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Tokamak/Stellarator (Vs. FRC) : Transport and Other Fundamentals

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Tokamak/Stellarator (Vs. FRC) : Transport and Other Fundamentals Tokamak/Stellarator (vs. FRC) : Transport and Other Fundamentals Y. Kishimoto+ and T. Tajima*,** + Kyoto university, Uji, Kyoto, Japan, 611‐0011, Japan * University of California, Irvine, CA 92697, USA ** Tri Alpha Energy (TAE), Inc., Rancho Santa Margarita, CA 92688, USA Collaborating with J. Q. Li+,+++, K. Imadera+, A. Ishizawa+, Y. Nakamura+ T.‐H. Watanabe1, H. Sugama1, K. Tanaka1, S. Kobayashi++, K. Nagasaki++ 1. National Institute for Fusion Study (NIFS) ** Institute of Advanced Energy (IAE), Kyoto University +++ SWIP, China Outline Motivation： –No easy solution for fusion reactor tokamak, spherical torus, stellarator (torsatron, heliotron, heliac, helias ..), miller, FRC, RFP, spheromak, dipole …. –Beam driven FRC, opportunity to reconsider plasma, highly nonlinear medium, for fusion study from the view of fundamental discipline, “Rigid” approach or “soft” approach in designing device ? ─ the former tries to kill the characteristics of self‐organization of plasma while the latter relies on it. Transport in “tokamak” (quasi‐rigid system) dominated by self‐ self‐organized criticality, and the recipe to break it Transport in “stellarator ” (rigid system) and reciprocal relation between linear and nonlinear response “magnetic shear sˆ ” as a parameter to regulate self‐organization ( sˆ 0 in FRC) Discussion and summary No easy solution for fusion reactor M. Kikuchi et al.,, ICPP2016, June 27‐July 1, 2016, Taiwan Tokamak approach Optimized for core confinement based on H‐mode & D‐shape but not for power handling New (but realistic) innovation necessary optimized both for “stability/confinement” and “power handing” “Rigid” or “soft” approach in designing device ? “Rigid‐approach”“intermediate” “Soft‐approach” Magnetic field fully Poloidal field : Only dia‐magnetic current determined from coil driven by current (BS‐current) RFC ST spheromak stellarator RFP tokamak High‐performance realized High performance in going on ? cf. H‐mode (ETB), ITB, their combination Self‐organization of “plasma” “Full self‐organization” of both under rigid magnetic field, “plasma” and “magnetic field” leading to L‐mode A relaxed state after MHD instability Self‐organization in high pressure (high‐ ) (high input power regime) How the state can be again more self‐ organized in high input power regime “Rigid” or “soft” approach in designing device ? “Rigid‐approach”“intermediate” “Soft‐approach” Magnetic field fully Poloidal field : Only dia‐magnetic current determined from coil driven by current (BS‐current) RFC ST spheromak stellarator RFP tokamak “plasma confinement” RFC (reversed field configuration) • • No non‐rational magnetic surface and magnetic well (average) : Dwell then no magnetic shear • magnetic shear : srˆ ln qr q 0 sˆ 0 • Large advantage in power handling • Looks like “miller (rigid system)” i.e. linear unrestricted divertor but essential difference, i.e. closed core field with null O/X points What determines spatio‐temporal size of particle diffusion? Collisional transport Turbulent transport time x ~ 1 p x ~ i a /sec) 3 ~ coll 0.5 ~ 1 (/xm 1 ~~auto d Density*confinement n T D i 2 1 2 D B T B a Central temperature aB232 aB ~ QnT~ E 3/2 C‐2U analysis : from Tajima et al. TT Opposite dependence to Serious challenge : aT 2 a2 T 2 the goal (Bohm scaling) scaling nob ~ a i ~ e i ~ i B LS B Using nT~ B2 assuming ~1O “Rigid” or “soft” approach in designing device ? : Takamak case Tokamak : “quasi‐rigid” system, toroidal field is given from outside while a freedom to control poloidal field by current drive R current J 2 rmBT qr~ BT R Bn P r Bp rq r q sˆ ~ 1 sˆ ~ 0 qr q r 2.0 4 1.5 3 J 1.0 qmin 2 q 0.5 1 0 0 00.20.40.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ()n sˆ 2 x ~2expHixixn 2 Tokamak is a system which allows meso scale fluctuation J.Y. Kim and M. Wakatani, PRL 73, 2200 (1994) • Mode-structure in non-uniform medium： Y. Kishimoto, J.Y. Kim, W. Horton, T. Tajima et al., (Extension to non-local ballooning theory) Plasmas Phys. Controlled Fusion 41, A663 (1999) j r, x A r 0 x j exp i0 j rsk1 ˆ 0th order eigen-function： , r 0 T(r) ks ˆ f 2 Arr exp - r 2sin00rr m 1 m m 1 radius f k V k V n n n rsk1 ˆ • Representation of 2d-structure： r , 0 T(r) 1 1/2 2sin 00 2 L r Ti ~ r f sˆ 0 ks ˆ rr m 1 m m 1 radius 000 cos n n n 1 r f 3 (c) rr n=15 Bloch angle 0 max 0 0 |s|ˆ ～ 1 2ks 0 ˆ EB 1 1 3 Β B ~ r (radius) … m-2 m-1 m m+1 m+2 … skˆ LT n n n nn “Constraint” on the profile and self‐similar relaxation • Constraint on the profile and relaxation Constraint on profile Kishimoto, Lebrun, Tajima, horton, Kim (fast time scale) , PoP 3, 1289 (1996) rL1 ~ (No zonal flow) r1 T0 t1,r1 T0 ~exp r0 ~ LtT 1 Self-organized profile TTRL Ttr100 ,0 Free energy is kept perturbation • Avalanches on the self‐organized profile Self‐similarity in the relaxation (slow time scale) ・ ・ rL1 ~ ・ T0 t1, r1 ・ ・ Relaxation of • Spatio‐temporal hierarchy self-organized profile 2 1 r tt t rr r r1 01 01 T ~exp 1 ~exp 0 Lt fast slow micro-scale macro-scale T 1 rLt11T relaxation relaxation variation variation Experimental study of “profile stiffness” D. R. Mikkelsen et al., Nucl. Fusion 43, 30 (2003) 9.9[MW] ・ Stiffness of thermal 6.8[MW] transport in ELMy H-modes 6.8[MW] is examined. 