2nd APTWG at Chengdu, Plenary session, presentation number PL-1
Key Questions and Issues in turbulent Transport in
Tokamaks
JAEA M. Kikuchi
Some questions along with writing a review on physics behind steady state
tokamak research
1.
2.
3.
4.
Avalanche dynamics in critical temperature gradient transport
Effect of non-resonant modes, higher order axisymmetric modes on GAM
Termination of ITB through temp curvature (0th order radial force balance)
Mystery of beta dependence of in EM Gyrokinetic , micro tearing?
Acknowledgements: P. Diamond, Hahm, Idomura, Miyato, B. Scott, F. Jenko
PL-1
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[1] Avalanche Dynamics in critical temperature gradient transport
Self-organized criticality: power law paradigm
P. Bak, Phys. Rev.
A38(1988)364
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
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).
Nano flare dN/dE~E-1.75
Micro flare
dN/dE~E-1.53
Largest solar flare
Superflare
dN/dE~E-1.9 by Kepler
Flare energy(Erg)
Prof. Shibata Plasma Conf. 2011, to appear Nature
1.1 Critical temperature gradient transport is now
experimentally confirmed for both electron and ion
• Electron transport : Hoang PRL2003
• Ion transport ： Mantica PRL2011
Hoang, PRL2003
Mantica PRL2011
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1. 2 Streamer and Avalanche
Definition 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
Yamada (Nature):The streamer is a poloidally
localized, radially elongated global structure (n≤3).
Avalanche : radially propagating intermittent flux
Note 1: Streamer in toroidal plasma has
ballooning character with low k//<<kq but
not zero, kt is also not zero
Note 2: Streamer in toroidal plasma (ex.
ETG streamer simulation by Idomura) do
have finite frequency w.
His paper says heat transport is caused
by quasi-linear effect with finite w.
So, there seems no pure “streamer” in
toroidal plasma turbulence.
Idomura NF2005 ETG turbulence simulation
1.3 Paradigm shift of transport : from random walk to avalanche transport
Critical temperature gradient transport
Random walk process
D
N++N-=N
N+-N-=m
Starling formula
2D
mD
x
N! (1/2)N
W= [0.5(N+m)!][0.5(N-m)!]
P=(4pDt)-1/2exp[-x2/4Dt)]
Gauss process
Diamond-Hahm, PoP1995
With reference to
Hwa’s joint reflection symmetry
T(r
)
Brokenline: critical temperature
Large dT/dr
void
Step length
clump
Small dT/dr
Large dT/dr
r
1.4 Void : Up-hill avalanche, Bump :Down-hill avalanche
T(r)
Large dT/dr
Void
Per Bak,PRL1987 : Self-organized criticality
Hwa,PRA1992 : joint reflection symmetry
Diamond, Hahm, PoP1995
Bump
Small dT/dr
Large dT/dr
r
Idomura Full f Gyrokinetic ES ITG turbulence simulation, NF2009
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.
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1.6 0th order radial force balance holds even in turbulent plasma
Idomura
Duzi=0 : determined by momentum balance eq.
Hole and Bump in P & T -> ??
dEr=(dEr/dr)dr=d(dPi/dr)/eZini – (K1/eZi) ddTi/dr -> dEr/dr ~(c1d2Pi/dr2+c2d2Ti/dr2)
Er shear is driven by the temperature curvature!
Void
Bump
: d2Ti/dr2 > 0 -> dEr/dr >0
: d2Ti/dr2 < 0 -> dEr/dr <0
0th 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.
Key question : Is this explanation correct?
JPS meeting : validity of 0th order force balance equation in time scale of fraction of ionion 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.
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[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?
20aTE3
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N. Miyato, NF2007 gyro fluid
[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.
With nonresonant modes
(n,m)=(0,0), (0,1)
Without nonresonant modes
(n,m)=0 ,1
With nonresonant modes
(n,m)=(0,0), (0,1)—(0,9)
All : ri/a=0.005
[3] Termination of ITB through temperature curvature
0th order force balance equation is constraint for turbulence in tokamak.
・[
]
or
Positive feedback loop for acceleration of Er shear stabilization through pressure buildup
3.1 Passing qmin=integer (ex.=4) with steep dP/dr is difficult
Y. 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 reactor
2
after
CTR-NB off
1
5
VT (10 m/s)
Disruption
0
before
CTR-NB off
-1
0.4 0.5
0.6 0.7
r/a
0.8
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3.2 Temperature curvature transition
K. Ida, Y. Sakamoto, et al., PRL2008
convex
concave
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Key question : we should establish control knob for d2T/dr2
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
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[4] Mystery of beta dependence of in EM Gyrokinetic , micro tearing?
Experiments :
JT-60 power degradation : Takizuka PPCF2008, Urano NF2006
Gyrokinetics:
Pueschel PoP2010 : ITG driven ion heat
flux is reduced with beta.
Pueschel PoP2010
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!!
Jenko,PRL2002
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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 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.
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