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

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

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 GTEDGE 1 code to model plasma transport Introduction -> Analysis Framework -> Data and Results -> Conclusions

Divertor D alpha signal and analysis periods for: and The ELMing H-Mode DIII-D Shots Chosen for Analysis Introduction -> Analysis Framework -> Data and Results -> Conclusions DIII-D discharges and are part of a current scan: I p, ≈ 1 MA; I p, ≈ 1.5 MA Both are ELMing H-mode shots with good edge diagnostics and long inter-ELM periods Δt ELM, ≈ 150 ms; Δt ELM, ≈ 230 ms Shots hereafter referred to by I p : 1 MA; 1.5 MA

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

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

Overview of the Analytical Ion Orbit Loss Model Utilized in GTEDGE and this work An analytical model for ion orbit loss (IOL) has been developed 2, and it is incorporated into the GTEDGE 1 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 F orbl (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

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

From the Ion Continuity Eq. to the Radial Ion Flux, Including Ion Orbit Loss (IOL) Effects The following analytical framework was derived 3 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 (F orbl ) is lost due to ion orbit loss. This loss must be compensated by an inward ion current, resulting in a net main ion radial flux 2 Introduction -> Analysis Framework -> Data and Results -> Conclusions

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

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

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 relation 3 Introduction -> Analysis Framework -> Data and Results -> Conclusions

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 V θj is inferred from experimental values; the calculation of ν dj will be discussed; and the other values are known Introduction -> Analysis Framework -> Data and Results -> Conclusions

V φj and ν dj : Computed Using Experimental V φk exp Values, Mom. Balance, and Perturbation Theory An expression for a common ν d0 is derived from toroidal momentum balance, assuming the V φj is ΔV φ different from V φk exp, less IOL intrinsic rotation loss: V ^ φj =V φk +ΔV φ +V ϕ j intrin Then, an expression for ΔV φ is derived from toroidal momentum balance, and the solutions for ΔV φ and ν d0 are improved iteratively 2. They are found to converge when bolstering the perturbation analysis V ^ φj and ν dj are then calculated from the results Introduction -> Analysis Framework -> Data and Results -> Conclusions

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

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

Deuterium Poloidal Rotation Velocity: Strong Peak near Separatrix, and a Radial Shift The deuterium poloidal rotation velocity is interpreted from experiment using radial momentum 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

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

Pinch Velocity Components: V θj and E r terms drive V rj pinch values in the edge, V φk also important In the 1 MA first slice, the E r and V θj are main pinch drivers, whereas V φk is more important in 1.5 MA Introduction -> Analysis Framework -> Data and Results -> Conclusions 5-10% 7-15%

Pinch Velocity Components: V θj and E r terms drive V rj pinch values in the edge, V φk also important In the 20-30% slices, V θj is a main pinch driver in both shots, and E r is also important in 1.5 MA Introduction -> Analysis Framework -> Data and Results -> Conclusions

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

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

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 E r and V θj profiles, and edge peaking in the ν dj profile Overshoot, then relaxation to an asymptotic value is prominent in the evolution of ν dj and several other parameters such as D j and 1 MA V rj pinch Introduction -> Analysis Framework -> Data and Results -> Conclusions

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 D j, X j, and V rj pinch values and structure – Similar ν dj and V θj 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 E r edge well further towards the core in the 1.5 MA, contributing to a smaller pinch velocity Introduction -> Analysis Framework -> Data and Results -> Conclusions

References 1.W. M. Stacey, Phys. Plasmas 5, 1015 (1998); 8, 3673 (2001); Nucl. Fusion (2000). 2.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. Plasmas (2013). 3.W. M. Stacey and R. J. Groebner. “Evolution of the H-mode edge pedestal between ELMs”. Nucl. Fusion 51 (2011) Introduction -> Analysis Framework -> Data and Results -> Conclusions

Backup Slides

V φj and ν dj : Computed with V φk exp and Perturbation Theory ALT An expression for a common ν d0 is derived from Carbon & Deuterium toroidal momentum balance with V φj =V φk +ΔV φ and accounting for V ϕ j intrin (IOL) Then, an expression for ΔV φ is also derived from toroidal momentum balance Introduction -> Analysis Framework -> Data and Results -> Observations -> Conclusion

V φj and ν dj : Computed with V φk exp and Perturbation Theory ALT The solutions for ΔV φ and ν dj 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

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