Dependences of Critical Rotational Shear in DIII-D QH-mode Discharges

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1 Dependences of Critical Rotational Shear in DIII-D QH-mode Discharges by T.M. Wilks 1 with K.H. Burrell 2, Xi. Chen 2, A. Garofalo 2, R.J. Groebner 2, P. Diamond 3, Z. Guo 3, and J.W. Hughes 1 1 MIT 2 General Atomics 3 UCSD Presented at the American Physical Society Division of Plasma Physics San Jose, CA November 2, 2016

2 Abstract Quiescent H-mode (QH-mode) has been identified as an attractive stationary operational regime in tokamaks due to the lack of edge localized modes (ELMs) in conjunction with good particle and impurity control due to the presence of an edge harmonic oscillation (EHO). The EHO allows operation of the QH-mode edge near but also below the peeling-ballooning ELM stability limit, and has been shown to have a dependence on the edge rotational shear. Previous analysis has demonstrated the existence of a critical edge rotational shear necessary for the existence of typical low-n EHO MHD activity, particularly with the transition to a wide pedestal regime with broadband turbulence. We build upon these results by further exploring critical edge rotational shear existence for the transition from a QH-mode to a typical ELMy H-mode in DIII-D, along with its associated turbulence and dependence on collisionality.

3 Outline Intro to QH-mode Existence of critical ExB shearing rate necessary for EHO to exist and/or suppress ELMs Calculation of critical ExB shearing rate and experimental dependencies Comparison to Guo-Diamond theory for critical ExB shearing rate

4 QH-mode is an attractive operating regime due to naturally ELM-free state with particle/impurity control Pressure Gradient QH-modes exhibit H-mode confinement without the presence of ELMs Impurity control Stationary over wide operating regimes Controlled density and betan with constant radiated power Additional edge particle transport from edge harmonic oscillation (EHO) /m 3 km/s n e 10*V θ Ψ V φ kev kv/m E r T e Ψ T i Typically QH-modes are performed with: Reverse Ip Low density USN or DN Highly conditioned walls Pedestal Current Plasma operates just below PB boundary

5 Edge Harmonic Oscillation (EHO) is a saturated benign kink-peeling mode EHOs typically: Are low n (1,2,3) dominated electromagnetic modes Increase particle transport to allow natural stability against ELMs can be thought of as a controlled and steady state ELM Are located in edge pedestal region as seen by BES and ECE measurements Chen NF 2017

6 Previous analysis shows evidence of critical ω ExB shear for EHO existence Comparison of total impurity rotation in the edge compared to the ExB rotation shows that the ExB rotation is the relevant quantity Garofalo, NF 2011 ω ExB normalized by the Alfven frequency shows clear separation between ELMy H-modes and QHmode plasmas Chen, NF 2016 This suggests further experiments investigating the presence of a critical ExB shearing rate required for QH-mode

7 DIII-D torque ramping experiments explore critical ω ExB shear at QH ELMy H-mode transition T inj ω ExB D α BB EHO What dependence does ω ExB have on other plasma parameters?

8 Critical shearing rate can be calculated 1) in the far edge 2) at the inner side of Er well 1) Average far edge shear: ωω EEEEEE = cccccccc Δ EE rr RRBB pp Δrr edge 100ms time slice averaging Spline fit with user chosen knots Depends on value at separatrix Typically 2 CER data point clusers available Uncertainties associated with derivatives of spline fits can be difficult to quantify 2) Maximum inner edge shear: ωω EEEEEE = MMMMMM RRBB pp cccccccc BB EE rr RR BBBB 2-10ms time slice averaging Spline fit with automatically chosen knots Does not depend on value at separatrix Typicall 3 CER data point clusters available

9 Previous analysis from DIII-D collisionality scan shows favorable ITER scaling for inner ω ExB shear Many spline fits performed and averaged to determine data points and uncertainties Additional data points needed to expand parameter space and confirm trend Chen NF 2017 y = 1.44e7x R 2 = 0.46

10 Inclusion of more DIII-D data points shows slightly less dependence on collisionality Critical shears normalized by Alfven frequency ωω AA = rr 2ππππ φφ μμ 0 mm ii nn ee pppppp Inner side of Er well Addition of low B φ discharges show decreased trend as predicted by previous research Outliers disinguished by variations in amplitude of EHO and some broadband MHD noise Outlier

11 Shear on the outer side of the Er well shows similar dependence on collisionality Shear on outer side of Er well shows similar positive trend compared to the inside of Er well Outer ExB rotational shear is less dependent on B φ than inner shear In depth analysis of outliers may provide a more definitive trend Normalized Critical ωω EEEEEE /ωω AA Shear (outer) [krad/s] Outer side of Er well

