磁気圏型プラズマ閉じ込め装置RT-1における自己組織化プラズマの密度限界の解明

織化プラズマの密度限界の解明

著者 森 敬洋

学位授与年月日 2020-03-23

RT

2020 1 28

RT-1 (EC) 1 RT-1 2 RT-1 . 3 2 RT-1 EC 2.45GHz 8.2GHz 2 EC 4 ECH τE 5

1 1 1 1.1 . . . 1 1.2 . . . 3 1.2.1 . . . 3 1.2.2 . . . 4 1.2.3 . . . 5 1.3 RT-1 . . . 6 1.4 . . 7 1.5 . . . 10 1.6 . . . 11 2 12 2.1 RT-1 . . . 12 2.2 RT-1 . . . 15 2.3 RT-1 . . . 17 2.4 . . . 20 2.4.1 . . . 21 2.4.2 . . 23 2.5 . . . 25 2.5.1 Bi-Maxwellian . . . 28 2.5.2 . . . 29

2.5.3 . . . 30 2.6 . . . 31 3 34 3.1 . . . 34 3.2 . 34 3.3 RT-1 36 3.4 2.45GHz . . . 38 3.5 8.2GHz . . . 44 3.6 3 2.45GHz . . . 48 3.7 . . . 49 4 EC 51 4.1 . . . 51 4.2 ECH EC . . . 51 4.3 . . . 54 4.3.1 . . . 57 4.3.2 . . . 59 4.3.3 . . . 59 4.4 . . . 62 4.5 Hall . . . 63 4.6 . . . 66 5 68 70 72 74

1

1.1

2 ∆m ∆E = ∆mc2 D + D → T(1.01MeV) + p(3.03MeV) (1.1) D + D →3 He(0.82MeV) + n(2.45MeV) (1.2) D + T _→4 He(3.52MeV) + n(14.06MeV) (1.3) D +3He →4 He(3.67MeV) + p(14.67MeV) (1.4) D T ( )

1.1. Rate cofficient of nuclear fusion reaction [1]. DT 1.1 [1] DT DT DT 30 6_{Li + n} → T +4He (1.5) 7 Li + n → T +4He + n (1.6) DT DT

1.2

1.2.1 1.2. [2]. . Pb PL . Pheat PF . Q = PF/Pheat . Q = 1 Q = _∞ . .

1.2.2

2

1.3. [3].

1.4. ITER [4].

ITER 1.4

1.5. LHD [5].

Large Helical Device( LHD) [5]

1.3

RT-1

DT

. . β = p B2_/2µ 0 (1.7) p β µ0 . β β Voyager β [6, 7] β [9, 10] [9, 10]. Ring Trap-1 (RT-1) RT-1 (EC) (ECH) β 1 β [11].

1.4

Coherent

1.6. [8].

• 2

• ( Π) (

Ω) kBT

1.7. RT-1 β [11].

•

• R L

R L

• (Ordinary Wave O ) (Extraordinary Wave X )

O X

• (Fast Wave) (Slow Wave)

v = ω/k(ω k )

(Neutron

Beam Injection: NBI) RT-1

ECH

1.5

RT-1

RT-1 8.2GHz

RT-1 RT-1

1.6

2 . 3 RT-1 COMSOL EC . 4 ECH . 5 .

2

2.1

RT-1

RT-1(Ring-Trap1) RT-1 ( a = 0.25m) He 30K . Bi-2223 2160 0.375m 0.18m (PCS) . 20K (2 )

(3 ) ( 2.2 ) . . ( a2 = 0.4m) z = 0.6m , . 3 RT-1 ( 2.1 ) 2.2 Null Separatrix . 2.1. RT-1 .

Levitation magnet 50G 100G 2930G 875G From 8.2GHz klystron From 2.45GHz Magnetron 2.2. RT-1 . 2.45GHz 1kw,1Hz Q ( ) . RT-1 (TG2400)2 10−6_Pa RT-1 ECH 8.2GHz ( 100kW 1s) 2.45GHz ( 20kW 2s) 8.2GHz 2017 6 30

2.45GHz . 2.3 . 2.3. ( ) ( ) RT-1 . .

