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2008 International Workshop on Frontiers in Space and Fusion Energy Science

2008 International Workshop on Frontiers in Space and Fusion Energy Science Plasma and Space Science Center, National Cheng Kung University. Progress of Steady-state Tokamak towards Fusion Energy Utilization in the Later Half of 21st Century. November 6-8 JAEA M. Kikuchi. 1.

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2008 International Workshop on Frontiers in Space and Fusion Energy Science

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  1. 2008 International Workshop on Frontiers in Space and Fusion Energy Science Plasma and Space Science Center, National Cheng Kung University Progress of Steady-state Tokamak towards Fusion Energy Utilization in the Later Half of 21st Century November 6-8 JAEA M. Kikuchi • 1

  2. 1. Y2008 is anniversary year for 50 years of Fusion Research 22nd IAEA Fusion Energy Conference held at Geneva last month

  3. 2. Fusion Research is a project to realize Sun on the Earth Plasma temperature of ITER is more than 10 time of center of Sun. 520Mdeg much higher than that of ITER was already achieved at JT-60U in 1996 so that we are confident to achieve such high plasma temperature in ITER. Galaxy Sun ITER

  4. 11 10 9 8 7 6 5 4 3 2 1 0 (B=109) 30 (G toe) Population Energy 20 World Population World Energy Consumption Non-fossil 10 Fossil New Stone Age Bronze/Iron Ages 0 B.C 6000 2000 4000 4000 A.D.1 2000 Year Toe=ton oil equivalent 3. A BIG transition in population and energy consumption at 2000 Question to 21st Century : Can we sustain large population & energy consumption w/o fossil fuels. Fossil Era will end in a moment

  5. 4. Industrial Revolution is needed to reduce of CO2 emission Revolution in energy user sectors (Transportation(CAR), Industry(Steel), Living) Revolution in energy sources (Fossil to Renewables & Nuclear) S750 12 10 8 6 4 2 0 S650 S550 De-Forest, Cemento CO2 emission from fossil fuel (GtonC/year) S450 Toyako summit(July,2008) 2100 2150 2000 2050 1950 1850 1900

  6. 5. Role of Fusion in the JAEA Vision toward low Carbon Society In October 16, JAEA press-released a vision to reduce CO2 emission of Japan to 1/10 in 2100. Point is importance of consideration on later half of this century. This is not a prediction, which is difficult. M ton CO2 Electricityproduction by sources Renewables Hydro Fusion Fission Coal Nat. Gas http://www.jaea.go.jp/02/press2008/p08101601/index.html (in Japanese) Fusion will not enter energy market in first half of this century First quarter is ITER Era. Second quarter is DEMO Era. If ITER&DEMO are successful, we could move to commercialization in second half of this century. It is important to make non-negligible contribution to energy. DEMO: Load map by Fusion Forum of Japan

  7. 6. Fusion has many attractive features as energy sources 3. In case of nuclear accident, radiological toxic hazard potential of T from Fusion is less than 1/1000 of that of 131I from Fission. LWR(TRU) Fusion Coal ash 4. Total radiological toxic hazard potential of Fusion waste decays within 100years to the level of coal ash. 5. CO2 emission from fusion is small and comes only during construction. M. Kikuchi, N. Inoue, "Role of Fusion Energy for the 21 Century Energy Market and Development Strategywith International Thermonuclear Experimental Reactor ", 18th World Energy Congress, Buenos Aires, 2001.

  8. 7. Magnetic Fusion Research Major magnetic confinement configurations Tokamak and Helical Helical Intrinsically steady Research issue: Confinement improvement at high T Tokamak Short pulse (<30s) confinement is good Research issue : Steady-state operation Lawson Diagram Plasma current Primary current Thermal transport at low *

  9. 8. Steady-state Tokamak Reactor To resolve pulsed nature of Tokamak system, use of bootstrap current and active current drive is essential. 80% bootstrap fraction in JT-60 is a basis for this concept M. Kikuchi, M. Azumi, PPCF 37(1995)1215

  10. 9. What is bootstrap current ? In toroidal magnetic confinement system, particles with small v// are trapped by the magnetic mirror (trapped particles) and have larger radial excursion with their “banana orbit”. This radial excursion produces shift of e. velocity distribution function counter to plasma current. Then, collisional diffusion across the trapped-untrapped boundary produces particle flow to untrapped region. This current can be a large fraction of plasma current, say 75% in SSTR. Parallel momentum and heat momentum equations Generalized Ohm’s Law Bootstrap Current Fraction Jbs~dP/dr/Bp Ibs/Ip~0.670.5p p=20<P>/Bp2 Mechanism of bootstrap current generation M. Kikuchi, M. Azumi, PPCF 37(1995)1215

