ohpr.dvi

Size: px

Start display at page:

Download "ohpr.dvi"

おきまさはやしもと
5 years ago
Views:

1 2004/03/23 TASK PAF

2 - - -

4 EC LH IC MHD

6 Focused Integration Initiatives are built from Fundamentals of varying complexity with selected algorithms using interoperable software Plasma Edge Sources Turbulence X-MHD 1 1/2 D Transport Materials Turbulence on Transport Timescale Global Stability Whole Device Modeling

7 We expect a 15 year timeline is required to produce the FPS New Capability Funding Years

8 What does integrated modelling mean? Physics Integration: Integration of MHD, transport, exhaust, energetic particle physics, etc Need to foster interactions between different physics areas Code Integration: Creating a set of validated, benchmarked codes Standardised inputs/outputs to allow modules from different codes to be linked Discipline Integration: Success of the TF relies on input from: Theoreticians to build/improve the appropriate mathematical models Modellers to construct efficient, accurate codes for the models Experimentalists to provide data to validate models. Involvement of each community will be important for the success of the TF

9 How will the work be organised? (1) We have organised the work into four areas Area 1: Identification of codes and models Take an initial census of codes and classify them Identify a number of integration projects to develop Make recommendations for code/model development and documentation Area 2: Interfacing procedure and numerical support Propose the global structure of integrated modelling Develop the interfacing procedure Identify a code version handling procedure Make recommendations for language, libraries, etc Develop the necessary numerical tools Evaluate the present numerical expertise and hardware within EFDA

10 How will the work be organised? (2) Area 3: Code validation and benchmarking Determine the validation process (the procedure and documentation) Develop an appropriate database for the validation procedure Make recommendations for validation experiments Provide a priority list for code integration (common task with Area 1) This process will provide/test physics understanding for existing data Area 4: ITER integrated scenario activity Not yet activated (later in 2004) Aim is to provide an assessment of ITER scenarios Will support ITER scenario development in existing devices

15 TASK MPI

16 TASK Transport Analyzing System for tokamak TASK/EQ TR TX WR EC, LH: WM IC, AW: FP DP LIB PL

17 TASK

18 TASK/DP : (, ) MHD Maxwellian Maxwellian Maxwellian n, u, T, B n, u, T, B, n, T, B, E

19 TASK/WR L λ d δ = λ/l 1 H n ] E(r) =Re [C(δ 2 r)e(δ 2 r)e i s(r) φ(r) Ces(r)+ iφ(r) s(r) =s 0 (τ)+kα(τ)[r 0 α r0 α (τ)] s αβ[r α r0 α (τ)][r β r β 0 (τ)] φ(τ) = 1 2 φ αβ[r α r α 0 (τ)][r β r β 0 (τ)] r 0 k 0 R α =1/λs αα, d α = 2/φ αα

20 dr α 0 dτ dk 0 α dτ ds αβ dτ dφ αβ dτ = K k α = K r α = 2 K r α r β ( 2 K = r α k + γ 2 K r β k γ s αγ 2 K k γ k δ s αδ 2 K r α k γ s βγ ) φ βγ ( 2 K r β k γ + 2 K k γ k δs αγs βδ + 2 K k γ k δ s βδ 2 K k γ k δφ αγφ βδ ) 18 C mn (v g0 C mn 2) = 2 ( γ C mn 2) v g0 γ (e ɛ A e)/( K/ ω) φ αγ

21 Beam Tracing in ITER-FEAT Plasma: R c =2m,d ini =0.05 m 4 θ t =0 θ t =10 θ t = d [m] ψ 1/2 d [m] ψ 1/2 d [m] ψ 1/ P abs [arb] P abs [arb] P abs [arb] ψ 1/ ψ 1/ ψ 1/2

22 Beam Tracing in ITER-FEAT Plasma: R c =2m,d ini =0.05 m 4 θ t =0 θ t =10 θ t = d [m] d [m] d [m] ψ 1/ ψ 1/ ψ 1/ P abs [arb] ψ 1/2 P abs [arb] ψ 1/2 P abs [arb] ψ 1/2 ]

23 TASK/FP f(p,p,ψ,t) f = E(f)+C(f)+Q(f)+L(f) (1) t E(f) : C(f) : Q(f) : L(f) : 0 p

24 TASK/WM (ψ, θ, ϕ) E = ω2 c 2 ɛ E +iωµ0 j ext ɛ Z[(ω nω c )/k v th ] [ t + v +(v d + v E ) + e α (v E + v d E) ] f α =0 m α ε k

25 LHD ICRF LHD (B 0 =3T,R 0 =3.8m) f =42MHz,n φ0 = 20, n e0 = m 3, n H /(n He + n H )=0.235, N rmax = 100, N θmax =16(m = 7...7), N φmax =4(n =10, 20, 30)

26 42 MHz 44 MHz 46 MHz 48 MHz 42 MHz 44 MHz 46 MHz 48 MHz P abs (arb.) f [MHz]

