Inter-ELM Edge Profile and Ion Transport Evolution on DIII-D

1. Inter-ELM Edge Profile and Ion Transport Evolution on DIII-D John-Patrick Floyd, W. M. Stacey, S. Mellard (Georgia Tech), and R. J. Groebner (General Atomics) 2014 Transport Task Force Meeting San Antonio, Texas 4/22/14

2. Summary • Introduction • Research goals • DIII-D Shots chosen for analysis • Analysis framework • Ion orbit loss considerations • Momentum balance and the pinch-diffusion relation • Inter-ELM evolution of edge transport parameters • Conclusions • References Introduction -> Analysis Framework -> Data and Results -> Conclusions

3. Research Goals and Methods • Characterize the inter-ELM transport evolution and pedestal dynamics in the edge pedestal region for several DIII-D shots • Determine the drivers of these effects from the theoretical framework, and compare these effects and drivers across several DIII-D shots • Aggregate inter-ELM data into a composite inter-ELM period, and divide it into minimum-width, consecutive slices to observe profile evolution • Use the GTEDGE1 code to model plasma transport Introduction -> Analysis Framework -> Data and Results -> Conclusions

4. The ELMing H-Mode DIII-D Shots Chosen for Analysis • DIII-D discharges 144977 and 144981 are part of a current scan: Ip,144977≈ 1 MA; Ip,144981 ≈ 1.5 MA • Both are ELMing H-mode shots with good edge diagnostics and long inter-ELM periods • ΔtELM,144977 ≈ 150 ms; ΔtELM,144981 ≈ 230 ms • Shots hereafter referred to by Ip: 1 MA; 1.5 MA DivertorDalpha signal and analysis periods for: 144977 and144981 Introduction -> Analysis Framework -> Data and Results -> Conclusions

5. 1 MA (144977) and 1.5 MA (144981) Shots: ELMing H-mode Density and Temp. Evolution Introduction -> Analysis Framework -> Data and Results -> Conclusions

6. Inter-ELM Evolution of the Radial Electric Field Erand Carbon Pol. Rot. Vel. Vθk: Both have large edge wells, Er’s moves inward; Vθk has a large rise near the sep. Introduction -> Analysis Framework-> Data and Results -> Conclusions

7. Overview of the Analytical Ion Orbit Loss Model Utilized in GTEDGE and this work • An analytical model for ion orbit loss (IOL) has been developed2, and it is incorporated into the GTEDGE1 modeling code utilized in this research • To be conservative, the full fraction of ions lost through IOL as predicted by this model is reduced by half for these calculations • Forbl(r) represents the fraction of total ions lost by IOL; its values are small away from the separatrix, but peak there late in the inter-ELM period Introduction -> Analysis Framework -> Data and Results -> Conclusions

8. Large Fractional Ion Loss By IOL Near the Separatrix, and the Associated Lost Ion Poloidal Fluid Velocity Introduction -> Analysis Framework -> Data and Results -> Conclusions

9. From the Ion Continuity Eq. to the Radial Ion Flux, Including Ion Orbit Loss (IOL) Effects • The following analytical framework was derived3 from first principles to calculate those important transport variables that are not measured • The main Deuterium ions (j=Deuterium, k=Carbon), must satisfy the continuity equation: • This is solved for the radial ion flux, a fraction of which (Forbl) is lost due to ion orbit loss. This loss must be compensated by an inward ion current, resulting in a net main ion radial flux2 Introduction -> Analysis Framework -> Data and Results -> Conclusions

10. Radial Ion Flux Dependence on Changing Ion Orbit Loss Fraction – It Is Significant Near the Edge Where IOL Is Largest • Variables directly taking IOL into account are denoted by a carat Introduction -> Analysis Framework -> Data and Results -> Conclusions

11. Evolution: Inward, then Reversing and Building; Edge Peaking and Overshoot Seen in Both Shots • Inward flux early, strong edge pedestal peaking Introduction -> Analysis Framework -> Data and Results -> Conclusions

12. Radial Ion Flux & Momentum Balance => Pinch-Diffusion Relation • The radial and toroidal momentum balance equations for a two-species plasma (equations for species j shown here) • Are combined to get the pinch-diffusion relation3 Introduction -> Analysis Framework -> Data and Results -> Conclusions

13. The Pinch-Diffusion Relation: Required by Mom. Bal. • The reordered pinch-diffusion equation: • The pinch velocity and diffusion coefficient expression forms are required by mom. balance • Vθj is inferred from experimental values; the calculation of νdj will be discussed; and the other values are known Introduction -> Analysis Framework -> Data and Results -> Conclusions

14. Vφj and νdj: Computed Using Experimental Vφkexp Values, Mom. Balance, and Perturbation Theory • An expression for a common νd0 is derived from toroidal momentum balance, assuming the Vφj is ΔVφ different from Vφkexp, less IOL intrinsic rotation loss: V^φj=Vφk+ΔVφ+Vϕjintrin • Then, an expression for ΔVφ is derived from toroidal momentum balance, and the solutions for ΔVφ and νd0 are improved iteratively2. • They are found to converge whenbolstering the perturbation analysis • V^φj and νdj are then calculated from the results Introduction -> Analysis Framework -> Data and Results -> Conclusions

