1. H. Weisen 1 21st IAEA FEC, Chengdu 2006 Peaked Density Profiles in Low Collisionality H-modes in JET, ASDEX Upgrade and TCV H. Weisen, C. Angioni, M. Maslov, A. Zabolotsky, M. Beurskens, C. Fuchs, L. Garzotti, C. Giroud, P. Mantica, D. Mazon, L. Porte, J. Stober, EFDA-JET contributors, ASDEX Upgrade Team and TCV Team21st IAEA FEC 20.10.2006 TCV

2. H. Weisen 2 21st IAEA FEC, Chengdu 2006 OUTLINE Motivation AUG-JET combined density profile database Most relevant and significant variables governing density profile peaking Regressions and ITER extrapolations Density profiles under intense electron heating Impact on fusion performance Conclusions Peaked Density Profiles in Low Collisionality H-modes in JET, ASDEX Upgrade and TCV

3. H. Weisen 3 21st IAEA FEC, Chengdu 2006 Importance of density peaking Peaked density profile  more fusion power P fus  n D n T  v   n 2 T 2  p 2 for 7  T  20 keV Peaked density profiles  more bootstrap current. Peaked density profiles  higher core density for given edge density. Peaked density profiles may compensate for lower than expected density limit in ITER (Borrass, NF 2004)  Peaked density profiles prone to neoclassical impurity accumulation at high Z and/or at low anomalous transport (e.g. C.Giroud, EX / 8-3)

4. H. Weisen 4 21st IAEA FEC, Chengdu 2006 Separate studies in AUG & JET Density profiles in ELMy H-mode more peaked at low collisionality eff =10 -14 Z eff R 0 n e T e -2 (SI,eV) C. Angioni et al, PRL 90 (2003) 205003H. Weisen et al, NF 45 (2005) L1-L4 COMBINED DATABASE (2006) 277 JET H-modes, 343 AUG H-modes Reduced colinearities between physics variables eff at r=0.5

5. H. Weisen 5 21st IAEA FEC, Chengdu 2006 Dimensionless physics variables Fundamental parameters from drift wave theory  * = 4.37  10 -3 (m eff  T e  ) 1/2 /(aB T ) eff = 2  10 -14  n e  R 0 /  T e  2  = 4  10 -3  p  /B T 2 (as used by ITPA) Dimensionless NBI source term from diffusion- convection equation in steady state Additional variables: N GR,q 95,T e (  =0.2)/  T e ,  R 0 ) Flux due to edge neutrals in core region poorly known, but typically one order of magnitude below NBI flux (Zabolotsky NF 2006, Valovic NF lett. submitted). Not included here.

6. H. Weisen 6 21st IAEA FEC, Chengdu 2006 Consistent definition for peaking Peaking factor: n e (  =0.2)/  n e  But different diagnostics & different analysis on JET and AUG  systematic errors  large errors on regressions Method: JET density profiles from interferometry remapped onto (virtual) AUG interferometer geometry, JET & AUG inverted using same geometry and same set of basis functions JET original and remapped/inverted agree within 2%, validates virtual interferometer method. Systematic errors may exist for other variables. –Introduced R 0 as a device label. –If regressed variable scales with R 0 that may indicate possible systematic errors in variables or inadequate choice thereof

7. H. Weisen 7 21st IAEA FEC, Chengdu 2006 Bivariate correlations Wide variety of discharges conditions, with and without beam fuelling Correlation of ln eff with N GR =  n e  /  n GR  is strong Correlations of ln eff with  * and  * in combined database are weak 0.1 10 111 0.2 10.010.25 00 ITER

8. H. Weisen 8 21st IAEA FEC, Chengdu 2006 Bivariate correlations Density peaking increases as eff drops, even in absence of NBI fuelling Greenwald fraction nearly as correlated with density peaking as ln( eff ) Peaking in NBI-only discharges correlates with source parameter Correlations with  *, q ,T e (0.2)/  T e ,  and  ce  E are insignificant 0.110 eff 10.21 111 222 00.3 0.52 ITER

9. H. Weisen 9 21st IAEA FEC, Chengdu 2006 Multivariate regressions n e2 /  n e  =a 0 +  i a i X i and n e2 /  n e  =a 0  i X i a i 1  n e2 /  n e   2  both forms equivalent Tested many combinations of variables Criteria*: 1.Statistical relevance of variable i StR i =a i  STD(X i )/STD(n e2 /  n e  ) (How much does the variation of variable i contribute to the variation of n e2 /  n e  ?) 2.Statistical significance StS i =a i /STD(a i ) (How well is the coefficient of variable i determined?) 3.RMSE of fit (How good is the fit?) * O. Kardaun, Classical Methods of Statistics, Springer Verlag, 2005

