Adachi, T. Aoki et al.: J. Synchrotron Rad. 13 (2006) 378. 11) : 7 (2010) 250. 12) : 9 (1996) 413. 13) http://www.lightsources.org. 14) No.243, 9 (1983). 15) PF KEK, 1992. 16) Photon Factory Activity Report 2010, KEK. 17) 25 (2012) 12. 18) 2 (1989) 69. 19) 3 (1990) 45. 20) 9 (1996) 384. 21) 14 (2001) 3. 22) SPring-8 Research Frontiers 2009. 23) SPring-8 JASRI. 24) 89 JASRI. 25) 24 (2011) 266. 26) 37 (1982) 906 ; 57 (1988) 1468. 27) D. A. G. Deacon, L. R. Elias, J. M. J. Madey et al.: Phys. Rev. Lett. 38 (1997) 892. 28) (,(1989) p.65. 29) SPring-8 2008 3 10. 30) SACLA 2011. 31) 64 (2009) 160. 32) 25 (2012) 57. 33) 24 (2011) 312.
344 34) K- J. Kim, Y. Shvyd ko and S. Reiche: Phys. Rev. Lett. 100 (2008) 244802. 35), KEK 2003. 36) ERL 24 (2011) 256. 37) 2001 1. 38) 14 (2001) 323.
309, 310 308 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 010 308 U UVSOR 323 X 333 306 307 308 313 305, 336 307, 314, 317 307 338 307 329 332 331 338 307, 308 339 308, 309 306 339 334 339 334 ( ) 333 306 309 330 315 307 316 309 313 307 306 308, 309 332 322 322
346 322 307 307 307 313 309 340 312 313 307 308 310 319 308 315 307 319 319, 326 307 309 309 307 307, 334 339 333 339 306 306 307 306 321 339 311, 312, 314 311 308 310 306 306 308, 315 313 307, 308 330 332 332 313 (Liouville) 312 310