  11. 10. Beam driven current The bootstrap current is driven by pressure gradient, which is difficult to control. So, some part of the plasma current have to be controlled by the external means, either NBI or RF(ex.ECCD). Generalized Ohm’s Law CD=RICDne/PCD~5x1019Am-2/W is required for SSTR JT-60U and N-NBI JT-60U and N-NBI Beam-driven current M, L: viscous and friction matrix Sb : momentum and heat momentum source Driven current up to 1MA agrees with Theory CD with Te and Eb Stacking factor T. Oikawa, et al., NF41(2001)1575 M. Kikuchi, M. Azumi, PPCF 37(1995)1215

  12. 11. Current Profile control Reversed shear is first proposed by Ozeki (1992) as MHD stable operation mode for the Steady-state Tokamak. T. Ozeki et al., 14th IAEA Conf. Wurzburg, Germany, IAEA-CN-56/D-4-1(1992) See also, T. Ozeki et al., PPCF 39(1997)A371 RS plasma is ideally stable if dP/dr at qmin is small. -- Closely related to position of ITB --- Original steady-state operation mode is normal shear mode with q(0)>1.5-2 for the ballooning mode stability. This requires wall stabilization, which led to strong activity of RWM stabilization of “toroidal” plasma (note : RWM can not be stabilized in ideal cylindrical plasma due to slipping of plasma with respect to the mode).

  13. 12. Current Hole as unique Structure Formation in Tokamak Current Hole (CH) is an extreme case of RS configuration with q(0) CH has been stably sustained above current diffusion time. T. Fujita et al., P.R.L. 87(2001)245001 N.C. Hawkes et al., P.R.L. 87(2001)115001 These experiments led to many PRLl works such as Huysmans2001, Martynov2003, Wang2004, Rodrigues 2005&2007 An explanation of CH by equilibria with negative current, Rodrigues 2007 Question still arise why CD at CH is difficult with this equilibria. CH has merit to increase bootstrap current by Jbs~1/Bp dependence and elongation by lower li. CH has demerit of a particle loss with lower Bt ripple. Reactor application not well assessed.

  14. L-mode Pressure Profile Hollow J profile Pressure Profile Normal J Profile J Profile J Profile Reversed shear mode High p mode H-mode Pressure Profile High p H-mode RS H-mode ETB : edge transport barrier ITB: internal transport barrier 13. Families of Improved Confinement Modes in Tokamak There are many improved modes starting from Wagner’s H-mode. “ITB” is accepted as common phenomena after Koide’s PRL 94. “ITB” is local relaxation of “long radial correlation” =20cm = “ITB” is associated with Turbulence de-correlation as measured in ITB of JT-60U. [1] Y. Koide, M. Kikuchi et al., PRL72(1994)3662, Naming of “ITB” [2] R. Nazikian, K. Shinohara et al., PRL94(2005)135002, “Turbulence de-correlation during ITB formation”

  15. Critical Temperature Gradient Model Heat Flux L-mode (dT/dr) crit Temperature Gradient Pressure surface center P. Bak, Phys. Rev. A38(1988)364 Chandraseckhar, Hydrodynamic and Hydromagnetic stability R=1800 R= 0 14. Understanding of L-mode : Self Organized Criticality Features of SOC same with L-mode 1. Profile resilience to keep SOC 2. Intermittent transport 3. Long correlation length 4. May explain offset-linear scaling M. Kikuchi et al., Nuclear Fusion 27(1987)1239 • [1] Y. Kishimoto et al., POP 3(1996)1289 • Semi-global ITG inclined by Bloch angle • Critical temp. gradient model =0(-c) • Intermittent transport induced by vortex dissipation • [2] K. Miki,Y. Kishimoto et al., PRL(2007)145003 • Explanation of Dimits shift by GAM dynamics • New intermittent transport by GAM below Dimits shift [3] F. Ryter et al., PRL(2005) Critical temperature Tc in electron transport in AUG. Critical temperature gradient also exists on ion (see JET IAEA08) “Self-organized criticality” is a common phenomena in Nature Sand collapse in sand hill and Bernard cell are typical examples of self-organized criticality

  16. ( 1 ) (Diamagnetic flow) u  a  u a  u b / / a (Parallel flow)  15. Toroidal symmetry plays important role in Tokamak Toroidal symmetry <R2a>=0 (=o(/L)2) <(F/B)ba>=<B-1(bxa> Mn(d/dt)<RV>=<R2a>=o(/L)2) Easier to drive plasma rotation and hence ExB shear turbulence suppression High p mode: Koide IAEA94 Impurity Toroidal Rotation: RS mode: Fujita NF38(1998)207 Er can be calculated as,