10. H. Weisen 10 21st IAEA FEC, Chengdu 2006 Multivariate regressions Strong correlation between eff and N GR  regress with only one and both, with and without device label R 0 (details: see poster/paper EX/8-4 or C.Angioni NF lett. submitted) Summary of multivariate study:  eff is the most relevant whenever included in a fit (mostly also most significant)   * is relevant and significant whenever included  N GR, R 0 and/or  * become significant and relevant only if eff is excluded   may be significant or not depending on other variables. Small contribution.  q 95,T e (  =0.2)/  T e ,  always insignificant and irrelevant

11. H. Weisen 11 21st IAEA FEC, Chengdu 2006 Multivariate regressions n e2 /  n e  = 1.35  0.015 –(0.12  0.01)ln eff +(1.17  0.01)  * – (4.3  0.8)  ITER: 1.45 All fits including eff predict peaked profile for ITER n e2 /  n e  >1.4 All fits excluding eff predict flat profile for ITER n e2 /  n e  ~1.2 However theory (dimensionless scaling) and appearance of strong R 0 dependence when eff omitted, suggest that it is wrong to exclude eff. JET/AUG study therefore suggests that ITER will have n e2 /  n e  >1.4 EXAMPLE

12. H. Weisen 12 21st IAEA FEC, Chengdu 2006 Other parameters Combined database does not (yet) have Ti and local shear, n C, but subset of JET data does. Impurities generally not more peaked than electrons, carbon even significantly less (Giroud EX/8-3). No correlation of n e2 /  n e  and l i or local magnetic shear from polarimetry (at odds with theory and with L-mode results elsewhere) No correlation between n e2 /  n e  and T e2 /  T e  (at odds with theory) Evidence for thermodiffusion : weak dependence on T i /T e in JET subset T i /T e influence qualitively consistent with theory: low T i /T e  flatter profiles Coefficient for source in fit for R/L n at mid-radius provides experimental value for  /D~1.5 consistent with anomalous transport theory (Garbet, 2004) R  n e /n e =0.97  0.34-(0.65  0.1)ln eff +(1.46  0.63)D    +(0.65  0.4)T i /T e ITER: R  n e /n e  2.6, n e2 /  n e   1.46 f nb =P nbi /P tot

13. H. Weisen 13 21st IAEA FEC, Chengdu 2006 Peaked, purely electron heated H-modes with  N =2 in TCV Theory suggests that strong TEM may reduce or completely remove density peaking by outward thermodiffusion (Garbet, PPCF 2004) Flattening with core ECRH observed in several devices, i.e. TCV L-modes (Zabolotsky EX/P3-7) and often attributed to TEMs. Suggest  -heated ITER may have flat density profile Flattening not seen in JET ICRH H-modes, possibly due to low power Recent 1.5 MW ECRH-heated TCV H-modes at eff  0.4 are peaked despite T e /T i  2 at  N  2 (L. Porte, EX/P6-20) Weak T e /T i influence on JET and these TCV results suggest thermodiffusive density flattening not significant in ITER, which will be closer to equipartition. OH ECRHECRH TCV H-modes

14. H. Weisen 14 21st IAEA FEC, Chengdu 2006 Implications for fusion power P fus increases by  30% for n e2 /  n e  =1.46 (ITER) at constant  and n D,T For inductive reference Q=10 scenario (Polevoi 2003), auxiliary heating can be reduced from 40MW with flat profile to 15MW.  Q~30 if  E unchanged! No correlation between n e2 /  n e  and dimensionless global energy confinement time  ce  E :  we expect current confinement predictions for ITER to hold, even if density peaking has is not explicitly accounted for in scaling laws for  E Ti profile as in inductive reference scenario assumed Improvement less strong if Ti profile is broader

15. H. Weisen 15 21st IAEA FEC, Chengdu 2006 Pressure profile merit factor Fusion power for fixed  maximized for dln  v  /dlnT i =2 (around 10keV)  p fus  p 2, P fus   p 2 dV =  p 2  V  Pressure profile merit factor  p 2  /  p  2 Density profile contribution to merit factor is  p 2  /  p  2 and density contribution increase towards lower collisionalities Effect of density peaking not cancelled by temperature flattening Regression for ITER :  p 2  /  p  2 ~1.55 and  p 2  T  2 /(  p  2  T 2  )  1.25 JET ITER

16. H. Weisen 16 21st IAEA FEC, Chengdu 2006 Conclusions Dominant contribution to density peaking in H-mode is anomalous Collisionality is most significant variable NBI fuelling in JET and AUG also significant Scaling with eff, T e /T i and beam source consistent with D/  eff ~2/3 Scaling does not follow simple theoretical expectations with q 95,l i,T e (0.2)/  T e  NBI-free, ECH heated H-modes in TCV with  N =2 and T e /T i =2 show that peaking is not suppressed by electron heating Extrapolations to ITER predict n e2 /  n e   1.4 Pressure profile merit factors  p 2  /  p  2 and  p 2  T  2 /(  p  2  T 2  ) increase towards low eff similarly to n e2 /  n e  ~30% extra fusion power due to density peaking in ITER inductive reference scenario (fixed  and n D,T )