1. Key Questions and Issues in turbulent Transport in Tokamaks JAEA M. Kikuchi 2 nd APTWG at Chengdu, Plenary session, presentation number PL-1 1PL-1 Acknowledgements: P. Diamond, Hahm, Idomura, Miyato, B. Scott, F. Jenko Some questions along with writing a review on physics behind steady state tokamak research 1.Avalanche dynamics in critical temperature gradient transport 2.Effect of non-resonant modes, higher order axisymmetric modes on GAM 3.Termination of ITB through temp curvature (0 th order radial force balance) 4.Mystery of beta dependence of in EM Gyrokinetic, micro tearing?

2. [1] Avalanche Dynamics in critical temperature gradient transport Self-organized criticality: power law paradigm P. Bak, Phys. Rev. A38(1988)364 Micro flare dN/dE~E -1.53 Flare energy(Erg) Prof. Shibata Plasma Conf. 2011, to appear Nature Nano flare dN/dE~E -1.75 Superflare dN/dE~E -1.9 by Kepler Typical example are, [1] Per Bak’s sand collapse in sand hill [2] Gutenberg-Richter law in Earthquake [3] Solar flare distribution revisited by Shibata Largest 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).

3. 1.1 Critical temperature gradient transport is now experimentally confirmed for both electron and ion Electron transport : Hoang PRL2003 Ion transport ： Mantica PRL2011 3 Hoang, PRL2003 Mantica PRL2011

4. Idomura NF2005 ETG turbulence simulation 1. 2 Streamer and Avalanche Definition of streamer from Yoshizawa-Itoh-Itoh, p278 Convective cell (  ~ 0) Zonal flow : k ~ (k r,0,0) Streamer : k ~ (0, k ,0) Third component is k // or k t Note 1: Streamer in toroidal plasma has ballooning character with low k // <<k  but not zero, k t is also not zero Note 2: Streamer in toroidal plasma (ex. ETG streamer simulation by Idomura) do have finite frequency . His paper says heat transport is caused by quasi-linear effect with finite . So, there seems no pure “streamer” in toroidal plasma turbulence. Yamada (Nature):The streamer is a poloidally localized, radially elongated global structure (n≤3). Avalanche : radially propagating intermittent flux

5. 1.3 Paradigm shift of transport : from random walk to avalanche transport Random walk process mm N + +N - =N N + -N - =m W= [0.5(N+m)!][0.5(N-m)!] N! (1/2) N Starling formula P=(4  Dt) -1/2 exp[-x 2 /4Dt)]  x Gauss process void clump Large dT/dr T(r ) r Small dT/dr Brokenline: critical temperature Step length Critical temperature gradient transport Diamond-Hahm, PoP1995 With reference to Hwa’s joint reflection symmetry Large dT/dr

6. Idomura Full f Gyrokinetic ES ITG turbulence simulation, NF2009 Per Bak,PRL1987 : Self-organized criticality Hwa,PRA1992 : joint reflection symmetry Diamond, Hahm, PoP1995 Void Bump Large dT/dr T(r) r Small dT/dr Large dT/dr 1.4 Void : Up-hill avalanche, Bump :Down-hill avalanche

7. 1.5 Probability of avalanche If there is no constraint, probabilities of void and bump are same (symmetric) Actually, there is asymmetry on probability. There is a mechanism for symmetry breaking for avalanche propagation distribution. 7

8. 1.6 0 th order radial force balance holds even in turbulent plasma Er shear is driven by the temperature curvature! Hole and Bump in P & T -> ??  u zi =0 : determined by momentum balance eq.  E r =(dE r /dr)  r=  dP i /dr)/eZ i n i – (K 1 /eZi)  dT i /dr -> dE r /dr ~ (c 1 d 2 P i /dr 2 +c 2 d 2 T i /dr 2 ) Void : d 2 T i /dr 2 > 0 -> dE r /dr >0 Bump : d 2 T i /dr 2 dE r /dr <0 Idomura

9. 0 th order radial force balance equation induces “symmetry breaking”. If background Er’>0, bump is destabilized & hole is stabilized. If background Er’ is negative, hole is destabilized & bump is stabilized.

10. 10 Key question : Is this explanation correct? JPS meeting : validity of 0 th 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.

11. 20aTE311 [2] No-resonant mode & higher harmonics axisymmetric modes [1] History of non-resonant mode discussion X. 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?

12. With nonresonant modes (n,m)=(0,0), (0,1) N. Miyato, NF2007 gyro fluid Without 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 :  i /a=0.005

13. [3] Termination of ITB through temperature curvature 0 th order force balance equation is constraint for turbulence in tokamak. ・ [ ] or Positive feedback loop for acceleration of Er shear stabilization through pressure buildup

14. 14 3.1 Passing q min =integer (ex.=4) with steep dP/dr is difficult Y. Sakamoto : NF 2005 (NF top 10) - Avoid disruption when plasma pass q min =integer. - ITB strength can be controlled by toroidal rotation. Question : How actively control toroidal rotation in reactor Disruption

15. 15 3.2 Temperature curvature transition K. Ida, Y. Sakamoto, et al., PRL2008 concave convex

16. 16 Key question : we should establish control knob for d 2 T/dr 2 Can 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 possible Can local ECH help to control temperature curvature? -- not yet done. Dueck PRL2012

17. 17 [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

18. 18 Summary [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 0 th 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] 0 th 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.