  17. 16. Gyro-kinetic PIC/ Vlasov simulation clarifies turbulence Zonal flow dynamics Use of canonical Maxwellian is essential for Zonal flow simulation Y. Idomura, et al, NF43(2003)234(2006 NF prize nominees) Global ETG turbulence simulation clarify Shear-less ETG : Zonal flow due to 2D turbulence (HM-equation) Y. Idomura, Physics of Plasmas 13(2006)080701 With shear : ETG mode coupling to produce streamer Full f Vlasov, source-driven ITG simulation Y. Idomura et al., 22nd IAEA FEC (2008) LTi/R kept constant and 1/f spectrum in L-mode : SOC

  18. 17. MHD Regime of exploitation changed to high p regime 3 2 1 0 Steady-state requires operation at high poloidal beta to increase bootstrap current fraction High beta poloidal steady N~4.5 (wall stabilization) p N~3.3 (No wall-limit) This constraint led to advanced tokamak research to move to high beta poloidal and hence high q. High beta pulsed To achieve high power density for the reactor, beta regime above no-wall limit is required. 0 5 10 t (%) pt=N2/4 t=NIp/aBt Poloidal p=4Pdv/Ip2

  19. 18. Kinetic Alfven Wave and Stabilization of Resistive Wall Mode Early1990’s, wall stabilization was thought to be difficult. Why? Reasons : [1] Wall is not ideal wall but is resistive wall. [2] Ideal MHD can not be stabilized by plasma rotation for resistive wall since RWM is attached to wall while plasma is rotating (slipping of plasma w.r.t. mode. Wall condition Br=0 will not work. ( Say, [1] C.G. Gimblett, N.F. 26(1986)617 : Ideal MHD plasma will not be stabilized by rotation with Resistive wall) Non-ideal effect to damp the RWM is required. [1] Hasegawa-Chen , Kinetic Alfven Wave(KAW) (1974, first proposed as heating method) RWM is fixed to wall • Mechanism of Kinetic Damping: • - Mode conversion of Shear Alfven wave to Kinetic W (KAW)r=k//vA . • KAW have parallel electric field and wave can be damped by the Landau damping. • A. Hasegawa, Liu Chen, Phys. Fluids 19(1976)1924. • Sound Wave Damping: • gives too weak damping Plasma rotation KAW(>me/mi) Stabilization of RWM

  20. DIII-D JT-60U 19. Resistive Wall Mode can be stabilized by Vc/VA~0.3% H. Reimerdes et al. (DIII-D) , PRL98(2007)055001 M. Takechi et al. (JT-60U) , PRL98(2007)055002 C=(-NW)/(W-NW)

  21. 20. Reactor relevant high bs discharge was achieved at low q Y. Sakamoto et al., IAEA08

  22. 21. Plasma rotation changes MHD operator to non-Hermitian Standard MHD Equation Linear MHD operator without flow:t2 = Ls Lsis a self-adjoint and stability can be judged by the sign of energy integral. Frieman-Rotenberg Equation Linear MHD operator with flow:t2+2(u)t = (Ls+LD) Ld = [(u)u-u(u)] is self-adjoint, but2(u)t is not. Stability can not be judged by the sign of energy integral. Initial value problem (Aiba, IAEA 2008), or Laplace transform (Hirota). E. Frieman and M. Rotenberg, Reviews of Modern Physics 32(1960)898

  23. q~6.5,~0.55, p~0.84-1.88 c a 22. ELM change its character by Rotation N. Oyama et al, PPCF49(2007)249：ELM can be soften by toroidal rotation. Issue : asymmetry in rotation direction and off-set Vt/2R (kHz) Rotation shear d/dq<120kHz Change in Stored Energy H Burst Toroidal Rotation profile Energy loss is excessive for Type I ELM, and may shorten the divertor life time of ITER. Grassy ELM regime is preferable.

  24. 23. Ballooning/Peeling Mode changes by rotation shear M. Furukawa, S. Tokuda, PRL94(2005)175001 N. Aiba, S. Tokuda et al., IAEA2008 Ballooning mode equation with flow Solve F-R eq. for peeling mode as initial value problem [t2-Ut] = (f)-g Eigenfunctions of the n=500 mode. (up: static, down M0=0.29) Dependence of /wA0on 1/n Flow shear Stabilization by flow shear /wA0of the infinite-n ballooning mode at s=0.78.