2.2 RT-1

MHD (2.1) . . ∇p = j × B (2.1) ( ) MHD Grad-Shafranov ( )

RTEQ RT-1 [20] RT-1 WE7000 2.4 RT-1 2.4. RT-1 4 r = 1.01m z = ±0.20m z = _±0.36m p [20] . . 2.5 .

2.5. [20] Seapratrix .

2.3 RT-1

RT-1 3 Mach-Zehnder (= ) [14] RT-1 3 2.6

(Phase Locked Oscillator : PLO)

PLO 18.752GHz

Phase different IF signal 2.6. [22] 75MHz Multiplier 4 75.308GHz 300MHz (IF) . IF (Local

Oscillator Unit : LOU) 300MHz

∆φ .

[13]. N ne N = ! 1₋ ωe ωc "1/2 (2.2) = ! 1₋ ne nc "1/2 (2.3) nc ω nc ≡ ω2meε e2 (2.4) ∆φ ∆φ = # (kp− k0) dl (2.5) = # (N _{− 1)} ω cdl (2.6) ≈ − ω 2cnc # nedl (2.7) ∆φ 2π 2π . 2π(1 ) (2.5) = 2π # nedl = 7.46× 106f m−2 (2.8) RT-1 f = 75GHz # nedl = 5.6× 1017m−2 (2.9)

2.7(a),(b) IF1(r=450mm) IF2(r=620mm) IF3(r=700mm) 3 r L#1 L#2 Levitation magnet Center stack Pumps From 8.2GHz klystron Interferometer1 Levitation magnet Interferometer2 vertical chord (r=60cm) Interferometer3 vertical chord (r=70cm) 50G 100G 2930G 875G (a) (b) From 8.2GHz klystron From 2.45GHz magnetron L#3 2.7. RT-1 (a) RT-1 (b) RT-1 Separatrix (φ = 0.006) IF1 1.60m,IF2 0.87m,IF3 0.76m IF1-3

2.4

0

1 K 0 K 2.4.1 n B 1 exp i(k · r − ωt) vph = ω/k k E B1 vk (k ) j j = $ k nkqkvk (2.10) nk qk k D D = ε0E + P , (2.11) j = ∂P ∂t = −iωP (2.12) E P ε0

D D = ε0E − i ωj ≡ ε0K · E. (2.13) K k mk dvk dt = qk(E + vk × B) (2.14) B = B0+ B1 vk, E, B1 1 1 1 −iωmkvk = qk(E + vk × B) (2.15) B0 z vk,x = −iE x B0 Ωkω ω2 _{− Ω}2 k − Ey B0 Ω2_k ω2_{− Ω}2 k , vk,y = Ex B0 Ω2 k ω2_{− Ω}2 k − iEy B0 Ωkω ω2 _{− Ω}2 k , (2.16) vk,z = −iE z B0 Ωk ω Ωk k Ωk = −q kB0 mk (2.17) (2.16) vk E j (2.10) D (2.13) STIX parameter[13] ϵ· E = ε0K · E = ⎛ ⎜ ⎝ S _{−iD 0} iD S 0 0 0 P ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ Ex Ey Ez ⎞ ⎟ ⎠ (2.18)

S = 1 2(R + L), D = 1 2(R − L), R _{≡ 1 −}$ k ω2 pk ω (ω− Ωs) , L ≡ 1 −$ k ω2 pk ω (ω + Ωs) , P _{≡ 1 −}$ k ω_pk2 ω2 , ωpk2 ≡ nkq2k ε0mk 2.4.2 ∇ × E = −∂B ∂t , (2.19) ∇ × H = j + ϵ0 ∂E ∂t = ∂D ∂t (2.20) k_{× E = ωB}1, k_{× H = −ωϵ}0K · E k× (k × E) + ω 2 c2ϵ· E = 0 (2.21) n _≡ kc ω (c ) n = |n| n (2.21) n_{× (n × E) + ϵ · E = 0} (2.22)

n B0 θ n zx

x (2.22)

