1 [1] [2] Telegdi [3] [4] Livingston Livingston-Blewett [2] [5] : Livingston Livingston-Blewett p.6 2
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- こうじ さどひら
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2 1 [1] [2] Telegdi [3] [4] Livingston Livingston-Blewett [2] [5] : Livingston Livingston-Blewett p.6 2
3 Collider (Equivalent Energy) Accelerator Energy (ev) TeV 1GeV MeV : Livingston Livingston Rutherford MeV N. Tesla
4 Step -up Transformer Spark Ga p HV Outp ut 3: Tesla J. D. Cockroft E. T. S. Walton 1925 ±V V±V 3V± V 5V± V AC 0 2V 4V 6V 0 4: Cockroft - Walton H. Greinacher J. D. Cockroft E. T. S. Walton 800 kv p + 3 Li 2He 4 VandeGraaf 1931 pelletron tandem 20 MeV 2 1cm [6] 4
5 1 30 kv SF kv 150 kv 220 kv SF kv E V (x, y, z) E = V C E E s 0 C A ds = S ( A) ndxdy V = 0 C E s ds = C E ds = S ( E) ndxdy = S ( V ) ndxdy =0 S C n E B E = B t 0 E s ds = E ds = ndxdy = C C S( E) B ndxdy = t S t Φ Φ S D. W. Kerst Univ. Illinois MeV 3 G. Ising 1925 R. Wideröe K + Na + kev UC Berkeley D. H. Sloan E. O. Lawrence 1931 Hg MeV Cyclotron E. O. Lawrence 1930 d (mv) =ee + ev B dt 5
6 HF Ion So urce Beam 5: Wideröe HF E r D-Electrode V ion q B D-Electrode 6: (r, θ, z) d dt (mṙ) mr θ 2 = ee r + er θb z eżb θ B z (ṁ =0) (ṙ =0) θ = eb z m ω c ω c p θ p θ = mv θ = mr θ p θ r = eb z 6
7 f = ω c /2π D p θ m 0 c 2 = 938.3MeV f(mhz)=15.2b z (Tesla) 10 MeV r(m) = 0.457/B z (Tesla) ω 20 MeV B z r 4 E. C. McMillan UC Berkeley V. I. Veksler USSR 1945 f = ω/2π bunching v 1 L E f(e) = v L 1 V = V 0 sin ωt ωt nπ n + π π 0 φ s 0 0+2nπ 0 2π π (1 + 2n)π π (1 + 2n)π 7
8 VêV wtêp : V = V 0 cos ωt 0 <φ s <π 0 <φ s <π/2 π/2 <φ s <π φ s 2π φ s π/2 0 frequency-modulated cyclotron synchrocyclotron 600 MeV 0.17 Tesla Dubna 6.0m 7200t KEK PS 40 MeV 500 MeV β MeV 12 GeV β β 5 v v 0 B v F = ev B 8
9 z 0 r 8: 0 B r 8 B z B = 0 B r z = B z r 1 λ β r πr 0 r B z [7] d 2 x ds n r0 2 x = 1 p r 0 p p = const. d 2 z ds 2 + n r0 2 z =0 9
10 x z p s B z r 0 B z = B 0 (1 n x ) + r 0 n n B z λ β,vertical = 2πr 0 n λ β,horizontal = 2πr 0 1 n 0 < n < 1 weak focusing n 0.75 n Dubna ynchro-phasotron m 10 GeV 1.3Tesla 150 cm 40 cm 35, 000 t N. Christofilos 1952 Brookheaven E. D. Courant M. S. Livingston H. Snyder [8] 2 2 z = x + jy = re jφ x y 2m m Z X + jy = z 1/m =(x + jy) 1/m = r 1/m e jφ/m 10
11 2m /2m m =2 4 Z X + jy = z 1/2 =(x + jy) 1/2 = r 1/2 e jφ/2 XY = y X 2 Y 2 = x 1 y = 4 X Y =0 dx dx =2X X dx B y X Y B x s K x (s) K y (s) d 2 x ds 2 + K x(s) =0 d 2 y ds 2 + K y(s) =0 x(s) = ɛ h β h (s)cos(ψ x (s)+δ) y(s) = ɛ v β v (s)cos(ψ y (s)+δ) 11
