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%