⎛ ⎜ ⎝

S − n2_cos2_{θ −iD n}2_{cos θ sin θ}

iD S _{− n}2 ₀

n2cos θ sin θ 0 P − n2_sin2

θ ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ Ex Ey Ez ⎞ ⎟ ⎠ = 0 (2.23) E ̸= 0 0 An4 − Bn2+ C = 0, (2.24) A = S sin2θ + P cos2θ, (2.25) B = RL sin2θ + P S(1 + cos2θ), (2.26) C = P RL. (2.27) (2.24) k ω k ω θ = 0 (2.24) P = 0, n2 = R, n2 = L (2.28) n2 _{= R R n}2 _{= L L} θ = π/2 (2.24) n2 = RL S , n 2 = P (2.29)

n2 _{= P (Ordinary mode wave) n}2 _{= RL/S}

(Extraordinary mode wave)

n 0 n2 = 0 vph = ω k = c n (2.30)

P = 0 or R = 0 or L = 0 (2.31) n2 = ∞ 0 tan2θ =−P S (2.32)

2.5

K k fk(r, v, t) . ∂fk ∂t + v · ∇rfk + qk mk (E + v × B) · ∇vfk = 0 (2.33)

. ∇ · E = 1 ϵ0 $ k qk # fkdv (2.34) 1 µ0∇ × B = ϵ0 ∂E ∂t + $ k qk # vfkdv (2.35) ∇ × E = −∂B ∂t (2.36) ∇ · B = 0 (2.37) fk, B, E 0 exp i(k· r − ωt) fk = fk0(r, v) + fk1 (2.38) B = B0+ B1 (2.39) E = 0 + E1 (2.40)

. v _{· ∇}rfk0 + qk mk (v_{× B}0)· ∇vfk0 = 0 (2.41) $ k qk # fk0dv = 0 (2.42) 1 µ0∇ × B 0 = $ k qk # vfk0dv = j0 (2.43) ∂fk1 ∂t + v · ∇rfk1 + qk mk (v × B0)· ∇vfk = − qk mk (E1+ v × B1)· ∇vfk0 (2.44) ik· E1 = 1 ϵ0 $ k qk # fk1dv (2.45) 1 µ0 k_{× B}1 = −ω + ϵ0E1+ i ω $ k qk # fk1dv , (2.46) B1 = 1 ω (k× E1) (2.47) K(D = ϵ0K · E) . D = ϵ0E + P (2.48) j = ∂P ∂t = −iωP (2.49) 1 ϵ0 D = E1+ i ϵ0ω $ k qk # vfk1dv ≡ K · E1 (2.50) fk1 K .

2.5.1 Bi-Maxwellian 0 Bi-Maxwellian f0(v_⊥, vz) = n0F_⊥(v_⊥) Fz(vz) (2.51) F_⊥(v_⊥) = m 2πT_⊥ exp ! −mv 2 ⊥ 2T_⊥ " (2.52) Fz(vz) = ! m 2πTz "1/2 exp ! −m(vz − V ) 2 Tz " (2.53) . K . K = I +$ i,e Π2 ω2 + $ n ! ζ0Z (ζn)− ! 1− 1 λT " (1 + ζnZ (ζn)) " e−bXn + 2η02λTL , (2.54) Xn = ⎡ ⎢ ⎣ n2_I n/b in(In′ − In) −(2λT)1/2ηn_αnIn −in(I′

n − In) (n2/b + 2b)In − 2bIn′ i(2λT)1/2ηnα(In′ − In)

−(2λT)1/2ηnn_αIn −i(2λT)1/2ηnα(In′ − In) 2λTη2nIn ⎤ ⎥ ⎦ (2.55) Z (ζ) _≡ 1 π1/2 # _∞ −∞ exp(−β2₎ β − ζ dβ, In(b) is the modified Bessel function

ηn ≡ ω + nΩ 21/2_k zvTz , ζn ≡ ω_{− k}zV + nΩ 21/2_k zvTz λT ≡ Tz T_⊥, b ≡ ! kxvT⊥ Ω "2 , α ≡ kxvT⊥ Ω v2_{Tz ≡} Tz m, v 2 T_⊥ ≡ T_⊥ m L Lzz = 1 .