27 q q a q q min q 0 q min 0 ρ min 1 ρ R 0 a B 0 n e (0) 3m 1m 3T m 3 T (0) 3 kev q(0) 3 q(a) 5 ρ min 0.5 n 1 Flat density profile

28 Alfvén resonance q min =2.4 q min =2.5 q min =2.6 Higher freq. Lower freq. TAEs Double TAE RSAE

29 (q min =2.6) Without EP n F = 0 m -3 fi [MHz] f r [MHz] With EP m kev 0.5m Eθ m = 3 f r = 38.0 khz f i = Hz ρ fi [MHz] n F = m f r [MHz] Eθ m = 2 m = 3 f r = 55.3 khz f i = 75.7 Hz ρ With EP m kev 0.5m Eθ m = 3 ρ f r = 37.2 khz f i = Hz fi [MHz] n F = m f r [MHz] Eθ m = 2 m = 3 ρ fr = 55.3 khz f i = Hz

30 TASK TASK ITPA MHD

31 PAF PAF: Plasma Analysis with Finite element method WF: WF2: (2D) WF3: (3D) MF: TF: (2D) FF: PF: (2D) MG: MX:

32 PAF/WF: ω : Ẽ(r,t)=E(r)e i ωt : E ω2 c 2 ɛ E =iωµ0 j ext ɛ : :

33 H. Kousaka and K. Ono: JJAP 41 (2002) 2199 FDTD: : f =2.45 GHz

34 E z (r, z) n e =10 16 m 3 n e =10 17 m 3 2D 3D (Real part) 3D (Imag part)

35 E z (r, z) n e = m 3 n e = m 3 2D 3D (Real part) 3D (Imag part)

36 E z (z) 2D Analysis 3D Analysis n e =10 16 m 3 n e =10 17 m 3 Ref.:H.KousakaandK.Ono JJAP 41 (2002) 2199 n e = m 3 n e = m 3

37 ICP Diameter=0.48 m Height=0.3m Frequency=13.56 MHz Antenna Plasma

39 x =0

40 PAF/TD n s, T s, φ (s = electron, ion)

41 n s, T s, Φ t n s = [n s µ s Φ+ ] D s n s + ν Is n s t 3 2 n st s = [ 5 2 T s (n s µ s Φ+ ) D s n s 3 2 ν snn s (T s T n ) Φ= 1 Z s en s ɛ 0 s n s χ s T s ] ν ss n s (T s T s )+P s s µ s : D s : χ s : Z s s P s : ν Is : ν sn : ν ss :

42 (n e =10 12 m 3 ) B Ψ P e Φ n e T e (n e =10 14 m 3 ) B Ψ P e Φ n e T e

44 R =25, =2, t =0.1, N p = (Preliminary) y x y x.

46 x = x + v(t t ) v t t x E(x ) Vlasov df(x,t ) = q dt m E(x,t ) f 0(v) v qn t ) 0 f(x, v, t) = dt ve(x,t )exp ( mv2 (2πT/m) 3/2 T 2T j(x, t) = f(x, v, t) K(x x,t t )= j(x, t) = dvqvf(x, v, t) qn 0 (2πT/m) 3/2 T dx K(x x,t t ) E(x,t ) [ t dt x x t t exp m 2T ( ) ] x x 2 t t

47 n(x) =n 0 e κx Φ(x) = κt q x 1 β 2 E(x) dx ɛ (x x ) E(x )=0 ɛ (x x )=δ(x x ) I i ω2 p0 ω e κ(x+x ) 2 (x x ) 2 U 2 κ 2 U 2 i n y β[(x x )U 0 κu 2 ] 0 i n y β[(x x )U 0 + κu 2 ] U 0 n 2 yβ 2 U U 0 U n = U n (ω(x x )/ T/m, κ 2 + n 2 yβ 2, ) T/m, β = T/m/c U n (ξ,η) = 1 [ dτ τ n 1 exp 1 ξ 2 2π 2τ 1 ] 2 2 η2 τ 2 +iτ 0

48 (ω 2 p/ω 2 ) max =2,(ω 2 p/ω 2 ) min =0, n y =0.2 β =0.1 E x E y P abs 37.7%

49 Absorption Rate n y

50 ( B(z) =B 0 1+ x ) L 1 β 2 E(x) dz ɛ (z,z ) E(z )=0 ɛ (z,z )=δ(z z ) I i ω2 p0 ω 2 (χ + χ )/2 i(χ χ )/2 0 i(χ χ )/2 (χ + χ )/ χ 0 χ 0 = (1 + κz)(1 + κz ) (1 + κ(z + z )/2) χ ± = (1 + κz)3/2 (1 + κz ) 3/2 U (1 + κ(z + z )/2) 2 0 (ξ ± ) [ ξu 2 (ξ) κ 2 2(1 + κ(z + z )/2) 2U 2(ξ) ξ = ω(z z ), ξ ± = (ω +Ω)(z z ), Ω= qb 0 T/m T/m m (1+(z +z )/2L), κ = U n (ξ) = 1 2π 0 dθ exp θn+1 [ 1 ξ 2 ] 2θ +iθ 2 ] T/m ωl

ohpr.dvi

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 :