12 2 y x : 4 beam 10: 12
13 s β h (s) β v (s) λ β 2π = λβ +s 0 s 0 dψ = λβ +s 0 s 0 dψ ds ds s 0 Courant-Snyder [9] 2ββ β 2 +4βK =4 ψ =1/β s ɛ h ɛ v [m] s ɛ h β h (s) ɛ v β h (s) 11 bv bh s 11: x(s) K x (s) x(s) =D(s) p p 0 K x (s) 1 1 L/L 0 = α p p/p 0 momentum compaction factor α p D(s) 13
14 λ β λ β ν L λ β ν h, v L λ β, h, v l m n lν h ± mν v = n p E momentum compaction ( τ = α p 1 ) p τ γ 2 p γ τ 0 transition energy γ t 1/ α p trannsition gamma φ E = ev 0 (sin φ sin φ s ) φ φ sin (ω s t + const) ω s ( )V0 /E ω RF 2πv/L h ɛ dx ds ɛ 1/p 1/γv ɛβ 1/γv 1/γv 8 Livingston Diagram E CM E CM 14
15 m 0 γ p Lab p Lab = γm 0 v +0=γm 0 v E Lab E Lab = γm 0 c 2 + c =(γ +1)(x) 2 E CM E 2 cp 2 0 E CM 2 = E Lab 2 c 2 p Lab 2 E CM γ CM m 0 c 2 γ CM = (γ +1)/2 γ/2 γ γ CM Frascati Bruno Touschek 1960 Frascati 160cm 200 MeV AdA σ reaction S 1 σ reaction S N + N + σ reaction N + N + S 1 f c σ reaction N + N + f c S σ reaction L L = N +N + f c f c S m 2 s 1 S β 15
16 9 γ 4 2 x, y, z, t z v x,y,z,t t =0 t = t x c t t r = ct x θ cos 2 θ x, y, z, t x z x = x y = y z = γ (z vt) t = γ ( t vz/c 2) x z z 1/γ 1/γ P rest = 2r em e 3c ( ) 2 dv = 2r e dt 3m e c ( ) 2 dp dt r e = e 2 4πɛ 0 m e c 2 ds dt/γ ( c dp ) 2 ds ( ) 2 de ds ρ P = 2 ( 3 r em e c 3 v ) 4 γ 4 c ρ 2 [10] ρ E V s V s (Volts) = E(GeV)4 ρ(m) 2 γ γ 2 16
17 1/γ 2πρ/γ 1 1 v/c 2 2πρ γ ( 1 v ) c 4πρ γ 1 2γ 2 = 2πρ γ 3 2 λ c 4πρ 3γ 3 2πc/λ c ω c radiation damping radiation excitation [11] 0 τ ɛ τ x τ y 2τ ɛ τ x τ y ms 0 RF bucket τ q V s 0 η E/E ATF 10 [12] TM 010 b d TM
18 r, θ, z E r =0 E θ =0 E z = E 0 J 0 (χ 01 r/b)cos(ω 010 t) H r =0 H θ = H 0 J 1 (χ 01 r/b)sin(ω 010 t) H z =0 0 0 E 0 H 0 = ζ 0 = ɛ 0 µ 0 = Ω χ χ 01 = c ω 010 = χ 01c b d S 2856 MHz b =40.2mm E 0 d v E 0 d T = sin ( ω 010d ) 2v) ( ω010d 2v V a = E 0 dt cos (ω 010 t + φ) T Transit Time Factor Q U P wall Q = ω U P TM 010 Q = ζ 0 ζ m χ 01 d d + b ζ m σ µ ωµ ζ m = 2σ 2856 MHz Ω d = 35mm Q 15,
19 jωl R sh = R a /2 1/jωC 12: R sh R sh (V a) 2 2P wall R a =2R sh 12 L C LC = ω010 2 Ra Q = ω 010 L L C 12 LCR LCR 3 d =0.44λ PF 14 Q 3 OHO97 KEK 19
20 1 0.8 T^2 RêRmax QêQmax pdêl 13: d ( ) 14: PF π 20
21 12 R 2 15 L L i 1 ~ C C' C i 2 ~ 15: 2 C C/C ĩ 1 e jωt ĩ 2 e jωt tilde ĩ A ĩ Ae jφ phasor ( jωl + 1 ) ĩ 1 + ĩ1 ĩ 2 jωc jωc =0 0 π ( jωl + 1 jωc ĩ 1 ĩ 2 ) ĩ 2 + ĩ2 ĩ 1 jωc =0 ĩ 1 ĩ 2 ω = ω 0 1 LC ω = ω π ω C C 21
22 C C ω π ω 0 ( 1+ C C ) >ω π C C / π r 0 0 cell - 1 cell - 2 cell - 1 cell - 2 E H 0 - mode p - mode 16: x Ae j(ωt βx) n = n = ĩ n e jωt = i 0 e jnφ e jωt ĩ n n φ ( jωl + 1 ) ĩ n + 2ĩ n ĩ n 1 ĩ n+1 jωc jωc =0 22
