1. US-Japan Workshop on Fusion Power Plants and Related Advanced Technologies with participations of EU and Korea （ 22-24 Feb. 2011 ）

2. J. Miyazawa, 第 424 回 LHD 実験グループ全体会議 （ 30 Aug. 2010 ） 2/15

3. J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） 3/14

4. J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） 4/14 Conventional procedure (inductive approach) New procedure using DPE (deductive approach)

5. J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） DPE: Direct Profile Extrapolation From the definition: f  = f T f n f B -2  f T = f  f n -1 f B 2 (1) Gyro-Bohm:  E GB  a 2.4 R 0.6 B 0.8 P -0.6 n 0.6 n T a 2 R / P  a 2.4 R 0.6 B 0.8 P -0.6 n 0.6 T  a 0.4 R -0.4 B 0.8 P 0.4 n -0.4  f T =  f a/R 0.4 f B 0.8 f P 0.4 f n -0.4 (2) delete f T from Eqs. (1) and (2)  f P =  -2.5 f  2.5 f a/R -1 f B 3 f n -1.5 (3) Then, f a is determined so as to satisfy P reactor = f a 3 f a/R -1 f n 2 (  P  ’ – P B ’) (dV/d  ) exp d  =  -2.5 f  2.5 f a/R -1 f B 3 f n -1.5 P exp (in this study, f a/R =  = Z eff = 1) 5/14 f X : enhancement factor of X （ e.g. f T = T reactor (  ) / T exp (  ), f n = n reactor (  ) / n exp (  ), f P = P reactor / P exp ） Equilibrium in LHD Volume integration of (alpha heating – Brems.) One can calculate the alpha heating power per unit volume by assuming f B, f n, and f  f a (= f R ) is obtained if f B, f n, f  and  are given f a (= f R ) is obtained if f B, f n, f  and  are given Plasma volume × f a 3 f a/R = 1 (f a = f R )  : confinement enhancement factor

6. J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） 6/14 × f n × f T × f  Heating power × f P Mag. Field × f B Confinement ×  Plasma volume × f a 3

7. J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） 7/14 What is this lower envelope?

8. J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） P reactor = f a 3 f a/R -1 f n 2 (  P  ’ – P B ’) (dV/d  ) exp d  ∝ f a 3 f a/R -1 f n 2 f T X ∝ f a 3 f a/R -1 f n 2 (f  f n -1 f B 2 ) X ∝  -2.5 f  2.5 f a/R -1 f B 3 f n -1.5 P exp  f a 3 ∝  -2.5 f  2.5-X f B 3-2X f n -3.5+X P exp. (X = 3.5)  f a ∝  -5/6 f  -1/3 f B -4/3 P exp 1/3 8/14  Eq. (3) f n dependence disappears… R reactor = C exp  -5/6 f  -1/3 B -4/3 C exp A small C exp results in a compact reactor Temp. dependence: f T X

9. 輻射損失の効果 J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） (  P  ’ – P B ’) (dV/d  ) exp d  ∝ f T X  ∝ T X (X =3.5 @ T ~ 7.1 keV w/o Bremsstrahlung) 9/14 T 0 ~10 keV Actually, the plasma size becomes minimum at T 0 ~10 keV (due to Brems. and volume-integration) Temp. dependence of DT fusion reaction rate Temp. dependence of an index X ( ~ T X ) ~ T 3.5 Bremsstrahlung

10. J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） 10/14 C exp １） Set f n = f  =  = 1: f T = f B 2 ２） Scan B reactor = f B B exp : Heating power: f B 3 P exp Volume-integration: (P  ’ – P B ’) (dV/d  ) exp d  R reactor = [(Heating power) / (Volume-integration)] 1/3 R exp ３） The minimum of R reactor / B reactor -4/3 is the C exp (Note: in some cases, f n = 1 might be inadequate!)

11. 11/14 J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） R reactor = C exp  -5/6 f  -1/3 B -4/3 FFHR-d1

12. J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） 12/14 FFHR-d1

13. J. Miyazawa, 第 424 回 LHD 実験グループ全体会議 （ 30 Aug. 2010 ） 13/15

14. J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） 14/14 C exp* is smaller in the vertically elongated magnetic configuration The optimum magnetic field strength is ~ 1.5 T

15. J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） R reactor = C exp  -5/6 f  -1/3 B -4/3 15/14 R reactor = C reactor B -4/3

16. J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ） 16/14

17. FFHR-2m2 17/14 J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ）

18. f P =  -2.5 f  2.5 f a/R -1 f B 3 f n -1.5 に f T = f  f B 2 f n -1 = const を適用  f P ∝  -2.5 f a/R f  ◎ エンベロープでの加熱パワーは f B と f n には依らず、 f  に比例 ◎ 閉じ込め改善度  によって大幅減 ◎ f  ~ 5 で磁場を低減、  ~ 1.2 で加熱パワーを低減できれば FFHR2m2 は可能 FFHR の仕様で閉じ込め 改善なしならば 1.3 GW の加熱パワーが必要 （全核融合出力 6.5 GW ） f  = 8 で中心 β は 16 % (!) ベータ限界は？ 18/11