APS 2013, Denver, USA, 1O. Sauter, http://infoscience.epfl.ch/record/190561
On the non-stiffness of edge transport in L-modes
O. Sauter, R. Behn, S. Brunner, Y. Camenen2,
S. Coda, B. P. Duval, L. Federspiel,
T. P. Goodman, A. Karpushov, D. Kim,
A. Merle, G. Merlo, and the TCV team
Ecole Polytechnique Fédérale de Lausanne (EPFL)
Centre de Recherches en Physiques des Plasmas (CRPP)
Lausanne, Switzerland2Aix-Marseille Université, CNRS, Marseille, France
APS 2013, Denver, USA, 2O. Sauter, http://infoscience.epfl.ch/record/190561
Outline• Center, core and edge transport zones in L-, H-modes
• Experimental – theoretical link
• Definition of top of pedestal edge in L-modes
• Ip scaling of edge gradients => We Ip
• Edge non-stiffness explains triangularity effects on e
• Micro-turbulence simulations: core versus edge
• Edge region: new view on low/high ne ohmic conf.
• Conclusions
APS 2013, Denver, USA, 3O. Sauter, http://infoscience.epfl.ch/record/190561
• 3 zones with different characteristic transport properties• central: sawteeth or low heat flux => Te<Te,crit
• core: above critical gradient, stiff region• edge: main focus on H-mode: barrier ; L-mode: ???
Center/core/edge transport zones in L-, H-modes
L-mode H-mode
• L-mode edge: this talk
(main)
core: ~constant R/LTe
H-mode
L-mode
H-mode pedestal
APS 2013, Denver, USA, 4O. Sauter, http://infoscience.epfl.ch/record/190561
"Usual link" with theory
slope~
nT PB
• How does depend on T, T, etc ?• gyro-Bohm:(X. Garbet et al, PPCF 46 (2004) 1351)
TL
RnTWP 0])[(
s: stiffness parameter
stiffness
TVnPdVSQV 2
0||')('
0~()
H
L
R
L
R
ReB
Tq
cTT
Ls
APS 2013, Denver, USA, 5O. Sauter, http://infoscience.epfl.ch/record/190561
Stiffness parameter not sufficientX. Garbet et al, PPCF 46 (2004) 1351)
• The stiffness parameter varies with Ta and • Assumes similar R/LTe driven transport• s() not sufficient to characterize transport
=> need a more detailed study in L-mode
APS 2013, Denver, USA, 6O. Sauter, http://infoscience.epfl.ch/record/190561
Ip-scan in ohmic L-mode plasmas
• We increases with Ip ... but Te transport independent of Ip!
ST mix~Ip
Log plot
APS 2013, Denver, USA, 7O. Sauter, http://infoscience.epfl.ch/record/190561
Simple 3 zones profile defines L-mode pedestal
• Simple Te()=Te0[H(inv-)+H(-inv) exp(-(-inv))• Models well the central and core profiles• Shows the non-stiff part: The edge pedestal scales with Ip
ped,Te(L-mode) ≈ 0.85
APS 2013, Denver, USA, 8O. Sauter, http://infoscience.epfl.ch/record/190561
T is constant in edge region, not R/LTe
R/LTe ~ const in core regionR/LTe ≠ const in edge region
Te ≠ const across core regionTe ~ const across edge region
BC is CRUCIAL for core prof. BC is NOT crucial for edge
APS 2013, Denver, USA, 9O. Sauter, http://infoscience.epfl.ch/record/190561
T fit in edge better defines exp. R/LTe
cst/Te
R/LTe ~ stuck in core region
R/LTe ~ const in core regionR/LTe ≠ const in edge region
BUTTe CHANGES with plasma
parameters
Te ≠ const across core regionTe ~ const across edge region
APS 2013, Denver, USA, 10O. Sauter, http://infoscience.epfl.ch/record/190561
Non-stiff edge: Te Ip
The edge region provides pedestal value~Ip (from =1 values) to core stiff region to lead to We~Ip
T
e [e
V/m
]
APS 2013, Denver, USA, 11O. Sauter, http://infoscience.epfl.ch/record/190561
• ped,L,ne≈0.92 > ped,L,Te (note: source(ne)≠0 in edge region)
Density shows similar core-stiff, edge-non-stiff
• Experiments performed at same line-averaged ne
• Broader effect of sawteeth on ne than on Te
• A scalelength ne=0.75 Te=> R/Lne=0.75 R/LTe
APS 2013, Denver, USA, 12O. Sauter, http://infoscience.epfl.ch/record/190561
What about the effect of edge triangularity?