23 i 0 exp (-2jφ) i 0 exp (-jφ) i0 i0 exp (jφ) i0 exp (2jφ) L L L L L C' C' C' C' C C C C C n = : ω = ω 0 [1 + k (1 cos φ)] 1/2 ω 0 [ 1+ k 2 (1 cos φ) ] ω 0 1/ LC k 2C/C 2 C C ω φ 0 φ π d v p λ g = 2πd φ v p = ω 2π λ g = ωd φ v b v b = v p 23
24 18 φ =0 φ = π ω 0 ω π TM 010 ω π ω 0 ω 0 k a 4 β g =2π/λ g v 4 g v g = ω = d ω β g φ k 2 ω 0d sin φ L L/v g filling time t s v g % φ =2π/3 2π/3 φ d 1 φ φ =2π/3 π π π φ φ π π 0 0 APS(Alternating Periodic Structure) [13] [14] Los Alamos SCS(Side Coupled Structure) [15] ACS(Annular Coupled Structure) [16] DAW(Disk-and-washer Structure) [17] (bi-periodic structure) ω φ 0 0 KEKB ARES λ β g waveguide g v g group velocity g 24
25 ω ω= (vp/d)(2π φ) ω p ω acc grad. = vg/d ω 0 ω = (vp/d)φ φ = 2πd/λ 0 φacc π 18:
26 19: 14 UHF n irrotational mode 26
27 1 : n L1 L2 L3 R1 R2 R3 C1 C2 C3 waveguide coupler cavity 20: L C R I I 0 e jωt 21 ω L1 L2 L3 1 : n R1 R2 R3 C1 C2 C3 waveguide 2I0e jωt coupler cavity beam 21: γ Cockcroft-Walton 750kV β = v/c = % β ( 1m) RFQ DTL RFQ MeV DTL 100MeV (1) RFQ RFQ Radio-Frequency Quadrupole Linear Accelerator Kapchinskii Teplyakov 27
28 1970 [18] RFQ 4 vane RFQ bunching TE 211 A B A' B' B B' A A' 22: RFQ (2) DTL DTL Drift Tube Linac (Alvarez) [19] TM Drift Tube Drift Tube β λ Drift Tube Drift Tube Q β 0.5 ( 200 MeV) (3) 28
29 - 23: RFQ magnetic alloy µ µ MHz Kilpatrick [20] W (Volts) E (Volts/Centimeters) WE 2 e E = % µ SLAC P. Wilson 1 GHz 10 GHz E surfacebreakdown (MV/m) f(ghz) 29
30 RF Input: frf f = c/λ Coupling Loop Stem Drift Tube Beam β1λ β2λ β3λ βnc c = average beam velocity at the n-th drift tube 24: (Alvarez) 25: Kilpatrick 30
31 E surfacebreakdown 60f 7/8 [21] 2856 MHz 160 MV/m 1/ MV/m 2856 MHz 40 MV/m 11.4 GHz 75 MV/m R. H. Fowler L. Nordheim 1928 [22] Fowler-Nordheim j F j F = φ 0.5 φ E 2 exp ( φ 1.5 ) E ( Amp/cm 2 ) E V/m φ ev 1 j F = φ 0.5 φ 1.75 E 2.5 exp ( φ 1.5 ) E ( Amp/cm 2 ) [23] E E macro E β E = βe macro β conditioning 2856 MHz β kw MW 7 UHF 7 [24] [25] 31
32 2 10 MHz 200 MHz (magnetron) (klystron) (TWT: traveling wave tube) (gyrotron) 8 S MW 10 MeV MW [27] 400 MHz 10 GHz 9 TE 26 (V b ) 1/100 V b I Child-Langmuir I = PV 3/2 P I Amperes V Volts P 10 6 AV 3/ µp 8 [26] Varian SLAC MARK III [28] 2856 MHz 40 MW 2 µs 60 Hz 21 32
33 : ne ω p = 2 ε 0 γ 3 m 0 [29] n e ε 0 γm 0 v 0 λ p =2πv 0 /ω p ω p ω q ω q /ω p [30] λ q = ω p ω q λ p >λ p λ q /4 λ q /4 33
