Comparison of Critical Values of R/L Te. for ETG Modes Based on an Analytic Expression. with GKS Simulations for DIII-D Discharges

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1 Comparison of Critical Values of R/L Te for ETG Modes Based on an Analytic Expression with GKS Simulations for DIII-D Discharges J.C. DeBoo, D.R. Baker and G.M. Staebler DIII-D National Fusion Facility General Atomics 9 th Joint US-European TTF Workshop April, Madison Wisconsin DeBoo TTF

2 Motivation Understanding electron thermal transport remains a key area of study in the overall understanding of transport in tokamak plasmas. Electron Temperature Gradient (ETG) modes can lead to enhanced electron heat flux when coupling of these modes leads to the formation of so called streamers. Full gyrokinetic stability (GKS) code calculations can be used to find the critical electron temperature gradient scale length for ETG modes but the code requires significant computing time. An analytic expression for (R/L Te ) crit can be useful if accurate enough Compare an analytic expression for (R/L Te ) crit with GKS code results DeBoo TTF

3 Expression for (R/L Te ) crit for ETG Modes From Jenko* ( R/ L ) = max{( + τ)(. +. 9s/ q) T e crit x(. ε)[ +. ε( dκ/ dε)], 8. R/ L n } For magnetic shear s. and normalized pressure gradient α. Where s = (r/q)(dq/dr) ; α = -q R(dβ/dr) ; τ = Z eff (T e /T i ) ; ε = r/r ; κ = elongation and R/L n = (R/n)(dn/dr) *F. Jenko, W. Dorland and G.W. Hammett, Phys. Plasmas 8 () 96 DeBoo TTF

4 Experimental Profiles From DIII-D Discharges Used For Comparison Three pairs of discharges studied L-mode vs H-mode: compares varying T e /T i with both T e and T i varied L-mode pair 76 and 767: vary T e /T i with fixed T i L-mode pair 67 and 678: vary s/q by varying q General discharge characteristics L-Mode H-Mode B T (T)..9 I p (MA).8-.. n e ( 9 m - ) κ DeBoo TTF

5 Comparison of L-Mode and H-mode Profiles L-mode H-mode T (kev) e T i (kev) T e / T i 79 6 n e ( 9 m - ) Z eff 8 7 q 6 DeBoo TTF

6 Analytic Expression Agrees Reasonably Well With GKS Code And Shows Similar Trend Across Pla sma J Analytic expression not evaluated where s <. J The two most dominant terms in the analytic expression are the terms containing τ = Z eff T e /T i and s/q L-mode 79 expression sqterm GKS kapterm tauterm epsterm H-mode R/L Te R/L Te DeBoo TTF

7 Alpha Values Are Close To But Typica lly Above The Model Criteria For Applicability J The model is expected to be applicable to Tokamak discharges with α. Alpha DeBoo TTF

8 Plasma Profile Comparison For T e Variation At Fixed T i T e (kev) T i (kev) T e / T i n e ( 9 m - ) Z eff 8 7 q 6 DeBoo TTF

9 Agreement Between GKS Code Results and Analytic Expression Remains Good with T e /T i Variation J Excellent agreement toward outside of plasma J Agreement becomes worse in region where T e /T i begins to differ in the two discharges 76 Lower T e case 767 Higher T e case expression expression GKS GKS experiment experiment R/L Te R/L Te DeBoo TTF

10 Plasma Profile Comparison At Two q Values T e (kev) T i (kev) T e / T i n e ( 9 m - ) Z eff 8 7 q 6 DeBoo TTF

11 Agreement Between GKS Code Results and Analytic Expression Remains Good At Low and High q Values J Agreement improves toward outside of plasma where s/q is larger 67 Lower q case 678 Higher q case expression expression GKS GKS experiment experiment R/L Te R/L Te DeBoo TTF

12 Larger s/q Is Stabilizing For ETG Modes J The critical R/L Te is larger at larger s/q GKS code Analytic Expression Larger s/q Smaller s/q R/L Te s/q DeBoo TTF

13 R/L Te Values From The Expression Are Systematically Below Values From The GKS Code, But Are Generally Within % Critical R/L Te Expression / GKS result DeBoo TTF

14 When Averaged Over All Cases Studied A Slight Trend Toward Better Agreement Is Observed Toward The Plasma Edge J Values from the expression are averaged by radial location over all cases studied J Error bars represent ± σ in the distribution R/L T e Expression / GKS result DeBoo TTF

15 SUMMARY Critical R/L Te values for ETG modes from the GKS code were compared to values from an analytic expression developed in F. Jenko, et al., Phys. Plasmas 8 () 96. Although the region of applicability of the expression is marginally violated for the normalized pressure gradient α (α.) for the experimental discharges studied, the expression agrees reasonably well with GKS code calculations. R/L Te values from the expression are systematically below values from the GKS code but are generally within % of GKS results with a slight trend toward better agreement toward the plasma edge. DeBoo TTF

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