Importance of edge region for global profiles leads to revisit previous studies
• Significant confinement improvement with <0• Same profiles with half heating power
Y. Camenen et al, Nucl. Fusion 47 (2007) 510
<00.4MW
>00.8MW
APS 2013, Denver, USA, 13O. Sauter, http://infoscience.epfl.ch/record/190561
<0 effect similar to Ip↑: increases Te,ped
Ip=200kA; 0.4MW
=+0.35 =-0.301.4 Te(=+0.35)
APS 2013, Denver, USA, 14O. Sauter, http://infoscience.epfl.ch/record/190561
=+0.35 =-0.30
<0 effect similar to Ip↑: increases Te,ped
Ip=200kA; 0.4MW
In the core: • same : Te exp[-(-inv)]• stiff core "propagates" improved BC at =0.85
In edge region: • Te const• Te increases with <0• Te(=0.85) ↑ with <0
APS 2013, Denver, USA, 15O. Sauter, http://infoscience.epfl.ch/record/190561
New explanation of effects reconciles with previous theoretical results
A. Marinoni et al, PPCF Plasma 51 (2009) 055016 (local calculations)
e,
>0 /
e,<
0
Non-linear GS2
experimentLinear and nonlinear simulations show an effect of plasma boundary shape only outside ~0.7 since shape does not penetrate much
APS 2013, Denver, USA, 16O. Sauter, http://infoscience.epfl.ch/record/190561
New nonlinear simulations towards edge region
• Compare positive and negative with half heat flux• Compare core and edge stiffness from scan in R/LTe
stiff core independent
non-stiff edge dependent
APS 2013, Denver, USA, 17O. Sauter, http://infoscience.epfl.ch/record/190561
Nonlinear GENE local: and core-edge
• Reduced mi/me ratio, =0, 2 spec., Zeff=1, electrostatic model• When rescaled to have values around one we see:
• Much larger reduction for negative at =0.95• "smaller slope" at =0.95, consistent with being less stiff
(as Marinoni et al)
APS 2013, Denver, USA, 18O. Sauter, http://infoscience.epfl.ch/record/190561
GENE + full mass + collisions + C +
• correct me/mi, , 3 spec. reduce significantly the resulting Qe
• When rescaled to effective experimental heat flux:• "stiffness" does not change significantly• Can use reduced for preliminary results
me,,,C
0.6MW
1.2MW
APS 2013, Denver, USA, 19O. Sauter, http://infoscience.epfl.ch/record/190561
Nonlinear local rescaled gyrokinetic have consistent trends with edge non-stiffness
• Electron Power "flux" rescaled to experimental value• Flux tube simulations at 3 radii: 0.5, 0.7 and 0.95• Much less steep at =0.95, similar at 0.5 and 0.7
=> Consistent with edge non-stiffness for >0.85
0.6MW
1.2MW
APS 2013, Denver, USA, 20O. Sauter, http://infoscience.epfl.ch/record/190561
Additional results to be found in paper
• Power scan shows same results as Ip scan: edge gradient changes providing improved BC at V=0.85
• Density scan shows a different behavior. • Value at =1 increases significantly => link with SOL• Te across edge region remains high while ne increases• Te(edge) collapses at high density, change global q profile• Explains change in global confinement and density limit
time history(also in N. Kirneva et al , to appear in NF)
• Ti non-stiff in the core as well, in ohmic Ip scan, but Ti consistent with neoclassical i. It also explains independence of vtor on Ip shown in TCV
APS 2013, Denver, USA, 21O. Sauter, http://infoscience.epfl.ch/record/190561
Conclusions• Core transport limits R/LTe (and R/Lne to some extent)• Even with favourable Ip scaling, profiles remain self-similar• Thus values at ~0.8 are changing with Ip: Te(in edge)~Ip
• This is possible with non-stiff transport in [0.85,1]• Definition of core and edge region and their interface:
• R/LTe ~ const and ~fixed in core (but Te not const)• Te ~ const and "free" in edge (but R/LTe not const)
• Explains effects of negative (which does not penetrate)• Explains good P scaling of edge I-mode• Explains profile consistency• Explains "I-family", + can have wide variety of parameters• Explains low/high density confinement effects combined
with q>1 effects on confinement (see paper)