1 / 17

4th IAEA Technical Meeting on Spherical Tori 14th International Workshop on Spherical Torus

4th IAEA Technical Meeting on Spherical Tori 14th International Workshop on Spherical Torus 7-10 October 2008, Frascati, Roma, Italy Figure-of-merit Analysis of Low-power Spherical Tokamak Reactors G.O. Ludwig 1), M.C.R. Andrade 1), M. Gryaznevich 2), T.N. Todd 2)

yaron
Download Presentation

4th IAEA Technical Meeting on Spherical Tori 14th International Workshop on Spherical Torus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 4th IAEA Technical Meeting on Spherical Tori 14th International Workshop on Spherical Torus 7-10 October 2008, Frascati, Roma, Italy Figure-of-merit Analysis of Low-power Spherical Tokamak Reactors G.O. Ludwig 1), M.C.R. Andrade 1), M. Gryaznevich 2), T.N. Todd 2) 1) Laboratório Associado de Plasma, INPE, São José dos Campos, SP, Brazil 2) EURATOM/UKAEA Fusion Association, Culham Science Center, Abingdon, UK e-mail contact of main author: ludwig@plasma.inpe.br

  2. Introduction A new approach to fusion power has been recently considered – to demonstrate early power production in a low-power reactor with reduced wall load (FT/P3-20). The reduced load allows using presently available first wall technologies, but the use of the small fusion power output of the pilot plant has to be optimized either by energy multiplication methods (the fusion hybrid) or in applications such as waste transmutation. In this article the performance of low-power tokamak reactors is analyzed using a simple global model. A general figure of merit X, which encompasses all the relevant tokamak parameters, is introduced by a normalization of the global power balance equation. The value of X defines the performance of tokamak reactors in a simple way. Its use allows to search for sets of machine parameters that satisfy a given performance goal. The figure of merit approach is applied both to describe ITER-like reactors and to analyze the performance of low-power, low-aspect-ratio tokamaks with increased toroidal field. It is found that spherical tokamak (ST) reactors with X≈0.6, a≈1 m, B0≈3 T and Q≈1 can produce Pfusion=25 MW and <500 kW/m2 of wall loading. Hans Albrecht Bethe “The fusion hybrid” Phys. Today, May 1979

  3. Plasma model • Binomial profiles and equivalent minor radius • x=x0[1-(ρ/ap)2]αx, x={n, T, j}, ap=(Ap/π)1/2 • Area of the poloidal cross-section, plasma volume and plasma surface • Ap≈πκa2(1-δ2/4), Vp≈2π2κR0a2[1-aδ/(4R0)-δ2/4 ], As≈4π2aR0[(1+κ2)/2]1/2 • Cylindrical safety factor (q*>1.8); maximum beta for stability (βN~0.03→0.06 m×T/MA) • q*=[2B0/(μ0R0 jp)](1+κ2)/(2κ), jp=Ip/Ap, β≤βN[10-6Ip/(aB0)]=5βN[(1+κ2)/2](1-δ2/4)ε/q* • Plasma energy • W=3nTVp=4.81×104n20TkeVVp(J), n=<ne+ni>/2, T=<neTe+niTi>/ <ne+ni> • (n is the volume average density and T is the density-averaged temperature)

  4. Alpha particles heating • Total power deposited by alpha particles • Pα=fD(1-fD)fDT2fαgαne2<σv>EαVp=1.43×1027[4 fD(1-fD)fDT2fα]gαne202<σv>Vp(W) • Reactivity of the D-T reaction (10%, exact reactivity is used in the final calculations) • Cα=2.2×10-26, α=4, 2.2 keV<T<5.9 keV • Eα=3.56 MeV, <σv>≈CαTα m3/s, Cα=1.1×10-25, α=3, 4.4 keV<T<12.2 keV • Cα=1.1×10-24, α=2, 8.3 keV<T<22.3 keV • Deuterium fraction, dilution fraction and impurities • fD=nD/(nD+nT)=0.5, fDT=(nD+nT)/ne=[Z-2(Z-2)nα/ne-Zeff]/(Z-1) • ne=Zni, Zeff=ΣiniZi2/ne, n=[1+fDT+nα/ne+(1-fDT-2nα/ne)/Z]ne/2 • (if fDT≈1 and nα/ne<<1, then Zeff≈1 and n≈ne) • Alpha heating profile factor (approximate value over limited temperature range) • gα≈(1+αn)2(1+2αn+ααT)-1[(1+αn+αT)/(1+αn)]α

