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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 - PowerPoint PPT Presentation
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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 MeetingSan 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 GTEDGE1 code to model plasma transportIntroduction -> Analysis Framework -> Data and Results -> Conclusions
Divertor Dalpha signal and analysis periods for: 144977 and 144981
The ELMing H-Mode DIII-D Shots Chosen for Analysis
Introduction -> Analysis Framework -> Data and Results -> Conclusions
• 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
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 Er and 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
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
50% 100%/0.5* predictedorbl orblF F
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 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
0j j j j
nbj j e ion nbj e ionj jj
n n nS n n S n S
r t t t
ˆ ( ) (1 2 ( )) ( )rj orbl rjr F r r 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
ˆ( )ˆ ( ) (1 2 ( )) ( )rj orbl rjr F r r
Evolution: Inward, then Reversing and Building; Edge Peaking and Overshoot Seen in Both Shots
•Inward flux early, strong edge pedestal peakingIntroduction -> Analysis Framework -> Data and Results -> Conclusions
ˆrj
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
( ) ( )Arjj j j dj jk j j j jk k j j jB e n m V n m V M n e E
1 1 jj r j
j j
pV E V B
B n e r
1 pinchrjj j rj
j j j
p n Vp r n D
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
ˆ j j j pinchrj j rj
j
n D pn V
p r
2
Aj j dj jpinch r
rj dj jk j jk kj j j j
M m m BE EV V Vn e B B e B B e B
21j j jk dj j
jjk kj
m T eD
ee B
• Vθj is inferred from experimental values; the calculation of νdj will be
discussed; and the other values are knownIntroduction -> Analysis Framework -> Data and Results -> Conclusions
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 Vφk
exp, 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
exp/ 1kV V
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 radialmomentum balance
• An inward shift in the velocity profile “well” and large edge values are seen in both shots
expint . exp
exp
ˆ 1j jerpj r
j j
B V pV E
B n e r
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 pedestalIntroduction -> Analysis Framework -> Data and Results -> Conclusions
2 2
Ajpinch
rjj j
j dj jk r j dj jk jj jk k
j j j
M EV
n e B B
m E m V Bm Ve B e B e B
Pinch Velocity Components: Vθj and Er terms drive Vrjpinch
values in the edge, Vφk also important
• 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
2
2
Ajpinch
rjj j
j dj jk r
j
j jk k
j
j dj jk j
j
M EV
n e B B
m E
e B
m Ve B
m V B
e B
5-10%
7-15%
Pinch Velocity Components: Vθj and Er terms drive Vrjpinch
values in the edge, Vφk also important
• In the 20-30% slices, Vθj is a main pinch driver in both shots, and Er is also important in 1.5 MA
Introduction -> Analysis Framework -> Data and Results -> Conclusions
2
2
Ajpinch
rjj j
j dj jk r
j
j jk k
j
j dj jk j
j
M EV
n e B B
m E
e B
m Ve B
m V B
e B
Deuterium Diffusion Coefficient: Small values; strong difference in edge structure between shots
• Pedestal top separates two distinct radial zonesIntroduction -> Analysis Framework -> Data and Results -> Conclusions
21j j jk dj j
jjk kj
m T eD
ee B
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
1 exp
1 1.5 1
( )rj orbj j rj orbj
jj j Tj
Q E T F
n T L
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 Er and Vθj profiles, and edge peaking in the νdj
profile• Overshoot, then relaxation to an asymptotic value is
prominent in the evolution of νdj and several other parameters such as Dj and 1 MA Vrj
pinchIntroduction -> 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 Dj, Xj, and Vrj
pinch 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
References1. W. M. Stacey, Phys. Plasmas 5, 1015 (1998); 8,
3673 (2001); Nucl. Fusion 40 965 (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 20 092508 (2013).
3. W. M. Stacey and R. J. Groebner. “Evolution of the H-mode edge pedestal between ELMs”. Nucl. Fusion 51 (2011) 063024.
Introduction -> Analysis Framework -> Data and Results -> Conclusions
Backup Slides
Vφj and νdj: Computed with Vφkexp and
Perturbation Theory ALT•An expression for a common νd0 is derived from Carbon & Deuterium toroidal momentum balance
with Vφj=Vφk+ΔVφ and accounting for Vϕjintrin (IOL)
•Then, an expression for ΔVφ is also derived from toroidal momentum balance
0 exp intrin exp intrin
A Arj rkj j j j k k k k
j kd
j j k j k k k k
B e M n e E B e M n e E
n m V V V n m V V
Introduction -> Analysis Framework -> Data and Results -> Observations -> Conclusion
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
* * * *
* *
1 1
1
A Arj rkj j j j k k k kkj jk
kj dk j j kj dk jk dj j j kj dk
jk kj
jk dj kj dk
B e M n e E B e M n e E
n m n mV
exp/ 1kV V
Shot 144981: Observations From a Partial ELM Overlap - 5-10% composite inter-ELM slice vs. 0-10%
Introduction -> Analysis Framework -> Data and Results -> Conclusions
• Small overlap with the ELM event measured by the divertor Dα detector had extreme effects on the calculated transport values
5-10%
0.5-10%