(Tz = T⊥) V = 0 ηn = ζn, λT = 1 . K = I +$ i,e Π2 ω2 3 _∞ $ n=_−∞ (ζ0Z (ζn)) e−bXn + 2ζ₀2L 4 (2.56) 2.5.2 K (k, ω) = KH(k, ω) + iKI(k, ω) (2.57) . ∂W0 ∂t = −ωr 1 2ϵ0E ∗ 0 · KI · E0− ∇ · P (2.58) ( ). Pab Pab = ωr ϵ0 2E ∗_{· K} I · E (2.59) Pab = ωϵ0 2{|Ex| 2

ImKxx +|Ey|2ImKyy +|Ez|2ImKzz

+ 2Im (Ex∗Ey) ReKxy + 2Im

5 Ey∗Ez

6

ReKyz + 2Im (Ex∗Ez) ReKxz}

b ≪ 1

G_±n ≡ Imζ0Z_±n = (kz/|kz|)π1/2ζ0exp(−ζ_±n2 )

(ImKxx)_±n = (ImKyy)_±n = (Πj/ω)2G±nαn (ImKzz)_±n = (Πj/ω)22ζ_±n2 G±nbαnn−2 (ReKxy)_±n = −(Πj/ω)2G±n(±αn) (ReKyz)_±n = −(Πj/ω)2(2b)1/2ζ_±n2 G_±nαnn−1 (ImKxz)_±n = −(Πj/ω)2(2b)1/2ζ_±n2 G_±n(±αn)n−1 αn = n2(2· n!)−1(b/2)n−1 P_±nab = ω ! Πj ω " Gn 7ϵ0 2 8 αn|Ex− iEy|2 (2.60) ζn = (ω + nΩi)/(21/2kzvT i) = (ω − n|Ωi|)/(21/2kzvT i) +n −n 2.5.3 ECH b _{≪ 1, ζ}0 ≫ 1 Kxx = Kyy = 1 + Xζ0Z₋₁/2, Kzz = 1− X + N_⊥2χzz, Kxy = −iXζ0Z₋₁/2, Kxz = N_⊥χxz, Kyz = iN_⊥χyz, χxz ≈ χyz ≈ 2−1/2XY −1 vT c ζ0(1 + ζ1Z−1), χzz ≈ XY−2 7vT c 82 ζ0ζ₋₁(1 + ζ1Z₋₁), X _≡ Π 2 e ω2, Y ≡ Ωe ω , ζ−1 = ω − Ωe 21/2_k zvT , N_⊥ = k⊥c ω

P₋₁ P₋₁ = ωXζ0 π1/2 2 exp ! −(ω − Ωe) 2 2k2 zv2T e " 7_ϵ0 2 8 |Ex− iEy|2 (2.61) ω = Ωe ζ₋₁ = 0, Z₋₁ = iπ1/2, Kxx = 1 + ih, Kxy = h, χyz = χxz = 21/2X(vT e/c)ζ0 = X/(2N∥), χzz = 0, h ≡ π1/2ζ0X/2 K K = ⎡ ⎢ ⎣ 1 + ih h N_⊥χxz −h 1 + ih iN_⊥χxz N_⊥χxz −iN_⊥χxz 1− X ⎤ ⎥ ⎦ (2.62)

2.6

. (Ray-trace) EC k r dr dτ = − ∂D ∂k/ ∂D ∂ω = vg, (2.63) dk dτ = ∂D ∂r/ ∂D ∂ω (2.64) τ vg D(k, ω; r, t) D = det D, D = c 2 ω2 9 kk− k2I + ε (k, ω; r, t): (2.65)

ε Ww ∂Ww ∂t + ∂ ∂r(vgWw) = 2γWw = −ε0E ∗ _{· ε} A · E (2.66) γ εA EC XL O-X . ∇ × ∇ × E = ω 2 c2 ε· E + iωµ0jext (2.67) . ε µ0 jext . Maxwell Maxwell MHz GHz EC RT-1 • EC