  25. 24. Steady-state Tokamak subject to NTM Since steady-state tokamak best utilizes the bootstrap current, NTM (Neoclassical Teaing Mode) becomes important issue. NTM : local loss of P at magnetic island leads to the loss of bootstrap current, which de-stabilizes tearing mode. Z. Chang et al., PRL74(1995)4663 - First measurement of NTM NTM suppression by ECCD becomes crucial for SSTR 3.0 P q 2.0 1.5 1.0 Bootstrap current 1.0 0.0 r/a • Completely suppressed by ECRF using the auto-tracking EC mirror system for the first time in JT-60U ( Isayama, NF03). Loss of bootstrap current due to island formation ITER : e* ~ 0.03 , 1ce JT-60U : e* ~ 0.03 , 1ce DIII-D : e* ~ 0.03 , 2ce AUG : e* ~ 0.16 , 2ce

  26. Early injection Late injection Real-time FB on Real-time FB off • • • 25. NTM Physics • NTM behavior of JT-60U can be explained by Modified Rutherford Equation (Hayashi, NF03) kBS ~ 4-5, kGGJ < 10, kpol ~ 1, kEC ~ 3-4, Wd ~ 0.02 • Early injection is effective for NTM suppression (Nagasaki, NF03, NF05) Hysterisis nature • JECCD~0.5Jbs can stabilize NTM with Optimum ECCD (Isayama, NF07)

  27. (b) nonlinearly destabilized DTM ( r = 0.16-0.32 ) strongly coupled DTM ( r = 0-0.16 ) (c) weakly coupled DTM ( r > 0.32 ) r q m/n=3/1 m/n=3/1 m/n=3/1 kinetic energies r/a 9/3 6/2 t(pa) t(pa) t(pa) 6/2 6/2 9/3 9/3 26. Three Different DTM regimes in RS Tokamak RS configuration in some cases becomes unstable to DTM (Double Tearing Mode) . Three distinct linear and non-linear behaviors were identified, which depend on proximity of 2 rational surfaces. Y. Ishii et al., P.R.L.89(2002)205002 Linear mode structure

  28. magnetic energy of 3/1-mode kinetic energy of 3/1 magnetic energy of 3/1 27. New Reconnection Process associated with DTM Point reconnection : Triangular deformation of the inner island forms the localized current structure (current point) : nl~, ~0 lin in the explosive growth phase weakly depends on  =3x10-6 =5x10-6 =1x10-5 =2x10-5

  29. 28. Alfven Eigen Modes (TAE, EAE, NAE, RSAE) Shear Alfven wave resonance: =k//VA, N=ck/ Toroidal coupling of m and m+1 produces frequency range Alfven resonance is prohibited. [ (k2//m- (VA) (k2//m+1- (VA)-2 (VA=0 k//m=(n-m/q)/R k//m=- k//m+1 --> q=(m+1/2)/n Kimura NF98;TAE q<1(tornado) Kramer PRL98;EAE,NAE Spinor : sin(m)+sin((m+1)) =sin[(m+0.5)]cos(0.5 Mobius band ( periodic with two circulation) can not resonate. ShinoharaNF01; Slow Freq. Sweeping, Fast FS shear Alfven Eigen mode can be destabilized by the coupling with Energetic Particles if the  pressure gradient is high enough. )/eBr 2004 Award for Excellence in Plasma Physics Research Recipient Takechi PoP05;RSAE ShinoharaNF02;ALE Ishikawa NF07 EP transport

  30. 29. Interlink among Steady-state Tokamak Physics Steady-state Tokamak Reactor (~1990) High Beta Plasma current Confinement Divertor Energetic Particle To reduce power required for SS Ideal MHD NICD BS current(1971) H-mode(1982) Troyon scaling(1984) fbs~p Power~Ipne TAE Shear-Alfven Resonance Gap To increase bs fraction High p H/Imp H(1994) ETB High p operation RS/C Hole ECCD NBCD To increase power density Er shear High N above no-wall lim Compensation of lost bs current ITB (Internal Transport Barrier) RWM ELM NTM AE AE DTM Kinetic damping RMP Rotation drive

  31. 30. JT-60 shut down and new Generation devices in Asia

  32. Summary [1] Steady-state tokamak is an important concept in tokamak confinement. [2] This has to be realized under the large bootstrap fraction, say, 75%. [3] Simultaneous achievement of current drive, reactor relevant confinement, MHD stability is key to achieve SSTR. [4] Progress of understanding is remarkable and many new interesting processes came in and theoretical predictability was greatly improved. [5] But further research is needed to develop consistent reactor scenario.

  33. 2.2 Generalized Ohm’s Law in Tokamak Ref. M. Kikuchi, M. Azumi, PPCF 37(1995)1215 Parallel momentum and heat momentum balance equations Flux surface average Linear force-flow relation Thermodynamic forces Generalized Ohm’s Law

  34. 2.4 Resistivity and Bootstrap current Resistivity Hirshman-Hawryluk-Birge NF17(1977)611 M. Kikuchi, M. Azumi, PPCF 37(1995)1215 Zarnstorff 1990 Kikuchi 1990 Bootstrap current Generalized Ohm’s Law L31, L32 are calculated by L and M

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