12 Critical shearing rates show some dependence on temperature but not density Normalized Critical ωω EEEEEE /ωω AA Shear (outer) [krad/s] Outer side of Er well Normalized Critical ωω EEEEEE /ωω AA Shear (outer) [krad/s] Outer side of Er well [ /mm 3 ] Slightly negative temperature dependence with Alfven normalization Little to no density dependence after Alfven normalization

13 Recent theory from Guo and Diamond predicts critical ExB shearing rate dependencies Phase slip model: Is derived from cross phase dynamics Predicts a phase locked state with periodic slips that breach the PB boundary (ELMs) Predicts a phase slip state w/ higher ExB shear that pumps PB modes continuously (EHO) Assumes no dynamic noise Further simplifications for experimental comparison k y *Δx = constant L p /Δx = constant VV EEEEEE,cccc = ττ 1 AA 1 εε ββ2 kk yy Δxx LL pp Δxx [Guo,Diamond, PRL 2015] 1 2 ~ TT ii LL pp Alfven time Poloidal wave number Mode width Pressure gradient scale length

14 Guo and Diamond scaling shows preliminary agreement to QH-mode shot database for outer Er shear Critical ωω EEEEEE Shear (outer) [krad/s] Critical Outer ωω EEEEEE Shear [krad/s] TT ii /L p Dependence of Critical Outer ωω EEEEEE Shear y = 0.36x+2075 R 2 = 0.43 Outer side of Er well Critical Outer ωω EEEEEE Shear [krad/s] ρ* Dependence of Critical Outer ωω EEEEEE Shear Outer side of Er well TT ii /L p Pedestal ρρ Y-intercept may be caused by Doppler shift at reference mode surface neglected in G-D theory No apparent outer shear correlation with ρ* may be due to ρ* calculation at pedestal

15 Inner Er shear has little correlation with G-D theory and inconclusive scaling with ρ* TT ii /L p Dependence of Critical Inner ωω EEEEEE Shear ρ* Dependence of Critical Inner ωω EEEEEE Shear Critical Inner ωω EEEEEE Shear [krad/s] Inner side of Er well Critical Inner ωω EEEEEE Shear [krad/s] y = -8.4e8x+1.1e7 R 2 = 0.41 Inner side of Er well TT ii /L p No apparent inner shear correlation with G-D scaling Pedestal ρρ Small ρ* variation does not conclusively prove dependence. Larger parameter space is required.

16 Conclusions Experiments support a requirement for critical ExB shearing rate necessary for EHO to suppress ELMs, but scaling is still undetermined Critical ω ExB : with νν ee for both inner and outer E r shear Has no dependence on nn ee pppppp Slightly with TT ii pppppp with ρρ for inner E r shear and no correlation with outer shear New theoretical predictions for ω ExB shearing rate dependencies, and database study is being constructed with TT ii pppppp /LL pp for outer Er shear and no correlation with inner shear Inclusion of mode characteristics is required

17 Future Work: Improvements to Model Comparison are clearly needed Less simplification of scaling is needed to bring in phase dynamics Broad displacement profile structure what k y and Δx is used for scaling? More data required to expand parameter space for validation of Guo-Diamond theory ββ scans Lower temperature discharges at similar shape BOUT++ simulations can capture effects of changing ω ExB profile

18 Select references 1. A.M. Garofalo et. al., Nucl. Fusion 51, (2011) 2. Xi Chen et. al., Nucl Fusion 56, (2016) 3. Z.B. Guo and P.H. Diamond, PRL 114, (2015) 4. Xi Chen et. al., Nucl. Fusion 57, (2017) 5. T.S. Hahm and K.H. Burrell, PoP 2, 1648 (1995) 6. K.H. Burrell et. al., PoP 8, 2153 (2001) 7. K.H. Burrell et. al., PoP 12, (2005) 8. P.B. Snyder et. al., Nucl Fusion 47, (2007) 9. K.H. Burrell et. al., Nucl Fusion 49, (2009) 10. K.H. Burrell et. al., PRL 102, (2009) 11. A.M. Garofalo et. al., Nucl Fusion 51, (2011) 12. K.H. Burrell et. al., PoP 19, (2012) 13. K.H. Burrell et. al., Nucl Fusion 53, (2013) 14. W.M. Solomon et. al., PRL 113, (2014) 15. K.H. Burrell et. al., PoP 23, (2016)

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