•

3

3.1

RT-1 Full wave

3.2

Full wave x 2.45GHz 10kW |B| = Bz ne Bz = 0.05T ne = 2.0× 1017(0.1· ; 0.5_{· y}2_{+ x}2_{− 0.04)m}−3 ( 3.1 ) 0m ≤ x ≤ 1.2m,0m ≤ y ≤ 1.2m

3.1. 2.45GHz λ2.45GHz = _fc ≈ 120(mm) 1/20 1 6-0.6mm COMSOL 2.45GHz O-mode,X-mode 3.2 3.3 2.45GHz R=0( ),S=0( ),P=0( ),L=0( ) O-mode P=0 X-mode X-mode R=0 Ez P=0 RT-1 EC

(a) _|E| (b) Ex (c) Ey (d) Ez 3.2. 2.45GHz O-mode(Ez )

3.3 RT-1

RT-1 ECH 2.45GHz 8.2GHz COMSOL Full-wave 2.45 GHz 8.2 GHz 8.2 GHz EC 2.45 GHz , RT-1 2.45GHz 150mm,8.2GHz 50mm magnet 115 A 2160 lifting

(a) _|E| (b) Ex (c) Ey (d) Ez 3.3. 2.45GHz X-mode(Ey ) magnet 430 A 68 RT-1 ( 3.4 ) ne(r, z) = n0× exp + −a ! ψ(r, z)− ψ(rmax, 0) ψ(1, 0) "2! B(r, z) B0(r, z) "_−b, (3.1) φ(r, z) : (r, z) φ(1, z) : (r = 1.0m, z = 0.0m) B(r, z) : (r, z) B0(r, z) : φ(r, z) z = 0m (n0, a, b, rmax) : 3.1

3.4. RT-1 n0 = 3.5 × 1017m−3, a = 9.33, b = 1.084, rmax = 0.547m Separtrix 3.5

3.4 2.45GHz

RT-1 2.45 GHz ECH 3.6 2.45 GHz-ECH 0 18 kW 0.28 mPa 3.2 mPa RT-1 ne = 1.6× 1017m−3 2.45 GHz EC

3.5. RT-1 ne = 0.8× 1017m−3 . ne = 1.6× 1017m−3 n0 = 3.5×1017_{m−3 a = 9.33, b = 1.084, r} max = 0.547m 2.45GHz O-mode X-mode 3.7 3.7 a 3.7 b X-mode R = 0 O-mode P = 0 EC O-mode X-mode RT-1 P = 0 R = 0 O-mode,X-mode EC (ECR)

2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 Diamagnetism (mWb) 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Line average density (1017m-3)

density limit 2.45 GHz cut off 3.6. RT-1 2.45 GHz ECH (He ). n0 n0 (a) n0 = 3.5× 1016m−3, (b) n0 = 7.0 × 1016m−3, (c) n0 = 2.5×1017m−3 3 2.45GHz nc n0 ≤ nc,n0 ≈ nc,n0 ≥ nc 3.8 3.8 a n0 = 3.5× 1016m−3 2.45 GHz ECR n0 n0 = 7.0× 1016m−3 EM Omode P=0 2 ECR n0 = 2.5× 1016m−3

(a) O-mode (b) X-mode 3.7. 3.6 2.45 GHz R = 0 P = 0 L = 0 S = 0 ECR ). ECR RT-1 RT-1 ECR EC Pabs = ω2_pe 2kzvT e < π 2 exp ! −(ω − ωce) 2 2k2 zv2T e " ϵ0 2 |Ex− iEy| 2 (3.2) ωpe , vT e vT e = ; 2Te/me z

(a) n0 = 3.5× 1016m−3 (b) n0 = 7.0× 1016m−3

(c) n0 = 2.5× 1017m−3

3.8. 2.45GHz (O-mode

k kz z . Ex Ey x y Pabs ECR 3.9 Te 10 eV 3.9. 2.45 GHz ECH , (W/m3_{), n} 0 = 3.5× 1016m−3 . EC ECR (MW/m3)

