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- つねたけ はぎにわ
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2 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 CPU 640, 40 TFLOPS, 10 TB, 10 MW (ASCI: Accelerated Strategic Computing Initiative! Advanced Simulation and Computing Program)
3 analysis synthesis
4 イオン 電子 クーロン力
5 dr j dr j = v j ; dv j = q m = v jke k + v drift (R j ;μ j ; t); dv jk (1) r j v j h i E(r j ; t) + v j B(r j ; t) dt dt R=μ= = q m E k(r j ;μ j ; t) dt dt
6 @n (n su s ) = 0; n s m s du s s fl m ρ p (2) (r; v) f (r; v; t), f (R;μ;v k ; t) (r) n(r; t), u(r; t), p(r; t) f + f f v B(r; t)] [E(r; = + coll + q m ψ! f k e k + v drift f v + q m E f @ f d pn fl = + n sq s (E + u B) + R s ; (ρ du mu) = 0; ρ m + + j B; E + u B = j; d dt
7 (3)
8 r 2 Φ = ρ ext = 0 r 2 A k = μ 0 j k ; r 2 Φ = ρ ext = 0 ) 2 1=d r E B = 1 + μ 0 j r
9
10 1. (consistency) 0 2. (accuarcy) 3. (stability) 4. (eciency)
11 (1) Lipschitz
12 (2) Explicit x (n+1) = F(x (n) ; t) t L x V V < x= t Implicit x (n+1) = F(x (n) ; x (n+1) ; t)
13 (3) (!$ I $ A) x = 0 $ A(!) x = 0 $ A(!) x = jxj!
14 CPU CPU CPU CPU CPU CPU Memory CPU CPU CPU CPU CPU CPU CPU Mem Mem Mem Mem Mem Mem CPU
15 =) 32bit CPU CPU 12 GB 64bit CPU : CPU 2 GB
16 ο 0:1mm ο 0:1mm ο 3mm ο 30 mm ο 1m ο 3m 140 GHz ο 100 GHz ο 100 GHz ο 3GHz ο 50 MHz ο 100 khz ο 10 khz ο 1s ο 1s ο EC LH IC MHD
17 (1) JFT-2M OFMC
18 (2)
19 70 20 TASK/WR Poloidal angle Toroidal angle beam 2m curvature Initial Ray/Beam Pro le Initial beam radius 0:05 m P abs Pro le j CD Pro le
20 f = 200 GHz, N = 0:2, r = 0:05 m r = 1:5m r=0.05 m r=1.5 f(p 0,p 0 )-f (-p 0,p 0 ) = f(p 0,p 0 ) = f = 200 GHz, N = 0:2, r = 0:05 m TASK/FP
21 =)
22 E θi P e E θi ITER P e ρ ρ TASK/WM
23 (3) DIII-D, JT-60 ITER JT-60 ITER JET, DIII-D
24 (1) Ware
25 @B = 1 V + S s V 0 hjrρji 3 2 n st s V Es V 0 hjrρj 2 in s χ s 0 B V *jrρj 2 R 2 + FR 0 hr 2 i hj Bi ext + P s (2) V:ρV 0 = dv=dρ 0 (n sv 0 ) hjrρjin s V s hjrρj 2 id s 05=3 V 2 n st s @t» 0 F R V 0 FR 0 hr 2 i F
26 χ TB = F(s;ff;»;! E1 ) ff 3=2! 2 pe >< >: 1 + G 1! 2 E1 1 + G 1! 2 E1 1 0 p 2s )(1 2s0 + 3s 02 ) 2(1 CDBM 2.5 F(s;ff;»;! E1 ) s ff c2 v A 2.0 ω E1 =0 ω E1 = dq F 1.0 ω E1 =0.2 ω E1 =0.3 qr s r q ff q 2 R dfi 0.5 dr» r R ψ dr 1 1 q 2! s - α 8 qr de B A sv E B! E1 1 dr for s 0 = s ff < 0 F BM = 1 + p 2s 05=2 1 9 p 0 2s + 3s02 + 2s 03 ) 2(1 for s 0 = s ff > 0 E B
27 JT-60U : T [kev] Wdia [MJ] Ip [MA] τε / τε ITER89-P ne [10 19 m -3 ] TASK/TR Ip JT-60U T i (0.34a) t [s] Wdia t [s] n (0) t [s] t [s] T e (0) τ Ε / τ Ε ITER89-P P NBI Sn n (0.7) β N β N PNBI [MW] Sn [10 16 s -1 ] Ip [MA] Wdia [MJ] ne [10 19 m -3 ] T [kev] τ P NBI I BS n e (0) T i τ 1 W B t [s] t [s] t [s] <T e > t [s] Ip <n e > τ2 I OH <T i > Wi We T e τ Ε PNBI [MW] q T [kev] JT-60U r / a JT-60U r / a q t = 2.0 t = 2.8 t = 3.6 t = 4.4 t = 5.2 r [m] T [kev] t = 2.6 t = 2.5 t = 2.4 t = 2.3 t = 2.2 t = 2.1 t = 2.0 t = 2.8 t = 2.7 r [m] t [s] t [s]
