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Direct Profile Extrapolation Method for the Deductive Procedure of Fusion Reactor Design

US-Japan Workshop on Fusion Power Plants and Related Advanced Technologies with participations of EU and Korea （ 22-24 Feb. 2011 ）. Direct Profile Extrapolation Method for the Deductive Procedure of Fusion Reactor Design. J. Miyazawa National Institute for Fusion Science, Japan.

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Direct Profile Extrapolation Method for the Deductive Procedure of Fusion Reactor Design

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  1. US-Japan Workshop on Fusion Power Plants and Related Advanced Technologies with participations of EU and Korea（22-24 Feb. 2011） Direct Profile Extrapolation Method for the Deductive Procedure of Fusion Reactor Design J. Miyazawa National Institute for Fusion Science, Japan

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

  3. How Do You Estimate the Fusion Output? • In general fusion reactor design activities… - Radial profiles: parabolic for both T and n - MHD equilibrium: vacuum config. is often useed in helical reactor design - Density: density limit scaling - Temperature: energy confinement scaling - Assumptions: T(r), n(r), equilibrium, nDL, DL factor, tEscaling, H-factor, … • In the DPE method proposed here… - Profiles and equilibrium obtained in the experiment are directly used - Gyro-Bohm type parameter dependence is assumed - Degree of freedom in determining profiles is largely reduced (= high reliability) J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

  4. A New Procedure of Fusion Reactor Design Conventional procedure (inductive approach) New procedure using DPE (deductive approach) J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

  5. DPE: Direct Profile Extrapolation fX: enhancement factor of X（e.g. fT = Treactor (r) / Texp(r), fn = nreactor (r) / nexp(r), fP = Preactor / Pexp） From the definition: fb=fT fn fB-2fT = fbfn-1fB2 (1) Gyro-Bohm: tEGB a2.4 R0.6 B0.8 P-0.6 n0.6 nT a2 R / P  a2.4 R0.6 B0.8 P-0.6 n0.6 T  a0.4 R-0.4 B0.8 P0.4 n-0.4 fT = gfa/R0.4fB0.8 fP0.4 fn-0.4 (2) delete fT from Eqs. (1) and (2)fP = g-2.5 fb2.5fa/R-1 fB3 fn-1.5 (3) Then, fa is determined so as to satisfy Preactor= fa3fa/R-1fn2(zPa’ – PB’) (dV/dr)expdr= g-2.5 fb2.5fa/R-1fB3fn-1.5 Pexp (in this study,fa/R = z=Zeff = 1) One can calculate the alpha heating power per unit volume by assuming fB, fn, and fb Independent of a and R g : confinement enhancement factor fa/R = 1 (fa = fR) Independent of a and R Plasma volume × fa3 Equilibrium in LHD Volume integration of (alpha heating – Brems.) fa (= fR) is obtained if fB, fn, fb and g are given J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

  6. Exp. Example Mag. Field × fB Reactor × fn × fT × fb Plasma volume × fa3 • fa（= fR） is determined so as to fulfill the power balance • fn=2, fb=5 and g=1.3 reproduce the profiles assumed in FFHR2m2 Heating power × fP Confinement × g J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

  7. Mag. Field Strength Determines the Plasma Size Design window for fn = 1 • Breactor is scanned for various fn (fband g are fixed to 1 ) • The minimum Rreactor is given as a function of Breactor What is this lower envelope? J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

  8. Rreactor∝ Cexp Breactor-4/3 Cexp Rreactor =Cexpg-5/6 fb-1/3 B-4/3 Preactor = fa3 fa/R-1fn2(zPa’ – PB’) (dV/dr)expdr ∝ fa3 fa/R-1fn2fTX ∝ fa3 fa/R-1fn2 (fb fn-1fB2)X∝ g-2.5 fb2.5fa/R-1fB3 fn-1.5 Pexp fa3 ∝ g-2.5 fb2.5-XfB3-2Xfn-3.5+XPexp. (X = 3.5) fa ∝ g-5/6 fb-1/3 fB-4/3Pexp1/3 Temp. dependence: fTX A small Cexp results in a compact reactor Eq. (3) fn dependence disappears… J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

  9. Cexp is Given at a Fixed Temperature Temp. dependence of DT fusion reaction rate Temp. dependence of an index X (<sv> ~ TX) <sv> ~ T3.5 輻射損失の効果 Bremsstrahlung Bremsstrahlung 輻射損失の効果 (zPa’ – PB’) (dV/dr)expdr ∝ fTX<sv> ∝ TX (X =3.5 @ T ~ 7.1 keV w/o Bremsstrahlung) Actually, the plasma size becomes minimum atT0 ~10 keV (due to Brems. and volume-integration) J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

  10. How to Get Cexp １）Set fn = fb = g = 1: fT = fB2 ２）Scan Breactor = fBBexp: Heating power:fB3Pexp Volume-integration: (Pa’ – PB’) (dV/dr)expdr Rreactor= [(Heating power) /(Volume-integration)]1/3Rexp ３）The minimum of Rreactor / Breactor-4/3is the Cexp (Note: in some cases, fn = 1 might be inadequate!) Cexp J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

  11. Cexp is a Good Measure of Plasma Performance FFHR-d1 FFHR-d1 Rreactor =Cexpg-5/6 fb-1/3 B-4/3 • Cexp can measure the plasma performance, like the fusion triple product of nTt • Although an inverse correlation between Cexp and nTt is recognized… • The maximum of nTtdoes not necessarily correspond to the minimum of Cexp • nTtis given by the averaged (or, the central) values, while the whole profiles of n and T are used to get Cexp • Cexp that directly shows the design window is a better index than nTt!! J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

  12. Seek the Minimum Cexp FFHR-d1 FFHR-d1 • To design a helical DEMO reactor FFHR-d1 of (Rc, Bc, Creactor) ~ (14 m, 6.5 T, 170), we are now trying to get the minimum Cexp in LHD (Cexp ~ 225 in the 14th cycle exp.) • How can we minimize the Cexp? magnetic config., high beta, high density, … J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

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

  14. Magnetic Configuration is Important • Cexp* is smaller in the vertically elongated magnetic configuration • The optimum magnetic field strength is ~ 1.5 T J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

  15. How Large Enhancement is Needed? Rreactor =Cexpg-5/6 fb-1/3 B-4/3 Rreactor =CreactorB-4/3 • If the design point is already fixed and the experimetal result is not enough, the beta should be increased with fb = g-2.5 (Cexp / Creactor)3 J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

  16. Summary • DPE: a new method to predict the fusion out put - Using “real” profiles and equilibrium - Gyro-Bohm is assumed - fa (= fR) is estimated for assumed fB, fn, fb, g • The plasma (device) size is proportional to Cexp - Rreactor ∝ CexpBreactor-4/3 • Seek the minimum Cexp - Cexp is a better index than nTt • A new procedure of fusion reactor design - Deductive approach is possible with DPE J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

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

  18. ベータ値増大は出力増大を伴う 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） fb = 8 で中心βは 16 % (!)ベータ限界は？ fP = g-2.5 fb2.5fa/R-1fB3fn-1.5にfT = fb fB2 fn-1 = const を適用fP ∝g-2.5fa/Rfb ◎ エンベロープでの加熱パワーはfBと fnには依らず、fbに比例 ◎ 閉じ込め改善度gによって大幅減 ◎ fb~ 5 で磁場を低減、g ~ 1.2 で加熱パワーを低減できればFFHR2m2は可能 J. Miyazawa, US-J Workshop （22-24 Feb. 2011）

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