34 0.1 Tesla PPM (periodic-permanent-magnet focusing) KEK 10 X : KEK UHF S X KEKB ATF / MHz/589 mm 2856 MHz/105 mm GHz/26.2 mm 4.5 µs 50 Hz 1.4 µs 3.6 Hz 1.2 MW 85 MW 73 MW 93.2 kv 397 kv 500 kv 19.8 A 485 A 275 A 0.70 x 10 6 AV 3/ x 10 6 AV 3/ x 10 6 AV 3/2 66% 44% 53% 55.6 db 54.3 db 50 db 17 mm 10 mm 3mm 25 mm 15 mm 4.6 mm 35 mm 45 mm 30.5 mm mm 640 mm 445 mm Tesla 0.13 Tesla ±0.32 Tesla 15mm 30 (λ q ) 4920 mm 1440 mm 720 mm (λ p ) 787 mm 332 mm 166 mm GeV CERN LEP = 4243 km 100 GeV 1TeV 30 km 10,. 34
35 KEK [31] SLAC [32] X (KEK JLC SLAC NLC ) DESY TESLA [33] CERN CLIC [34] 30 GHz 2 TRC [35] 207 TeV [36] MeV [37] 13.1 JLC/NLC 10 GeV / 1.4 ns 190 (100 Hz 120 Hz) / ( 2 GeV) S ms 100 Hz 120 Hz 20 3µm 20nm lattice σ z 5mm 80µm 1 2 =0 (chicane ) GeV X ( GHz) 500 GeV 90 cm MV/m 35
36 56 MV/m 75 MW µs µs DLDS [38] 100 MW 0.375µs σ x = 240nm σ x = 2.6nm 2km [39] mr (hour-glass) 100µm ( 10 4 Tesla) (beam strahlung ) Collimation / Final Focus (5 km) 2nd Bunch Compressor Positron Main Linac ( 12 km) (500 GeV) Electron Main Linac ( 12 km) (500 GeV) 2nd Bunch Compressor Pre-Linac (8 GeV) 1st Bunch Compressor Damping Ring (1.98 GeV) Detector Damping Ring (1.98 GeV) Pre-Damping Ring (1.98 GeV) Electron Linac (10 GeV) Electron Linac Electron Gun (1.98 GeV) Positron Linac (1.98 GeV) Positron Production Target 1st Bunch Compressor Pre-Linac (8 GeV) Electron Gun 27: 1 TeV 13.2 γ 1/207 TeV beam strahlung 36
37 2TeV+2TeV (µ + µ ) [40] 15 Hz 30 GeV ionization cooling [41] chicane 2TeV 100 GeV (recirculator linac ) µ + µ ν µ Linac Proton Linacs Synchrotron Target Solenoid Li/Be Absorbers m+ Collider Recirculation Linac m- Linac 28: 2 TeV 13.3 [42] 1.05 µm 440 fs = s PW = W J W/m 2 11 f: femto P: peta
38 4.5 µm z Z 0 = 377 Ω σ 1 P z = 2 E x H y dxdy = 1 E 2 x dxdy 1 E 2 x πσ 2 2Z 0 2Z 0 E x = GV 2E x σ 660 MV [43] [44] ω p v g 2πv g /ω p z v g c ω 2 = k 2 c 2 + ω p 2 13 ω k ω p n e m e ɛ 0 ω 2 p = n ee 2 ɛ 0 m e v g = ω k = c 1 ω p 2 ω 2 c (1 ω p 2 ) 2ω 2 ω ω p c γ = ω/ω p v p v p = ω k = c2 /v g c (1+ ω p 2 ) 2ω 2 13 [45] 38
39 c λ p λ p =2πv g /ω p 2πc ω p λ p /2 440fs 260 µm m 3 [46] E z =17GV/m Rayleigh L R Fresnel Fraunhofer 2σ λ L R = 2σ2 λ 80µm 1.4MV 200MV E z 200 GV/m 250MV [1] SEGRÈ, E.:From X-rays to Quarks (W. H. Freeman and Company, San Francisco, 1980). [2] LIVINGSTON, M.S.andBLEWETT, J.P.:Particle Accelerators (McGrawhill, 1962). [3] TELEGDI, V. L.: Szilard as Inventor: Accelerators and More, Physics Today, October 2000 (2000)25. [4] CHAO, A. W. and TIGNER, M.: Handbook of Accelerator Physics and Engineering (World Scientific, 1999). [5] - - (, 1999). [6] 6 (, 2001). [7] BRUCK, H.: ACCÉLÉRATEURS CIRCULAIRES DE PARICULES (INSTITUT NATIONAL DES SCI- ENCES ET TECHNIQUES NUCLÉAIRES, Saclay, 1966), 33. [8] E. D. COURANT, M.S.L.and SNYDER, H.S.: Phys. Rev., 88 (1952)1190. [9] COURANT, E.D.andSNYDER, H.S.: Annals of physics, 3 (1958)1. [10] SCHWINGER, J.: Physical Review, 75 (1949)1912. [11] SANDS, M.: Proceedings of the International School of Physics ENRICO FERMI, XLVI (1971)