28 @n s m s n s u s = 1 (rn su sr ) + S (rm sn s u 2 sr ) + 1 r m sn s u 2 s + e sn s (E r + u s B u s n st s +F C s + FW s + FX s + FL s ψ 5 +P C s + PL s + PH s rn s m s μ u s = @t (m sn s u sr )= 1 r sn s u s )= r (r2 m s n s u sr u s ) + e s n s (E u sr B ) + 1 r r 3 n s m s @r r NC s + F C s + FW s + FX s + FL s @t (rm sn s u sr u s ) + e s n s (E + u sr B ) + @ 2 u srn s T s n s T 3 + e s n s (E u s + E u s 2 n st s = 1 r
29 TASK/TX0:3m 2 =s10 m 2 =s JFT-2M NBI! =) =)
30 JFT-2M JFT-2M Ida et al.: Phys. Rev. Lett. 68 (1992) 182
31 ref: Z. Lin et al.: IAEA-2000 TH2-3
32 ref: W. Park et al.: IAEA-2002 TH5-1 (NTM) (RWM) (AE)
33 SOL JT-60U
34 EC LH IC MHD MHD MHD
35 ITER
36 TASK WR EQ WM TR DP FP
37 TASK EQ, TR, WR, WM EQ CDBM TR WR WM
38
ohpr.dvi
2003/12/04 TASK PAF A. Fukuyama et al., Comp. Phys. Rep. 4(1986) 137 A. Fukuyama et al., Nucl. Fusion 26(1986) 151 TASK/WM MHD ψ θ ϕ ψ θ e 1 = ψ, e 2 = θ, e 3 = ϕ ϕ E = E 1 e 1 + E 2 e 2 + E 3 e 3 J :
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IB IIA 1 1 r, θ, φ 1 (r, θ, φ)., r, θ, φ 0 r
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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
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( ) Note 3 19 12 13 8 8.1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R, µ R, τ R (1a) L ( ) ) * 3) W Z 1/2 ( - )
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I 1 m 2 l k 2 x = 0 x 1 x 1 2 x 2 g x x 2 x 1 m k m 1-1. L x 1, x 2, ẋ 1, ẋ 2 ẋ 1 x = 0 1-2. 2 Q = x 1 + x 2 2 q = x 2 x 1 l L Q, q, Q, q M = 2m µ = m 2 1-3. Q q 1-4. 2 x 2 = h 1 x 1 t = 0 2 1 t x 1 (t)
More information(e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a
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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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7 -a 7 -a February 4, 2007 1. 2. 3. 4. 1. 2. 3. 1 Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e z
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More information) 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)
4 4 ) 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) a b a b = 6i j 4 b c b c 9) a b = 4 a b) c = 7
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9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) 2. 2.1 Ĥ ψ n (r) ω n Schrödinger Ĥ ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ + Ĥint (t)] ψ (r, t), (2) Ĥ int (t) = eˆxe cos ωt ˆdE cos ωt, (3)
More information4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.
A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c
More informationC : q i (t) C : q i (t) q i (t) q i(t) q i(t) q i (t)+δq i (t) (2) δq i (t) δq i (t) C, C δq i (t 0 )0, δq i (t 1 ) 0 (3) δs S[C ] S[C] t1 t 0 t1 t 0
1 2003 4 24 ( ) 1 1.1 q i (i 1,,N) N [ ] t t 0 q i (t 0 )q 0 i t 1 q i (t 1 )q 1 i t 0 t t 1 t t 0 q 0 i t 1 q 1 i S[q(t)] t1 t 0 L(q(t), q(t),t)dt (1) S[q(t)] L(q(t), q(t),t) q 1.,q N q 1,, q N t C :
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2004/03/23 TASK PAF - - - EC LH IC MHD - - - - Focused Integration Initiatives are built from Fundamentals of varying complexity with selected algorithms using interoperable software Plasma Edge Sources
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