Observations of Rotation Reversal and Fluctuation Hysteresis in Alcator C-Mod Plasmas N.M. Cao 1, J.E. Rice 1, A.E. White 1, S.G. Baek 1, M.A. Chilenski 1, P.H. Diamond 2, A.E. Hubbard 1, J.W. Hughes 1, J. Irby 1, M.L. Reinke 3, P. Rodriguez-Fernandez 1, and the Alcator C-Mod Team 1 Massachusetts Institute of Technology (MIT), Cambridge, MA, USA 2 University of California, San Diego (UCSD), San Diego, CA, USA 3 Oak Ridge National Laboratory (ORNL), Oak Ridge, TN, USA October 23 rd, 2017 59 th Annual Meeting of the APS Division of Plasma Physics, Milwaukee, WI This work is supported by the US DOE under grant DE-FC02-99ER54512 (C-Mod)
Motivation: Hysteresis Experiments Provide Careful Probe of LOC/SOC Transition Toroidal rotation reversals are correlated with LOC/SOC transition from density ramps [Rice NF 2013] Question: What changes in turbulence are seen across the rotation reversal and LOC/SOC transition? Reversals exhibit hysteresis, so the same plasma parameters manifest different rotation states Approach: Compare turbulence physics at the same plasma parameters but differing rotation within a single shot Line-Average Electron Density Toroidal Velocity τ E 1160506007 APS-DPP 10/23/2017 2
1.6 Different Rotation but Nearly Indistinguishable Density and Temperature Profiles Profiles are shown here for 5.4 T, 0.8 MA LOC (t=0.96 s) and SOC (t=0.6 s) Electron profiles from same shot; error rigorously estimated with GPR [Chilenski NF 2017] Ion profiles from different but matched shots. 2.5 1.0 0.4 n e [10 20 m -3 ] 1.5 0.5 T e [kev] T i [kev] 2 a/l ne 8 a/l Te a/l Ti 1 4 0 0.2 0.4 0.6 0.8 1.0 r/a 0 0.2 0.4 0.6 0.8 1.0 r/a 1160506007 1120106012, 16 APS-DPP 10/23/2017 3
Linear Gyrokinetic Simulations Confirm Mode Stability Unchanged across LOC/SOC Transition Linear CGYRO runs at four different times were run in the rotation reversal region Matched profiles from LOC and SOC ±10% scan from SOC, shown in gray Dominant linearly unstable mode does not change in the rotation reversal region! Consistent with previous work looking at Alcator C-Mod plasmas [Sung NF 2013, White PoP 2013] k y ρ s 1.0 modes marginally stable ω R [ γ [ c s Τa] ion directed c s Τa] r/a = 0.575 APS-DPP 10/23/2017 4 k y ρ s
Spectral Power Density [a.u.] Fluctuation Measurements Change Across Transition Despite Similar Linear Stability Reflectometry spectra n e n0 changes inconsistent with pure Doppler shift from LOC to SOC Data from 88 GHz reflectometer; sensitive to k up to 10 cm -1 [Lin PPCF 2001] Rotation and fluctuation spectra robust to perturbation bistability cannot be explained through linear stability alone in Alcator C-Mod 2 r/a = 0.53 1160506007 APS-DPP 10/23/2017 5
Separation of Linear and Nonlinear Physics: Quasilinear Transport Approximation (QLTA) Quasilinear Weights [GB units] (errorbars show convergence error) k y ρ s 1160506007 In mqlta, flux is given by the sum over modes of a quasilinear weight (linear mode structure) with mode intensity (nonlinear saturation) Q i,anom = W Qi,k φ ത 2 k APS-DPP 10/23/2017 6 k Weights used in mqlta match weights from fully nonlinear simulation [Waltz PoP 2009]; cross-phases match experiment [White PoP 2010]
Mixed Mode Picture Plasma Behavior not Determined by Single Mode QL Weights [GB units] Ia Ib II III k y ρ s 1160506007 Separate Modes into families: I. Low-k, ω ion-directed; separated APS-DPP 10/23/2017 7 II. III. into (a) and (b) based on particle flux k y ρ s 1, hybrid mode; strong inward particle pinch High-k, electron-direction; exhausts mostly Qe E.g. Ion Flux given by: Q i = W Qi,Ia +W Qi,Ib +W Qi,II + W Qi,III =0 തφ 2 Ia തφ 2 Ib തφ 2 II തφ 2 III