  5. Alpha particles containment • Containment fraction as a function of plasma current (first-orbit loss model) • fα≈exp[-Cℓ√ε(Ic/Ip)ℓ+1], Ic=5.44√ε(1+κ2)/(2κ) MA (critical current) • left – adjustment of the pressure profile (ℓ≈3) to CTF simulations including collisionless prompt and TF ripple losses, and relatively close walls (K. McClements, 2008) • right – application to ST configuration (1.6≤A≤2.0, 2.0≤κ≤3.0) • Power loss by radiation (Bremsstrahlung) • Pr=5.35×103grZeffne202Te,keV1/2Vp(W), gr=(1+αn)3/2(1+αn+αT)1/2(1+2αn+αT/2)-1(profile factor)

  6. Ohmic heating • PΩ=9.61×10-10lnΛeiZeff[(2.31+Zeff)/(0.932+Zeff)]gΩgNC jp2Te,keV-3/2Vp(W) • Ohmic power profile factor • gΩ=(1+αj)2(1+2αj-3αT/2)-1[(1+αn)/(1+αn+αT)]3/2 • Neoclassical resistivity enhancement factor • gNC≈(1+2αj-3αT/2)∫01x2αj-3αT/2[1-fT(x)]-1 [1-CZfT(x)]-1dx, CZ=0.56[(3-Zeff)/(3+Zeff)]/Zeff • Fraction of trapped particles • fT(x)=1-[1-ε(1-x)1/2]2[1-ε2(1-x)]-1/2[1+1.46ε1/2(1-x)1/4]-1 • (the low-collisionality limit is, in general, a good approximation in the reactor regime) • Take lnΛei≈17, Zeff≈1.5, ne≈ni≈n and Te≈Ti≈T (simple approach)

  7. Power balance • Global power balance equation • ∂W/∂t=-W/τE+P (τE is the energy confinement time), P=Pα+PΩ+Paux-Pr(net heating power) • Convection and conduction power losses • Pc=W/τE, τE=CEH(10-6Ip)γIB0γB(10-6P)γPAiγAn20γnTkeVγTR0γRεγεκγκ (IPB98 scaling law) • H is the H-mode enhancement factor and Ai=2.5 for a 50:50 D-T mixture • (the explicit dependence on T is maintained for compatibility with older scaling laws) • Normalization • T=T/T0, n=n/n0, P=P/Pr(n0,T0), t=3Pr(n0,T0)t/W(n0,T0) • ∂(3nT)/∂t=-Pc+P=-n1-γnT1-γTP-γP/X+P(assume n0, T0 and Vptime independent)

  8. Reference temperature (threshold between alpha heating and radiation cooling) • Pα(n,T0)=Pr(n,T0), T0≈{3.75×10-24Zeffgr[Cα4fD(1-fD)fDT2fαgα]-1}2/(2α-1)(3<α<4) • Reference density (Murakami-Hugill density limit) • Pr(n0,T0)=PΩ(T0), n0≈4.24×10-7[(2.31+Zeff)(0.932+Zeff)-1lnΛei(gΩgNC/gr)]1/2jp/T0 • Dimensionless figure of merit (independent of Paux) • X=Pr1+γP(n0,T0)Pc-1(n0,T0)P-γP(n0,T0) • Normalized power balance equation • ∂(3nT)/∂t=n2[Σ(T0,T)-T1/2]+T-3/2-n1-γnT1-γTP-γP/X+Paux • Σ(T0,T)=gα(T0T)<σv>(T0T)[gα(T0)<σv>(T0)]-1≈Tα(normalized reactivity; weak function of T0) • Geometrical and safety factor aspects, plus all the profiles, impurities and neoclassical effects are contained in the figure of merit X, with additional weak dependence on the profiles through the reference temperature T0 in Σ.

  9. Steady-state operation (POPCON) • Auxiliary power contours in the normalized(T0,n0)coordinates • Paux=(n1-γnT1-γT/X)1/(1+γP)-n2[Σ(T0,T)- T1/2]+T-3/2 • Saddle-point geometry (Cordey pass) • (∂Paux/∂T)s=0, (∂Paux/∂n)s=0 → Cordey pass expression (ns,Ts) and equation relating Ts to X • 3D plots of Paux(Ts,ns) for X=0.832, 1.059 (ITER) and 1.104 (ohmic ignition). Low point indicates transition, on the Cordey pass, from the ohmic to the auxiliary heated domains.