40 [12], OHO 97 (, KEK, 1997). [13] AKAI, K., et al.: Proc. of 13th Int. Conf. High Energy Accelerators, 2 (1986)303. [14] NISHIKAWA, T.,et al.: Rev. Sci. Instr., 37 (1966)652. [15] KNAPP, E.A., et al.: Rev. Sci. Instr., 39 (1968)979. [16] KAGEYAMA, T.,et al.: Particle Accelerators, 32 (1990)33. [17] ANDREEV, V.G.: Soviet Physics - Technical Physics, 13 (1969)1070. [18] KAPCHINSKII, I.M.and TEPLYAKOV, V.A.: Prib. Tech. Eksp., 2 (1970)19. [19] ALVAREZ, L.W.,et al.: Rev. Sci. Instr., 26 (1955)111. [20] KILPATRICK, W.D.: Rev. Sci. Instr., 28 (1957)824. [21] WILSON, P. B., SLAC-PUB-3674 (1985)18. [22] FOWLER, R.H.andNORDHEIM, L.: Proc. Roy. Soc., A 119 (1928)173. [23] WANG, J.W.,SLAC/AP-51 (1986). [24] A. S. GILMOUR, J.: Microwave Tubes (Artech House, 1986). [25] (, 1987). [26], 48 (1928)284. [27] VARIAN, R.H.and VARIAN, S.F.: Proc. IEEE, 61 (1939)299. [28] CHODOROW, M., et al.: Rev. Sci. Instr., 26 (1955)134. [29] REISER, M.:Theory and Design of Charged Particle Beams (John Wiley & Sons, 1994). [30] (, 1964). [31] [32] project.slac.stanford.edu/lc/nlc.html. [33] [34] [35] trc/ilc trchome.html. [36] [37], 56 (2001)667. [38] TOGE, N., et al.: ISG Progress Report, KEK Report /SLAC R-559 (2000)177. [39] OIDE, K., SLAC-PUB-4660 (2000). [40] PALMER, R.B.,et al.: Proceedings of EPAC 96 (1996)861. [41] SKRINSKY, A.N.and PARAKHOMCHUK, V.V.: Soviet J. Part. Nucl., 12 (1996)223. [42] PERRY, M., et al.: Opt. Lett., 24 (1999)160. [43] BRYANT, P.and MULVEY, J.: The Generation of High Fields for Particle Acceleration to Very High Energies, Proceedings of the CAS-ECFA-INFN Workshop, Frascati 1984, CERN (1985). [44] RUTHERFORD-APPLETON-LABORATORY, : The Challenge of Ultra-Hhigh Energies, Proceedings of the ECFA-RAL meeting, Oxford 1982, ECFA (1983). [45] JACKSON, J.D.:Classical Electrodynamics, 2nd edition (John Wiley & Sons, 1975), chapter [46] NAKAJIMA, K.: Nucl. Inst. Meth., 455 (2000)
Fundamental Concepts of Particle Accelerators Koji TAKATA
Fundamental Concepts of Particle Accelerators Koji TAKATA 2 1920 1MeV 1200 700 3 40 3 1 5 1.1................................ 5 1.2 Livingston................................. 5 1.3 Rutherford.....................