P_abstotal Pabs

P_abstotal = $Pabs× meshwidth× meshhigh × 2π (3.3)

100 80 60 40 20 0 The e

fficiency of power absorption (%)

1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Line average density (x1017 m-3)

3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Peak density (x1017 m-3) Density limit 2.45 GHz cut off 3.10. O-mode 2.45GHz . 3.10 n0 = 2.5 × 1016m−3 ∼ 70% n0 = 4.2× 1016m−3 0 ECR RT-1

3.5 8.2GHz

8.2Ghz

8.2GHz 8.2GHz λ8.2GHz = _fc ≈ 36(mm) 1/20 1 1.8-0.18mm COMSOL 2.45GHz n0 n0 (a) n0 = 3.5× 1017m−3, (b) n0 = 1.0× 1018m−3, (c) n0 = 1.0× 1019m−3 3 8.2GHz nc n0 ≤ nc,n0 ≈ nc,n0 ≥ nc 3.11 8.2 GHz 3.11(a) n0 n0 = 3.5_×1017_m−3 _{ECR 3.11(b)} n0 = 1.0× 1018m−3 8.2GHz ECR ECR n0 n0 = 1.0× 1019m−3 3.11 c ECR (3.2) 3.12 Te 10 keV . n0 = 0.4× 1018m−3 ∼ 80% n0 = 0.9× 1018m−3 0 2.45GHz 2.45GHz,8.2GHz

(a) n0 = 3.5× 1017m−3 (b) n0 = 1.0× 1018m−3

(c) n0 = 1.0× 1019m−3

3.11. 8.2GHz (X-mode

) R = 0 P = 0 L = 0

100 80 60 40 20 0 The e

fficiency of power absorption (%)

2.0 1.5 1.0 0.5 0.0 Peak density (x1018 m-3) 1.0 0.8 0.6 0.4 0.2 0.0

Line average density (x1018 m-3) 8.2 GHz cut off & density limit

3.12. X-mode 8.2GHz

.

RT-1

3.6 3

2.45GHz

2 RT-1 3.13 3.13. RT-1 . 2.45GHz O-mode n0 n0 (a) n0 = 1.7× 1017m−3, (b) n0 = 2.8× 1017m−3, 2 2.45GHz nc nlim n0 ≈ nc,n0 ≈ nlim 3.14

(a) n0 = 1.7× 1017m−3 (b) n0 = 2.8× 1017m−3 3.14. 2.45GHz R-Z (O-mode ) P = 0 ECR ). R-Z 3.14(a) n0 ≈ nc EC ECR n0 nlim EC Separatrix 3 , EC 3

3.7

RT-1 EC

RT-1 EC 8.2 GHz 2.45 GHz EC ECH 2.45GHz 8.2GHz (EBW) [19] RT-1

4

EC

4.1

ECH ECH

4.2 ECH

EC

[21] (NBI) EC dWp0 dt = − 1 τE0 Wp0 − Prad0 (4.1)

Wp : τE0 : Prad0 : EC dWp1 dt = − 1 τE1 Wp1 − Prad1 + PECH (4.2) PECH : ECRH ’0’,’1’ ECH .

τE0 = τE1 Wp0 = Wp1 Prad0 = Prad1 ECH

(4.1),(4.2) . PECH = ! dWp0 dt − dWp1 dt " (4.3) (4.3) ECH ECH RT-1 Wp ( ) MHD Grad-Shafranov (β) RTEQ [20]. (4.4) [20]. βlocal,max = 18Wdiamag (4.4) βlocal,max % Wdiamag mWb βlocal,max ∼ 100%

(4.4) βlocal,max β βvolume,average βvolume,average = 1 10βlocal,max = 1.8Wdiamag (4.5) MHD β (1.7) p(r, z) p(r, z) = B(r, z) 2 2µ0 · β (4.6) Wp S Wp = # pdV (4.7) Separtrix R z ∆r, ∆z i,j Wp = $ i,j p(ri, zj)· ∆r · ∆z2πri = $ i,j B(ri, zj)2 2µ0 · β volume,average· ∆r · ∆z2π (4.8) r,z 1000 1[mWb] = 150[J] (4.9)

