Key Questions and Issues in turbulent Transport in TokamaksJAEA M. Kikuchi2nd APTWG at Chengdu, Plenary session, presentation number PL-11PL-1Acknowledgements: P. Diamond, Hahm, Idomura, Miyato, B. Scott, F. JenkoSome questions along with writing a review on physics behind steady state tokamak research

Avalanche dynamics in critical temperature gradient transportEffect of non-resonant modes, higher order axisymmetric modes on GAMTermination of ITB through temp curvature (0th order radial force balance)Mystery of beta dependence of in EM Gyrokinetic , micro tearing?[1] Avalanche Dynamics in critical temperature gradient transportSelf-organized criticality: power law paradigm

P. Bak, Phys. Rev. A38(1988)364

Micro flare dN/dE~E-1.53Flare energy(Erg)Prof. Shibata Plasma Conf. 2011, to appear NatureNano flare dN/dE~E-1.75SuperflaredN/dE~E-1.9 by Kepler Typical example are,

[1] Per Baks sand collapse in sand hill[2] Gutenberg-Richter law in Earthquake[3] Solar flare distribution revisited by ShibataLargest solar flare Shibata told us there is a possibility of super flare with 1000 times of observed largest flare in 1000 years as measured by Kepler satellite.

Upper bound of flare was unknown while upper bound of turbulent heat transport is well known, (Krommes Ann Phys. 1987, see Yoshizawa, Itoh, Itoh, IOP, Appendix 14A).1.1 Critical temperature gradient transport is now experimentally confirmed for both electron and ionElectron transport : Hoang PRL2003Ion transport Mantica PRL20113

Hoang, PRL2003Mantica PRL2011

Idomura NF2005 ETG turbulence simulation1. 2 Streamer and AvalancheDefinition of streamer from Yoshizawa-Itoh-Itoh, p278 Convective cell (w~0) Zonal flow : k~(kr,0,0) Streamer : k~(0, kq,0)Third component is k// or kt

Note 1: Streamer in toroidal plasma has ballooning character with low k// dEr/dr ~(c1d2Pi/dr2+c2d2Ti/dr2)Void : d2Ti/dr2 > 0 -> dEr/dr >0

Bump : d2Ti/dr2 < 0 -> dEr/dr 0, bump is destabilized & hole is stabilized. If background Er is negative, hole is destabilized & bump is stabilized.10Key question : Is this explanation correct?JPS meeting : validity of 0th order force balance equation in time scale of fraction of ion-ion collision time .

B. Scott : need to check for flat profile (dTi/dr = dTi/dr_c everywhere). Profile is peaked near mid-radius.Key question : What is the role of streamer on avalanche dynamics?Explanation by Idomura : If ITG mode is strongly destabilized somewhere, it will flatten Ti profile. This leads to formation of hole inside and bump outside.20aTE311[2] No-resonant mode & higher harmonics axisymmetric modes [1] History of non-resonant mode discussionX. Garbet PoP2002 : Gyro fluid simulation to show intrinsic rotation & ITB formation

J. Candy PoP2004 : Importance of non-resonant modes

N. Miyato NF2007 : Large mode change by neglecting non-resonant modes Importance of higher harmonic axisymmetric modes Key question : How much we should include non-resonant modes and ax. higher harmonics?

With nonresonant modes(n,m)=(0,0), (0,1)N. Miyato, NF2007 gyro fluidWithout nonresonant modes(n,m)=0 ,1

With nonresonant modes(n,m)=(0,0), (0,1)(0,9)[1] Non-resonant modes can change turbulence, sometimes may produce fake ITB[2] Higher m axisymmetric modes can change GAM through coupling to higher m. All : ri/a=0.005[3] Termination of ITB through temperature curvature 0th order force balance equation is constraint for turbulence in tokamak.

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orPositive feedback loop for acceleration of Er shear stabilization through pressure buildup143.1 Passing qmin=integer (ex.=4) with steep dP/dr is difficultY. Sakamoto : NF 2005 (NF top 10)

- Avoid disruption when plasma pass qmin=integer.- ITB strength can be controlled by toroidal rotation.

Question : How actively control toroidal rotation in reactorDisruption153.2 Temperature curvature transitionK. Ida, Y. Sakamoto, et al., PRL2008

concaveconvex

16Key question : we should establish control knob for d2T/dr2Can we actively control direction of intrinsic rotation? -- Diamond paradigm cf. Dueck mechanism for edge IR.Can we actively control NTV offset toroidal rotation? -- may be possibleCan local ECH help to control temperature curvature? -- not yet done.

Dueck PRL201217[4] Mystery of beta dependence of in EM Gyrokinetic , micro tearing?

JT-60 power degradation : Takizuka PPCF2008, Urano NF2006 Pueschel PoP2010 : ITG driven ion heat flux is reduced with beta.

Hatch PRL2012: Nonlinear destabilization of stable micro tearing mode enhances electron heat transport.

Micro tearing mode has dTe/dr threshold.

But Jenko PRL2002 showed dTe_c/dr matches toroidal ETG theory!!

Micro tearing mode do not enhance ion transport!!

Experiments :Gyrokinetics:

Pueschel PoP2010 Jenko,PRL2002 18Summary[1] Critical temperature gradient transport becomes firm basis of tokamak transport. It needs more understanding of detailed physics processes including experimental observation of streamer, relation between streamer and avalanche hole/bump formation and role of 0th order NC relation on hole/bump propagation.

[2] Accurate treatment of non-resonant/ high m axisymmetric modes are important for quantitative estimation of GAM/zonal flows.

[3] 0th order radial force balance has positive feedback effects on ITB acceleration. Finding control knobs is important.

[4] Present gyrokinetic EM simulation is puzzling on beta dependence even including nonlinear destabilization of micro tearing modes.