15. Interpreted Deuterium Mom. Transfer Freq.: Strong Peak at Pedestal, and ‘Overshoot” Behavior in 1 MA Introduction -> Analysis Framework -> Data and Results -> Conclusions

16. Toroidal Rot. Velocities, Corrected for IOL Intrin. Rot. • Intrinsic vel. loss through IOL deepens edge wells Introduction -> Analysis Framework -> Data and Results -> Conclusions

17. Deuterium Poloidal Rotation Velocity: Strong Peak near Separatrix, and a Radial Shift • The deuterium poloidalrotation velocity is interpreted from experiment using radialmomentum balance • An inward shift in the velocity profile “well” and large edge values are seen in both shots Introduction -> Analysis Framework -> Data and Results -> Conclusions

18. Pinch Velocity: Large negative peaking observed at the edge, structural difference between shots • Peaking behavior near the edge pedestal Introduction -> Analysis Framework -> Data and Results -> Conclusions

19. Pinch Velocity Components: Vθj and Erterms drive Vrjpinchvalues in the edge, Vφk also important 5-10% 7-15% • In the 1 MA first slice, the Er and Vθj are main pinch drivers, whereas Vφk is more important in 1.5 MA Introduction -> Analysis Framework -> Data and Results -> Conclusions

20. Pinch Velocity Components: Vθj and Erterms drive Vrjpinchvalues in the edge, Vφk also important • In the 20-30% slices, Vθj is a main pinch driver in both shots, and Eris also important in 1.5 MA Introduction -> Analysis Framework -> Data and Results -> Conclusions

21. Deuterium Diffusion Coefficient: Small values; strong difference in edge structure between shots • Pedestal top separates two distinct radial zones Introduction -> Analysis Framework -> Data and Results -> Conclusions

22. Deuterium Thermal Diffusivity: Significant Changes in the Edge during the inter-ELM period • Much stronger temporal variation in 1.5 MA shot Introduction -> Analysis Framework -> Data and Results -> Conclusions

23. Conclusions – Transport • Ion orbit loss is highest near the separatrix, where it has a significant impact on ion transport values • An inward radial flux is seen after the ELM • The pinch velocity (required by momentum balance) becomes significant near the separatrix, and is small towards the core; its max value (pedestal region), is dependent on the radial overlap of the well structures in the ErandVθj profiles, and edge peaking in the νdjprofile • Overshoot, then relaxation to an asymptotic value is prominent in the evolution of νdjand several other parameters such asDjand 1 MA Vrjpinch Introduction -> Analysis Framework -> Data and Results -> Conclusions

24. Conclusions – Shot Comparison • The large ELM/high current 1.5 MA shot has several significant transport differences from the smaller ELM/low current 1 MA shot • Differences in Dj, Xj, and Vrjpinch values and structure • Similar νdj and Vθj values and profile structure • Overshoot and relaxation behavior is more prevalent in the 1 MA profiles, but some is seen in the 1.5 MA • Radial ion flux takes longer to recover in the 1.5 MA • Smaller Er edge well further towards the core in the 1.5 MA, contributing to a smaller pinch velocity Introduction -> Analysis Framework -> Data and Results -> Conclusions

25. References • W. M. Stacey, Phys. Plasmas 5, 1015 (1998); 8, 3673 (2001); Nucl. Fusion 40 965 (2000). • W. M Stacey, “Effect of Ion Orbit Loss on the Structure in the H-mode Tokamak Edge Pedestal Profiles of Rotation Velocity, Radial Electric Field, Density, and Temperature”. Phys. Plasmas20 092508 (2013). • W. M. Stacey and R. J. Groebner. “Evolution of the H-mode edge pedestal between ELMs”. Nucl. Fusion51 (2011) 063024. Introduction -> Analysis Framework -> Data and Results -> Conclusions

26. Backup Slides

27. Vφj and νdj: Computed with Vφkexp and Perturbation Theory ALT • An expression for a common νd0 is derived from Carbon & Deuterium toroidal momentum balancewith Vφj=Vφk+ΔVφ and accounting for Vϕjintrin (IOL) • Then, an expression for ΔVφ is also derived from toroidal momentum balance Introduction -> Analysis Framework -> Data and Results -> Observations -> Conclusion

28. Vφj and νdj: Computed with Vφkexp and Perturbation Theory ALT • The solutions for ΔVφ and νdj are improved iteratively, and they converge when the ratio is much less than one, bolstering the perturbation analysis Introduction -> Analysis Framework -> Data and Results -> Observations -> Conclusion

29. Shot 144981: Observations From a Partial ELM Overlap - 5-10% composite inter-ELM slice vs. 0-10% 5-10% 0.5-10% • Small overlap with the ELM event measured by the divertor Dα detector had extreme effects on the calculated transport values Introduction -> Analysis Framework -> Data and Results -> Conclusions