Edge Rotational Shear Requirements for the Edge Harmonic Oscillation in DIII D Quiescent H mode Plasmas

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1 Edge Rotational Shear Requirements for the Edge Harmonic Oscillation in DIII D Quiescent H mode Plasmas by T.M. Wilks 1 with A. Garofalo 2, K.H. Burrell 2, Xi. Chen 2, P.H. Diamond 3, Z.B. Guo 3, X. Xu 4, J.W. Hughes 1, and R.J. Groebner 2 1 MIT 2 General Atomics 3 UCSD 4 LLNL Presented at the Transport Taskforce Workshop Williamsburg, VA April 26,

2 Outline Intro to QH-mode DIII-D QH ELMy H-mode transition experiments displaying critical ExB shear Simulations showing Er shear and temperature play a critical role for determining ELM stability Comparison to theory for critical ExB shearing rate and extrapolation to ITER Discussion 2

3 QH-mode is an attractive operating regime due to naturally ELM-free state with particle/impurity control Exhibit stationary ELM-free H- mode confinement over broad operational regimes Operates at reactor relevant values of edge collisionality and normalized beta Observed in several tokamaks around the world (JT60, JET, ASDEXU, DIII-D) Edge MHD modes that provide additional transport are currently being studied Coherent EHO (usually higher torque) Broadband MHD (usually lower torque) Pinj Tinj H98 Density QHmode 3

4 Edge Harmonic Oscillation (EHO) is a saturated benign kink-peeling mode that maintains particle transport QH-mode H-mode QH-mode n=2 dominant Pedestal Current UNSTABLE STABLE Plasma operates just below PB boundary n=1 dominant Pressure Gradient Coherent edge localized electromagnetic oscillation at low-n harmonics Saturated amplitude mode that lies just below the kink-peeling boundary in the peeling-ballooning stability diagram Provides edge particle transport to maintain a stationary plasma in the absence of ELMs Usually seen experimentally at high torque and ExB edge rotational shear what are other requirements? 4

5 Previous analysis shows evidence that ExB shear is important physics for maintaining QH-mode Comparison of toroidal rotational shear to ExB rotational shear suggests ExB shear is important to distinguish transition to ELMs Database of ELMy H-modes and H-modes suggest a threshold condition for transitions between regimes Need a dedicated experiment to expand dataset on critical ExB shearing rates Carbon Toroidal Rotational Shear Garofalo, NF 2011 ExB Rotational Shear 5

6 DIII-D torque ramping experiments explore critical ExB shear at QH ELMy H-mode transition Discharge starts in QHmode T inj QH : B φ = 1.44 T : B φ = 2.01 T H NBI Torque is ramped down to determine critical rotational shear value ω edge ExB shear at ELM onset and cessation are the same Comparison of B φ =2.01T and B φ =1.44T shows smaller critical rotational shear requirement for smaller magnetic field D α n=1 EHO 6

7 Pedestal Analysis of high versus low field show different profiles B φ =2.01T discharge has slightly lower density pedestal High field discharge has much larger ion and electron temperatures Ti/Te at the pedestal is 2.5 for high field and 1.6 for low field 10 7

8 Pedestal Analysis of high versus low field show different profiles Low field discharge has larger carbon toroidal velocity, but less poloidal rotation structure / 10 High field shot has significantly larger Er well (x2) and hence larger ExB shear / 8

9 Critical shearing rate is calculated at the inner side of Er well / / 2-10ms time slice averaging Spline fit with automatically chosen knots Does not depend on value at separatrix Typically 3 CER data point clusters available Uncertainties associated with derivatives of spline fits can be difficult to quantify 9

10 Large ExB shear in high field discharge mostly due to pressure gradient term (increased Ti) Toroidal / Poloidal Poloidal contribution is very small Toroidal contribution slightly larger for low field Pressure gradient contribution much larger for high field (due to increased temperature) 10

11 Experimental scaling of 43 critical ExB shearing rate conditions show some collisionality dependence 43 critical shearing rates calculated over 26 discharges High field discharges are all under similar experimental conditions not a broad operating range Addition of low field data points illustrates less of a trend with collisionality Representative High Field Representative Low Field Outliers distinguished by variations in amplitude of EHO and some broadband MHD noise Need to turn to modeling for more insight Outlier 11

12 BOUT++ is a powerful framework that can simulate EHO physics 2 fluid linear model ( 3 field elmpb ) applies peeling ballooning physics in the edge and scrapeoff layer regions P Uses experimental equilibrium and profiles, including effects of rotation 12

