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On the non-stiffness of edge transport in L-modes

On the non-stiffness of edge transport in L-modes. O. Sauter, R. Behn, S. Brunner, Y. Camenen 2 , 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)

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On the non-stiffness of edge transport in L-modes

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  1. 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, Switzerland 2Aix-Marseille Université, CNRS, Marseille, France

  2. 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 te Micro-turbulence simulations: core versus edge Edge region: new view on low/high ne ohmic conf. Conclusions Outline

  3. H-mode L-mode core: ~constant R/LTe H-mode pedestal Center/core/edge transport zones in L-, H-modes H-mode L-mode (main) • 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: ??? • L-mode edge: this talk

  4. "Usual link" with theory stiffness slope~nTrcPB • How does c depend on T, T, etc ? • gyro-Bohm:(X. Garbet et al, PPCF 46 (2004) 1351) cs: stiffness parameter

  5. Stiffness parameter not sufficient X. Garbet et al, PPCF 46 (2004) 1351) • The stiffness parameter varies with Ta and r • Assumes similar R/LTe driven transport • cs(r) not sufficient to characterize transport => need a more detailed study in L-mode

  6. Ip-scan in ohmic L-mode plasmas Log plot ST rmix~Ip • We increases with Ip ... but Te transport independent of Ip!

  7. Simple 3 zones profile defines L-mode pedestal • Simple Te(r)=Te0[H(rinv-r)+H(r-rinv) exp(-l(r-rinv)) • Models well the central and core profiles • Shows the non-stiff part: The edge pedestal scales with Ip rped,Te(L-mode)≈0.85

  8. T is constant in edge region, not R/LTe Te ≠ const across core region Te ~ const across edge region R/LTe ~ const in core region R/LTe ≠ const in edge region BC is NOT crucial for edge BC is CRUCIAL for core prof.

  9. T fit in edge better defines exp. R/LTe cst/Te Te ≠ const across core region Te ~ const across edge region BUT Te CHANGES with plasma parameters R/LTe ~ const in core region R/LTe ≠ const in edge region R/LTe ~ stuck in core region

  10. Non-stiff edge: Te  Ip Te [eV/m] The edge region provides pedestal value~Ip (from r=1 values) to core stiff region to lead to We~Ip

  11. 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 lne=0.75 lTe=> R/Lne=0.75 R/LTe • rped,L,ne≈0.92 > rped,L,Te(note: source(ne)≠0 in edge region)

  12. What about the effect of edge triangularity? Importance of edge region for global profiles leads to revisit previous studies d>0 0.8MW d<0 0.4MW • Significant confinement improvement with d<0 • Same profiles with half heating power Y. Camenen et al, Nucl. Fusion 47 (2007) 510

  13. 1.4 Te(d=+0.35) d<0 effect similar to Ip↑: increases Te,ped Ip=200kA; 0.4MW d=+0.35 d=-0.30

  14. d=+0.35 d=-0.30 d<0 effect similar to Ip↑: increases Te,ped Ip=200kA; 0.4MW • In edge region: • Te const • Te increases with d<0 • Te(r=0.85) ↑ with d<0 • In the core: • same l: Te exp[-l(r-rinv)] • stiff core "propagates" improved BC at r=0.85

  15. ce,d>0 / ce,d<0 New explanation of d effects reconciles with previous theoretical results Linear and nonlinear simulations show an effect of plasma boundary shape only outside r~0.7 since shape does not penetrate much experiment Non-linear GS2 r A. Marinoni et al, PPCF Plasma 51 (2009) 055016 (local calculations)

  16. New nonlinear simulations towards edge region stiff core d independent non-stiff edge d dependent • Compare positive and negatived with half heat flux • Compare core and edge stiffness from scan in R/LTe

  17. Nonlinear GENE local: d and core-edge • Reduced mi/me ratio, n=0, 2 spec., Zeff=1, electrostatic model • When rescaled to have values around one we see: • Much larger reduction for negative d at r=0.95 • "smaller slope" at r=0.95, consistent with being less stiff (as Marinoni et al)

  18. GENE + full mass + collisions + C + b 1.2MW me,b,n,C 0.6MW • correct me/mi, n, 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

  19. Nonlinear local rescaled gyrokinetic have consistent trends with edge non-stiffness 1.2MW 0.6MW • Electron Power "flux" rescaled to experimental value • Flux tube simulations at 3 radii: 0.5, 0.7 and 0.95 • Much less steep at r=0.95, similar at 0.5 and 0.7 • => Consistent with edge non-stiffness for r>0.85

  20. Additional results to be found in paper • Power scan shows same results as Ip scan: edge gradient changes providing improved BC at rV=0.85 • Density scan shows a different behavior. • Value at r=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 ci. It also explains independence of vtor on Ip shown in TCV

  21. Conclusions • Core transport limits R/LTe (and R/Lne to some extent) • Even with favourable Ip scaling, profiles remain self-similar • Thus values at r~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 d (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)

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