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 : J = 1 e 1 e 2 e = 1 3 ψ θ ϕ g : e i r/ x i g ij = e i e j
E ω c E = ω2 c 2 ɛ E +iωµ0 j ext ɛ : j ext : ( E) 1 = 1 J [ { ( g31 E3 x 2 J x E ) 2 2 x 3 { ( g21 E3 x 3 J x E ) 2 2 x 3 + g 32 J + g 22 J (x 1,x 2,x 3 ) (ψ, θ,ϕ) ( E1 x E ) 3 3 x 1 ( E1 x E ) 3 3 x 1 + g 33 J + g 23 J ( E2 x E )} 1 1 x 2 ( E2 x E )}] 1 1 x 2
ɛ z ê s = ψ ψ, ê b = ê h ê ψ, ê h = B 0 B 0 µ µ 1 g 11 d Jg 11 E 1 E 2 E 3 c 2 g 12 + c 3 g 13 0 c 3 J g 11 c 2 g 22 + c 3 g 23 0 c 2 J g 11 c 2 g 32 + c 3 g 33 = µ ɛ = µ ɛ sbh E s E b E h c 2 = B θ /B, c 2 = B φ /B d = c 2 (g 23 g 12 g 22 g 31 )+c 3 (g 33 g 12 g 32 g 31 ) g 11 =(g 22 g 33 g 23 g 32 )/J 2 µ 1
E(ψ, θ, ϕ) = mn E mn (ψ)e i(mθ+nϕ) G(ψ, θ, ϕ) = lk G lk (ψ)e i(lθ+kn pϕ) J( E) =G(ψ, θ,ϕ)e(ψ, θ, ϕ) = m n [J( E)] m n ei(m θ+n ϕ) N h : E n m kn h l J( E) n m n = n + kn h m = m + l
ɛ (ψ, θ, ϕ, k m n ) Z[(ω Nω cs )/k m n v Ts ] k m,n k m,n = iê h = iê h ( θ θ + ϕ ϕ )= iê h (e 2 θ +e3 Bθ Bϕ )=m +n ϕ B B ɛ sbh (J ɛ E) i = J g 1 µ ɛ sbh µ 1 E i m l 3 l 2 l 1 m n k 3 k 2 k 1 n m = m + l 1 + 1 2 l 2 n = n + k 1 + 1 2 k 2 m = m + l 1 + l 2 + l 2 n = n + k 1 + k 2 + k 3
TASK/WM Fortran77 + MPI 16 50 Elapsed Time [sec] 2800 2400 2000 1600 1200 800 400 Dispersed Gauss(PARA) ILDUBCG(PARA, BLK) ILDUCGS(PARA, BLK) ILDUBCGSTAB(PARA, BLK) Reduced Gaussi(PARA, BLK) ILDUBCG(PARA, BLK, APP) ILDUCGS(PARA, BLK, APP) ILDUBCGSTAB(PARA, BLK, APP) 0 1 2 3 4 5 6 7 8 Number of Processor
LHD (B 0 =3T,R 0 =3.8m) f =42MHz,n φ0 = 20, n e0 =3 10 19 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)
42 MHz 44 MHz 46 MHz 48 MHz 42 MHz 44 MHz 46 MHz 48 MHz P abs (arb.) 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 25 30 35 40 45 50 55 60 f [MHz]
PAF PAF: Plasma Analysis with Finite element method WF: (3D) MF: TF: (2D) FF: PF: (2D) MG: MX:
PAF/WF: ω : Ẽ(r,t)=E(r)e i ωt : E ω2 c 2 ɛ E =iωµ0 j ext ɛ : :
H. Kousaka and K. Ono: JJAP 41 (2002) 2199 FDTD: : f =2.45 GHz
E z (r, z) n e =10 16 m 3 n e =10 17 m 3 2D 3D (Real part) 3D (Imag part)
E z (r, z) n e =2 10 17 m 3 n e =3 10 17 m 3 2D 3D (Real part) 3D (Imag part)
E z (z) 2D Analysis n e =10 16 m 3 3D Analysis n e =10 17 m 3 Ref.: H.KousakaandK.Ono JJAP 41 (2002) 2199 n e =2 10 17 m 3 n e =3 10 17 m 3
ICP Diameter=0.48 m Height=0.3m Frequency=13.56 MHz Antenna Plasma
x =0
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
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 2 0 0 0 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
(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%
0.6 0.5 Absorption Rate 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 n y
( 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 )/2 0 0 0 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
ω 2 pe /ω2 =0.1
n y =0.2
n y =0.5