加速器の基本概念 V : 高周波加速の基礎
.... V : KEK koji.takata@kek.jp http://research.kek.jp/people/takata/home.html 2015 2015 4 16 1 2 (1) 3 (2) 4 5 6 ERL: Energy Recovery Linac LCLS: Linac Coherent Light Source LC : µ-µ Koji Takata (KEK)
OHO.dvi
1 Coil D-shaped electrodes ( [1] ) Vacuum chamber Ion source Oscillator 1.1 m e v B F = evb (1) r m v2 = evb r v = erb (2) m r T = 2πr v = 2πm (3) eb v
OHO OHO 1985 [1] ([2] [3] [4] [5] [6] [7] ) KEK KEK 1 Ernest Rutherford Cavendish (1917 ) α α N p O Rutherford [8] 800 kv Cavendish John
![OHO OHO 1985 [1] ([2] [3] [4] [5] [6] [7] ) KEK KEK 1 Ernest Rutherford Cavendish (1917 ) α α N p O Rutherford [8] 800 kv Cavendish John](/thumbs/102/156120900.jpg "OHO OHO 1985 [1] ([2] [3] [4] [5] [6] [7] ) KEK KEK 1 Ernest Rutherford Cavendish (1917 ) α α N p O Rutherford [8] 800 kv Cavendish John")
OHO OHO 985 [] [2] [3] [4] [5] [6] [7] ) KEK KEK Ernest Rutherford Cavendish 97 ) α α + 4 7 N p + 6 8 O Rutherford [8] 800 kv Cavendish John D. Cockcroft Ernest T. S. Walton 932) [9] [0] [] impulse generator
2 [1] KEK Report L C R L C R [2] 2
![2 [1] KEK Report L C R L C R [2] 2](/thumbs/91/105189328.jpg "2 [1] KEK Report L C R L C R [2] 2")
Fundamentals of RF Acceleration Revised Edition Koji TAKATA 2 [1] KEK Report L C R L C R [2] 2 3 Slater [3] Collin [4] [5] [6] [7] MIT Radiation Laboratory Series 8 Principles of Microwave Circuits [8]
Slater[] Collin[] [3] [4] AR 508.6MHz λ =58.9cm 4 9.7m APSAlternating Periodic Structure 50kW.M/m 3M cm 7.5 WR500 f c TE 0 f c = 393MHz 9 90k 0
![Slater[] Collin[] [3] [4] AR 508.6MHz λ =58.9cm 4 9.7m APSAlternating Periodic Structure 50kW.M/m 3M cm 7.5 WR500 f c TE 0 f c = 393MHz 9 90k 0](/thumbs/91/105189250.jpg "Slater[] Collin[] [3] [4] AR 508.6MHz λ =58.9cm 4 9.7m APSAlternating Periodic Structure 50kW.M/m 3M cm 7.5 WR500 f c TE 0 f c = 393MHz 9 90k 0")
00 3-00 3-00 9 30 OHO 97 4.... 4.. 8.3.... 9 3 3..... 3 3.... 5 3.3 π.... 9 3.4.... 0 3.5 APS... 4 4 7 4.... 8 4.... 30 5 35 A 40 L C R L C R Appendix Slater[] Collin[] [3] [4] AR 508.6MHz λ =58.9cm 4
500 MHz Koji TAKATA 1 *1 klystron KEK (Photon Factory PF ) [2] MW S *2 UHF * PF 2.5 GeV 3 PF 180 kw 1.2 MW *1 Gilmo
![500 MHz Koji TAKATA 1 *1 klystron KEK (Photon Factory PF ) [2] MW S *2 UHF * PF 2.5 GeV 3 PF 180 kw 1.2 MW *1 Gilmo](/thumbs/94/118415975.jpg "500 MHz Koji TAKATA 1 *1 klystron KEK (Photon Factory PF ) [2] MW S *2 UHF * PF 2.5 GeV 3 PF 180 kw 1.2 MW *1 Gilmo")
500 MHz Koji TAKATA 1 *1 klystron KEK (Photon Factory PF ) 1970 1960 [2] MW S *2 UHF *3 1976 PF 2.5 GeV 3 PF 180 kw 1.2 MW koji.takata@kek.jp *1 Gilmour [1] *2 2 GHz 4 GHz 2856 MHz 3000 MHz L 1 GHz 2 GHz
X線散乱と放射光科学
8 X II 305 8.1..................................... 305 8.1.1................. 305 8.1.2.................................... 307................................... 307............................ 308.........................