6.9[MW] H. Urano, et.al., Phys. Rev. Lett. 109, 125001 (2012) P. Mantica, et.al., PRL 102, 175002 (2009)] ・Recently, the dependence of stiffness on the hydrogen isotope mass was examined in conventional H-mode plasmas. Numerical laboratory for tokamak experiments based on global gyro‐kinetic modeling Gyro‐Kinetic based Numerical Experimental Tokamak : GKNET Imadera, Kishimoto et al. 25th FEC, TH/P5-8 ▶ Basic equation system • Flux driven full‐f global toroidal geometry with external source and sink fff R,,HvHSSC source sink collision tvR Gyro‐Kinetic based 11 Numerical Experiment of f Bdvd* f 1|| Tokamak (GKNET) Trei00() nr () • Electrostatic model with adiabatic electron • Full‐order of FLR effect • Conservative linear collision operator Heat input and dissipation balance, leading to a self‐ organized state ▶ Numerical method • Vlasov solver : 4th‐order Morinishi scheme • Time integration : 4th‐order RK scheme • Parallelization: 5D (R‐Z‐φ‐v‐μ) MPI decomposition Field equation is solved in real space (not k‐space) 11 Transport events with different time and spatial scales Time : Intermittent (bursting) behavior due to various types of avalanches Space : self‐similarity in relaxation and self‐organization in profile 1) Spatially Localized avalanches propagating with fast time scale (1) 12/ marginal ci~L Ti state (2b ) (2a ) 2) Radially extended global bursts ranging for meso‐ to macro scale) 12/ cTiT~L L 3) Spatially localized avalanches propagating with slow time scale coupled 3) with ExB staircase, causing long time scale breathing in 12/ transport cTi~L Transport events with different time and spatial scales Time : Intermittent (bursting) behavior due to various types of avalanches Space : self‐similarity in relaxation and self‐organization in profile LT1 LT LT 2 790t 800 *16[MW]→4[MW] at t=800 LT1 LT 2 t Weak barriertransport Quasi‐periodic bursts due to the radially extended global mode • Appearance of radially extended ballooning (A) t=566 mode and subsequent growth, leading to a burst over macro‐scale n=15 B 0 Β B C χ (B) t=574 t=722 i A t~20 0 ~ 0 520 530 540 550 560 570 580 590 600 0 50 (C) t=586 12 r~L ~a a r a Ti • Symmetry structure 100 r~60 70 dE with no titling: r 0 dr 000 cos 150 r~60 70 Symmetry recovery due to the cancellation between diamagnetic shear and mean ErxB shear • The effect of global temperature profile is cancelled by that of global mean radial electric field, so that the symmetry is recovered and the growth is enhanced. / / 2 r ∓ ~ 0 ̂ ̂ r ∞ ~~000cos vd 2 vd 2 v d1 vd1 E r v vd 2 –The system is self‐organized so as to d 2 v vd1 expel the input power efficiently to d1 outside by adjusting spatio‐temporal structure of turbulence and also profile. cT~ L Controversial discussion on Bohm/Gyro‐Bohm transition ? Averaged heat flux GT5D code: Plasma size [1] Z. Lin et al., PRL 88, 195004 (2002). among [1400, 1600] scaling at ITER‐size GKNET simulation Scaling using flux‐driven modeling total Q Fig. 4. Effective heat diffusivity of three global [Y. Idomura et al., gyrokinetic codes as a function of ρ∗. (copied Phys. Plasmas 21, from Fig.5 in Ref. 3) 020706 (2014).] [3] Sarazin, et. al, Nucl. Fusion 51 (2011) “Rigid” or “soft” approach in designing device ? “Rigid‐approach”“intermediate” “Soft‐approach” Magnetic field fully Poloidal field : Only dia‐magnetic current determined from coil driven by current (BS‐current) stellarator tokamak RFC • Both systems have “magnetic well” and “magnetic shear” (a rigid system) • However, the self‐organized state provides L‐mode even with zonal flows • How to revel new self‐organization which can sustain high pressure state Self‐organization in high pressure state : magnetic shear [Kishimoto,Li, et al., IAEA ’02] 10 (A) S=0.2 (A) 8 s=0.2 + /eB)] e 6 )(cT n /L (B) S=0.1 : weak magnetic shear e 4 s=0.4 turbulence + zonal flow - /[( e 2 (B) s=0.1 0 234567 e turbulence 1 (a) (B ) 10 Formation of large /2 s=0.1 2 scale structure 100 (A) /dx|> (z) -1 10 s=0.4 fluctuation energy <|d = turbulent part + laminar part 10-2 s=0.2 E ()ZF 234567 ZF ()turb () ZF EE e Coherency and phase between Ey and T The phase of the large scale structure is locked so as not to cause transport * QT~ EB Phase difference between potential and temperature causes net transport Horton Rev.
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