4.3

RT-1 ECH ECH off ECH on-off ECH . 4.1 ECH 20 15 10 5 0 EC H in pu t p ow er (kW ) 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Time (s) 6 5 4 3 2 1 0 D ia ma gn eti sm (1 0 -3 Wb)

ECH input power Diamagnetism

4.1. ECH .

ECH 17kW 8kW

5Hz ( ECH

4.1 ECH 0.1s ECH 2.2mWb 1.6mWb ECH ECRH 4.2 ECRH 4.1 1.8s 2.0s 4 2 0 -2 T he ti me d eri va tive o f D ia ma gn et ism (1 0 -2 Wb) 2.2 2.1 2.0 1.9 1.8 1.7 1.6 Diamagnetism (10-3Wb) 4.2. (4.1),(4.2) 4.2 (dWp dt )/(Wp) −1/τE

ECRH ECRH ECH ECRH (4.3) ECRH ECRH ECH 4.2 (dWp dt )/(Wp) −1/τE ECRH 10 (dWp dt )/(Wp) τE ECH Wp0 = Wp1 (4.3) 4.2 dWp dt − Wp ECH Wp0 = Wp1 dWp/dt

4.3.1 ECH ECH ECH ECH 4.3,4.4 100 80 60 40 20 0 Ab so rp tio n ef fici en cy (% ) 14 12 10 8 6 4 2 0 Modulation frequency (Hz) 4.3. EC (5-12Hz) 4.3 ECH 17kW 50%( ) He 1.77mPa, 2.2mWb 5-12Hz 4.4

100 80 60 40 20 0 Absorption efficiency (%) 100 80 60 40 20 0 Frequency (Hz) 4.4. EC (10-100Hz) ECH 17kW 40% He 1.77mPa, 10-100Hz ECH ECH ECH 4.3 ECH 50%-70%

4.4 ECH 55%-70% 100Hz ECH 5-100Hz 4.3.2 4.5 4.5 ECH 17kW 5Hz He 1.77mPa 2.2mWb 20% 55% RT-1 ECH 4.5 ECH 20% 55% 50-70% 4.3.3 4.6 4.6 10Hz ECH 2kW

100 80 60 40 20 0 Ab so rp tio n ef fici en cy (% ) 60 50 40 30 20 10 0

ECH modulation ratio (%)

4.5. ECH ECH 4-17kW He 1.77-11.8mPa IF1 4.6 2.45GHz ECH 2.45GHz ne = 0.8× 1017_m−3 100% 100% ¯ ne = 0.8 × 1017m−3 RT-1 2.45GHzECH ¯ ne = 1.6× 1017m−3 20% 4.6

120 100 80 60 40 20 0 Absorption efficiency (%) 1.6 1.2 0.8 0.4 0.0

Line averaged density (1017m-3)

2.45 GHz

cutoff density

Density limit

4.6. 2.45GHzECH 2.45 GHz ECR (875G) r = 0.6 m 4.7 ECR Separatrix −0.25m ≤ Z ≤ 0.25m ECR ECH EBW

16 14 12 10 8 6 4 2 0

The electron density

on the 2.45 GHz ECR layer (x10

16 m -3) -0.4 -0.2 0.0 0.2 0.4 Z (m) n0=3.5x1017m-3 n0=1.8x1017m-3 2.45 GHz cut off density (a) 2.45 GHz ECR (875G) 30 25 20 15 10 5 0

The electron density

on the 2.45 GHz ECR layer (x10

16 m -3) -0.4 -0.2 0.0 0.2 0.4 Z (m) n0=3.5x1017m-3 n0=1.8x1017m-3 2.45 GHz cut off density

(b) r = 0.6 m 4.7. 2.45 GHz ECR (875G) r = 0.6 m (n0 ≈ nc n0 ≈ nlim )

4.4

ECH (4.2),(4.1) 4.2 τE 4.8 4.8 ECH 17kW 40% He 1.77mP 10-40Hz τE 10-20ms 4.9 4.9 10Hz ECH 2kW

30 25 20 15 10 5 0 En er gy c on fin eme nt t ime ( ms ) 50 40 30 20 10 0 Modulation frequency (Hz) 4.8. ECH 4-17kW He 1.77-11.8mPa IF1 τE = 60ms ¯ ne = 1.6× 1017m−3 10ms

4.5 Hall

Hall

80 60 40 20 0 En er gy c on fin eme nt t ime ( ms ) 1.6 1.2 0.8 0.4 0.0

Line averaged density (1017m-3)

4.9.