Experimental Fluxes Provide a Constraint on Nonlinear Mode Saturation Levels Flux = weight intensity k QL Weights [GB units] Ia Ib II III 1160506007 Anomalous fluxes calculated using TRANSP and NEO Ib Normalized flux @ r/a=0.575 [GB units] Qualitatively different mixed saturation levels lead to the observed transport! Narrower-k: suggestive of SOC reflectometer spectra III Wider-k: suggestive of LOC reflectometer spectra Ia + II Ib III k y ρ s APS-DPP 10/23/2017 8
Conclusions and Future Work Rotation reversal hysteresis demonstrates that nearly identical n, T profiles can lead to different momentum transport and turbulent fluctuations A change in the most linearly unstable mode alone is unable to explain the rotation reversal and LOC/SOC transition in Alcator C-Mod Multi-Mode Quasilinear Transport Approximation suggests that a change in mix of mode saturation levels (e.g. a population collapse ) could be consistent with observed bistability of turbulent fluctuations and momentum transport Future work: extend predictions of mqlta to momentum fluxes, and compare against nonlinear simulation APS-DPP 10/23/2017 9
References Candy J. et al., J. Comput. Phys. 324, 73 (2016). Chilenski, M.A. et al., Nucl. Fusion 55, 023012 (2015). Diamond, P.H. et al., Nucl. Fusion 53, 104019 (2013). Grierson, B.A. et al., Phys. Rev. Lett. 118, 015002 (2017). Howard, N.T. et al., Plasma Phys. Control. Fusion 56, 124004 (2014). Reinke, M.L. et al., Plasma Phys. Control. Fusion 55, 012001 (2012). Reinke, M.L. et al., Rev. Sci. Instrum. 83, 113504 (2012). Rice, J.E. et al., Nucl. Fusion 51, 083005 (2011). Rice, J.E. et al., Nucl. Fusion 53, 033004 (2013). Sung, C. et al., Nucl. fusion 53, 083010 (2013). Sung, C. et al., Phys. Plasmas 23, 042303 (2016). White, A.E. et al., Phys. Plasmas 17, 056103 (2010). White, A.E. et al., Phys. Plasmas 20, 056106 (2013). Waltz. R.E. et al., Phys. Plasmas 16, 072303 (2009) APS-DPP 10/23/2017 10
Extra Slides APS-DPP 10/23/2017 11
What about momentum? Don t expect many intrinsic stress sources to be captured by local linear runs [Grierson PRL 2017] Turbulent momentum diffusion balances with intrinsic stress generation APS-DPP 10/23/2017 12
Hysteresis Observed Robustly in Multiple Plasma Conditions Hysteresis is observed at multiple currents, and survives perturbation from LBO. Low-power ICRF heating ramps also lead to hysteresis, with similar 1160506015 1160506007, 08, 24 1160506009, 10 APS-DPP 10/23/2017 13
Radial Dependence of Parameters Global versus Local Transition? Electron-direction quasilinear response is different at different radii. Turbulence Spreading may be responsible for excitation of marginally stable modes, leading to global transition rather than local transition Plays well with population collapse theory k y ρ s APS-DPP 10/23/2017 14
Nonlinear Heat Flux Spectra Possibly Consistent with mqlta Prediction Heat flux spectra at r/a=0.8 APS-DPP 10/23/2017 15
0.8 MA Reflectometer power spectra show differences APS-DPP 10/23/2017 16
Reflectometry Provides Local Fluctuation Measurements These data are collected from the 87.5 GHz and 88.5 GHz channels of the C- Mod O-Mode baseband reflectometer 2D scattering effects (e.g. scattering, diffraction, sidebands) complicate the analysis of the returned signal. Can be sensitive to k up to 10 cm -1 (see Lin PPCF 2001) Image from N.P. Basse APS-DPP 10/23/2017 17