. ev=,604k m 3 Debye ɛ 0 kt e λ D = n e n e Ze 4 ln Λ ν ei = 5.6π / ɛ 0 m/ e kt e /3 ν ei v e H + +e H ev Saha x x = 3/ πme kt g i g e n
003...............................3 Debye................. 3.4................ 3 3 3 3. Larmor Cyclotron... 3 3................ 4 3.3.......... 4 3.3............ 4 3.3...... 4 3.3.3............ 5 3.4.........
6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2
![6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2](/thumbs/92/109118076.jpg "6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2")
1 6 6.1 (??) (P = ρ rad /3) ρ rad T 4 d(ρv ) + PdV = 0 (6.1) dρ rad ρ rad + 4 da a = 0 (6.2) dt T + da a = 0 T 1 a (6.3) ( ) n ρ m = n (m + 12 ) m v2 = n (m + 32 ) T, P = nt (6.4) (6.1) d [(nm + 32 ] )a
Undulator.dvi
X X 1 1 2 Free Electron Laser: FEL 2.1 2 2 3 SACLA 4 SACLA [1]-[6] [7] 1: S N λ [9] XFEL OHO 13 X [8] 2 2.1 2(a) (c) z y y (a) S N 90 λ u 4 [10, 11] Halbach (b) 2: (a) (b) (c) (c) 1 2 [11] B y = n=1 B
K E N Z U 2012 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.2................................... 4 1.2.1..................................... 4 1.2.2.................................... 5................................
Mｏｔｔ散乱によるParity対称性の破れを検証
Mott Parity P2 Mott target Mott Parity Parity Γ = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 t P P ),,, ( 3 2 1 0 1 γ γ γ γ γ γ ν ν µ µ = = Γ 1 : : : Γ P P P P x x P ν ν µ µ vector axial vector ν ν µ µ γ γ Γ ν γ
V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H
199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)
main.dvi
MICE Sci-Fi 2 15 3 7 1 1 5 1.1 MICE(Muon Ionization Cooling Experiment)............. 5 1.1.1........................... 5 1.1.2............................... 7 1.1.3 MICE.......................... 10
B 1 B.1.......................... 1 B.1.1................. 1 B.1.2................. 2 B.2........................... 5 B.2.1.......................... 5 B.2.2.................. 6 B.2.3..................
Bethe-Bloch Bethe-Bloch (stopping range) Bethe-Bloch FNAL (Fermi National Accelerator Laboratory) - (SciBooNE ) SciBooNE Bethe-Bloch FNAL - (SciBooNE
21 2 27 Bethe-Bloch Bethe-Bloch (stopping range) Bethe-Bloch FNAL (Fermi National Accelerator Laboratory) - (SciBooNE ) SciBooNE Bethe-Bloch FNAL - (SciBooNE ) Bethe-Bloch 1 0.1..............................
Table 1: Basic parameter set. Aperture values indicate the radius. δ is relative momentum deviation. Parameter Value Unit Initial emittance 10 mm.mrad
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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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24 I 1.1.. ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x 1 (t), x 2 (t),, x n (t)) ( ) ( ), γ : (i) x 1 (t),
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
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m(ẍ + γẋ + ω 0 x) = ee (2.118) e iωt P(ω) = χ(ω)e = ex = e2 E(ω) m ω0 2 ω2 iωγ (2.119) Z N ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.120)
2.6 2.6.1 mẍ + γẋ + ω 0 x) = ee 2.118) e iωt Pω) = χω)e = ex = e2 Eω) m ω0 2 ω2 iωγ 2.119) Z N ϵω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j 2.120) Z ω ω j γ j f j f j f j sum j f j = Z 2.120 ω ω j, γ ϵω) ϵ
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80 4 r ˆρ i (r, t) δ(r x i (t)) (4.1) x i (t) ρ i ˆρ i t = 0 i r 0 t(> 0) j r 0 + r < δ(r 0 x i (0))δ(r 0 + r x j (t)) > (4.2) r r 0 G i j (r, t) dr 0
79 4 4.1 4.1.1 x i (t) x j (t) O O r 0 + r r r 0 x i (0) r 0 x i (0) 4.1 L. van. Hove 1954 space-time correlation function V N 4.1 ρ 0 = N/V i t 80 4 r ˆρ i (r, t) δ(r x i (t)) (4.1) x i (t) ρ i ˆρ i t
64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k
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99 3 (Coriolis) cm m (free surface wave) 3.1 Φ 2.5 (2.25) Φ 100 3 r =(x, y, z) x y z F (x, y, z, t) =0 ( DF ) Dt = t + Φ F =0 onf =0. (3.1) n = F/ F (3.1) F n Φ = Φ n = 1 F F t Vn on F = 0 (3.2) Φ (3.1)
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ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 +
2.6 2.6.1 ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.121) Z ω ω j γ j f j
68 JAXA-RR r v m Ó e ε 0 E = - Ó/ r f f 0 f 1 f = f 0 + f 1 x k f 1 = f k e ikx Ó = Ó k e ikx Ó k 3
67 1 Landau Damping and RF Current Drive Kazuya UEHARA* 1 Abstract The current drive due to the rf travelling wave has been available to sustain the plasma current of tokamaks aiming the stational operation.