  10. Auxiliary power contours and reactor performance Power contours corresponding to the previous 3D plots. The vertical line at T=1 indicates the condition Pα=Pr, and the dashed line the condition PΩ=Pr. The thick line shows the Cordey pass and the high point in the middle frame indicates ITER-like conditions TkeV=8.85, n20=0.891, Paux=11.2 MW, Pfusion=500 MW, τE=3.7 ms. The following figures show the normalized alpha, ohmic, radiation and auxiliary power contributions along the favorable Cordey pass conditions (minimum Paux), and the fusion gain Q, normalized fusion power, auxiliary power and total power deposited on the wall.

  11. Normalized alpha Pα, ohmic PΩ, radiation Pr and auxiliary Paux power contributions along the favorable Cordey pass conditions (minimum Paux).

  12. Fusion gain Q, normalized fusion power Pf, auxiliary power Paux and total power deposited on the wall Pwall (note change in vertical scale).

  13. Conclusions The figures show that a figure of merit X=0.6 or slightly above is adequate for low power reactors, giving 1<Q<3 with moderate levels of auxiliary power. Essentially, it is the value of X that defines the machine performance. Since X depends on the machine and plasma parameters, it is possible to search for sets of parameters that satisfy the performance goal. The table lists the main parameters of reactors with X=0.6 producing Pfusion=25 MW and <500 kW/m2 of wall loading. These results indicate the feasibility of ST low-power reactors with a≈1 m, B0≈3 T and Q≈1. New scaling laws for low A (EX/P5-17) give similar results with about half the plasma current, slightly lower density and larger temperature.

  14. 4th IAEA Technical Meeting on Spherical Tori 14th International Workshop on Spherical Torus 7-10 October 2008, Frascati, Roma, Italy Brazilian plans for fusion G.O. Ludwig Laboratório Associado de Plasma, INPE, São José dos Campos, SP, Brazil e-mail contact: ludwig@plasma.inpe.br

  15. National Fusion Network (RNF) – National Fusion Laboratory (LNF) • National Fusion Network established August 2007: ~70 participants, ~15 institutions (R$1,000,000.00 yearly budget) • Present activities • Network operation (mostly meetings, visits, collaborations with EU laboratories) • Executive project and ground work of the LNF in 2009 – construction starts 2010 • Conceptual design of a low-power hybrid reactor (possible new machine, but not reactor) • Agreement for cooperation between EURATOM and Brazilian Government in the Field of Fusion Energy Research should be put into final form (signed) October 21 • 21 researchers from 13 institutions in the present phase of the RNF/LNF project • Plasma Physics groups (2): tokamak operation and physics • Plasma Physics groups (4): theoretical and numerical modeling • Plasma, Atomic Physics groups (3): diagnostics development • Nuclear Engineering group (1): neutronics and thermo-hydraulics of fusion-fission reactors • Materials Engineering group (1): first wall materials (ITER divertors) • CNEN/CBPF: coordination • Next: Materials Engineering group: development and fabrication of superconductors (HTS?)

  16. Location of the future National Fusion Laboratory – LNF INPE site in Cachoeira Paulista: 5 km×2.23 km=11.16 km2 (200 km from São Paulo and Rio de Janeiro). LNF area≈0.7 km2. Transmission line: 138 kV, 1.8 km (500 kV, 5 km).

  17. Organizational structure (tentative) – LNF Fusion Laboratory building (5,000 m2) Departments Fusion Technology – tokamak operation, auxiliary heating systems, superconductor coils, power supplies, wall materials, divertors Technical Support and Services – machine shops, electronics, vacuum, optics and microwave laboratories Fusion Research building (5,000 m2) Departments Fusion Science – theoretical and numerical modeling, tokamak physics, plasma heating, current drive, diagnostics Reactors Engineering – reactors design, neutronics, thermo-hydraulics, materials engineering Administration 2008/2009 – R$1,000,000.00 for executive project and initial ground work. Land ownership being transferred from INPE (National Space Research Institute) to CNEN (National Nuclear Energy Commission). LNF will be created under the Research and Development Directorate of CNEN (Ministry of Science and Technology).

More Related