13 BOUT++ simulations show EHO radial mode structure tracks pedestal width and is field independent Effect of Magnetic Field on n=1 EHO Mode Structure x10 Pressure [kpa] Growth Rate, / Δx RMS Pressure perturbation (EHO) Much smaller growth rate for high field case EHO mode structure peaks at highest pressure gradient (consistent with linear 3 field theory) Broader profile structure for high field due to gradient at top of pedestal 13

14 ELITE simulations show high field (2.01T) shots consistently P-B stable UNSTABLE UNSTABLE UNSTABLE Edge Current STABLE STABLE STABLE Normalized Pressure Gradient Normalized Pressure Gradient Normalized Pressure Gradient Smaller growth rates correspond to a stable equilibrium as calculated by ELITE 14

15 ELITE simulations show low field (1.44T) shots consistently P-B unstable Edge Current UNSTABLE STABLE UNSTABLE STABLE UNSTABLE STABLE Larger growth rates correspond to an unstable equilibrium as calculated by ELITE 15

16 Linear BOUT++ simulations calculate EHO mode structures peaking on the low field side RMS Pressure Perturbation B φ = 1.44 T n=1 Total Pressure Perturbation B φ = 2.01 T n=1 Low field more localized at outboard midplane looks like a ballooning mode 16

17 Previous DIII-D experimental measurements of EHO show broad profile peaking at the pedestal Chen NF 2016 Full width half max of temperature and density perturbations generally track pedestal width Similar experimental trends point to modes from modeling results being an EHO Mode structure Dominant low toroidal mode numbers 17

18 High field (2.01T) shots have significantly higher temperature gradient and ExB shear Ratio ~ 2.5 Ratio ~ 3 Shape is the same, so difference in stability must come from trade off between ExB shear and diamagnetic stabilization (caused by temperature gradient) 18

19 Nonlinear dynamic phase slip model uses pedestal conditions to predict macroscopic plasma state Phase slip model assumptions: Plasma is marginally unstable to peelingballooning modes Governing competition is between the cross phase PB drive heat flux and ExB flow shear Key point is evolution of flux cross phase in time Predicts several states: Phase locked state that allows build up of heat flux before collapse ELM Coherent phase slip state that pumps PB modes continuously EHO Random phase slip state that shares energy between many modes Broadband MHD 19 [Guo,Diamond, PRL 2015]

20 Nonlinear evolution equation for cross phase can be simplified to describe a QH ELM transition Nonlinear equation for the cross phase competition between PB drive heat flux and ExB shear flow: based upon model for describing synchronization between populations of coupled oscillators d dt Θ k V Δ, Θ Evolution of cross phase Winding effect due to shearing modulates the cross phase Pinning force attracting the cross phase to a fixed value Phase scatter from multimode interaction and ambient small scale drift turbulence Simplify by neglecting noise: ~ ~ No B dependence!, / // Δ Δ / ~ L Δ Critical ExB Shear for EHO Temperature Poloidal wave number Mode width Pressure gradient scale length 20 [Guo,Diamond, PRL 2015]

21 Further simplified critical shearing rate can be calculated in the far edge of the Er well Average far edge shear: / Δ Δ 100ms time slice averaging Spline fit with user chosen knots Depends on value at separatrix Typically 2 CER data point clusters available 21

22 Critical shearing rate from DIII-D database scales well with Guo-Diamond theory Critical Shear Scaling Critical Shear [krad/s] Δx from BOUT++ simulations including ExB shear Temperatures, and, and pressure gradient scale length,, from experiment L Δ 22 [Guo,Diamond, PRL 2015]

23 Assuming Er contribution from rotation is small, ExB shear can be estimated for ITER Snyder NF 2011 Pressure gradient term only ITER Parameters T ped [kev] Ip [MA] R0 [m] B0 [T] Lp [m 1 ] Δ * [m] 2 Δ [krad/s] ,000 16,3000 *Based on pedestal width 23

24 Extrapolation to ITER looks favorable for QH-mode access Critical Shear Scaling Critical Shear Shear [krad/s] QH mode QH mode ITER ITER 2 L Δ 24

25 Discussion DIII-D Experiments support a requirement for critical ExB shearing rate necessary for EHO to suppress ELMs Database study of critical ω ExB : with based on experiment (possibly due to temperature dependence) BOUT++ simulations for varied magnetic field EHO mode structure similar for 1.44T and 2.01T Lower magnetic field shows significantly higher growth rate Primary different between shot comparison is pedestal temperature Theoretical predictions for ω ExB shearing rate dependencies shows reasonable scaling for / ITER shearing rate scaling with Guo-Diamond model predicts access to QH-mode (though significant extrapolation) 25

26 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) 16. P.B. Snyder et. al., NF 51, (2011) 26

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