Hall Honeywell SS496A

±640G Hall (R, Z) = (0.395m,_−0.40m) ECH 7Hz Hall Bz 4.10 ECH Hall ECH Hall [20] Hall 4.11 50Hz Hall Bz

2.5 2.0 1.5 1.0 0.5 0.0 D ia ma gn et ism( 10 -3 Wb) 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Time (s) -10 -8 -6 -4 -2 0 2 Bz (G ) 4.10. 7Hz Hall Bz Hall 3ms 3ms 3ms τE 10ms 3ms

10.0 9.8 9.6 9.4 9.2 9.0 -Bz (G) 1.84 1.82 1.80 1.78 1.76 Time (s) 2.40 2.35 2.30 2.25 2.20 D ia ma gn et is m (1 0 -3 W b) Hall probe Flux loop 4.11. 50Hz Hall Bz

4.6

ECH RT-1 MHD ECH

Wp0 = Wp1 (4.3) nc 100 1.5nc 0 EC τE 60ms 10ms

5

RT-1 EC ECR 2 . 1. RT-1 EC 2. ECH EC 1 RT-1 EC ECR EC RT-1 EC 2 EC RT-1 8.2 GHz 2.45 GHz EC

EC 2 3 2 ECH EC ECH 10Hz 2kW EC nc 100% 1.5nc 0 ECR τE 60 ms 10 ms RT-1 EC 2 3

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[2] ,

(2007). [3]

(2013).

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(1987).

[10] A. Hasegawa, L. Chen, and M. E. Mauel, Nucl. Fusion, 30, 2045 (1990).

[11] M. Nishiura, et al., Nucl. Fusions 55, 053019 (2015). [12] Z. Yoshida, et al., Phys. Plasmas 17, 112507 (2010). [13] T.H.STIX, Waves in Plasmas (AIP press, 1992)

[14] I. H. Hutchinson, Principles of Plasma Diagnostics Second Edition (Cambridge University Press, 2002)

[15] K. Miyamoto, Plasma Physics for Controlled Fusion (Iwanami Book, 2012)

[17] H. P. Laqua, et al., Phys. Rev. Lett. 78, 3467 (1997). [18] R. Ikeda, et al., Contrib. Plasma Phys. 50, 567 (2010).

[19] K. Uchijima, et al., Plasma and Fusion Research 6, 2401122 (2011).

[20] β (2010). [21] (2015). [22] RT-1 (2018). [23] RT-1 ICRF (2016).

1. T. Mori, M. NISHIURA, Z. YOSHIDA, N. KENMOCHI, S. KAT-SURA, K. NAKAMURA, Y. YOKOTA, T. TSUJIMURA, and S. KUBO

”Simulation of electromagnetic wave propagation in a magneto-spheric plasma”

Plasma Fusion Res. 14 (2019) 3401134-1-3401134-5 [doi:10.1585/pfr.14.3401134]

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2019 , 10pK22-3, (2019.9.10) 3. ( ) , , , , , , , , ” EC ” 75 , 16pD13-5, (2019.3.16)

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1. Takahiro Mori, Masaki Nishiura, Toru I. Tsujimura, Zensho Yoshida, Naoki Kenmochi, Shotaro Katsura, Kaori Nakamura, Yuuki Yokota, Shin Kubo

”Simulation of Electromagnetic Wave Propagation in a Magneto-spheric Plasma,”

The 27th International Toki Conference on Plasma and Fusion Research &The 13th Asia Pacific Plasma Theory Conference, P2-83, Ceratopia Toki, Toki-city, Gifu, Japan (2018.11.19-22)

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