5 1.2, 2, d a V a = M (1.2.1), M, a,,,,, Ω, V a V, V a = V + Ω r. (1.2.2), r i 1, i 2, i 3, i 1, i 2, i 3, A 2, A = 3 A n i n = n=1 da = 3 = n=1 3 n=1
4 1 1.1 ( ) 5 1.2, 2, d a V a = M (1.2.1), M, a,,,,, Ω, V a V, V a = V + Ω r. (1.2.2), r i 1, i 2, i 3, i 1, i 2, i 3, A 2, A = 3 A n i n = n=1 da = 3 = n=1 3 n=1 da n i n da n i n + 3 A ni n n=1 3 n=1
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1 1. (1) a + b = i +3i + k () a b =5i 5j +3k (3) a b =1 (4) a b = 7i j +1k. a = 14 l =/ 14, m=1/ 14, n=3/ 14 3. 4. 5. df (t) d [a(t)e(t)] =ti +9t j +4k, = d a(t) d[a(t)e(t)] e(t)+ da(t) d f (t) =i +18tj
Einstein 1905 Lorentz Maxwell c E p E 2 (pc) 2 = m 2 c 4 (7.1) m E ( ) E p µ =(p 0,p 1,p 2,p 3 )=(p 0, p )= c, p (7.2) x µ =(x 0,x 1,x 2,x
7 7.1 7.1.1 Einstein 1905 Lorentz Maxwell c E p E 2 (pc) 2 = m 2 c 4 (7.1) m E ( ) E p µ =(p 0,p 1,p 2,p 3 )=(p 0, p )= c, p (7.2) x µ =(x 0,x 1,x 2,x 3 )=(x 0, x )=(ct, x ) (7.3) E/c ct K = E mc 2 (7.4)
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I 1 Density Matrix 1.1 ( (Observable) Ô :ensemble ensemble average) Ô en =Tr ˆρ en Ô ˆρ en Tr  n, n =, 1,, Tr  = n n  n Tr  I w j j ( j =, 1,, ) ˆρ en j w j j ˆρ en = j w j j j Ô en = j w j j Ô j emsemble
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59 7 7.1 σ-ω σ-ω σ ω σ = σ(r), ω µ = δ µ,0 ω(r) (6-4) (iγ µ µ m U(r) γ 0 V (r))ψ(x) = 0 (7-1) U(r) = g σ σ(r), V (r) = g ω ω(r) σ(r) ω(r) (6-3) ( 2 + m 2 σ)σ(r) = g σ ψψ (7-2) ( 2 + m 2 ω)ω(r) = g ω ψγ
I-2 (100 ) (1) y(x) y dy dx y d2 y dx 2 (a) y + 2y 3y = 9e 2x (b) x 2 y 6y = 5x 4 (2) Bernoulli B n (n = 0, 1, 2,...) x e x 1 = n=0 B 0 B 1 B 2 (3) co
16 I ( ) (1) I-1 I-2 I-3 (2) I-1 ( ) (100 ) 2l x x = 0 y t y(x, t) y(±l, t) = 0 m T g y(x, t) l y(x, t) c = 2 y(x, t) c 2 2 y(x, t) = g (A) t 2 x 2 T/m (1) y 0 (x) y 0 (x) = g c 2 (l2 x 2 ) (B) (2) (1)
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9 7 A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B x x B } B C y C y + x B y C x C C x C y B = A
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2003-08-04 1984 VP-1001 CPU, 250 MFLOPS, 128 MB 2004ASCI Purple (LLNL)64 CPU 197, 100 TFLOPS, 50 TB, 4.5 MW PC 2 CPU 16, 4 GFLOPS, 32 GB, 3.2 kw 20028 CPU 640, 40 TFLOPS, 10 TB, 10 MW (ASCI: Accelerated
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