Nonlinear Evolution and Radial Propagation of the Energetic Particle Driven GAM

Transcription

1 Nonlinear Evolution and Radial Propagation of the Energetic Particle Driven GAM by R. Nazikian In collaboration with G.Y. Fu, R.V. Budny, G.J. Kramer, PPPL G.R. McKee, U. Wisconsin T. Rhodes, L. Schmidt, UCLA W.W. Heidbrink, D.C. Pace, UC Irvine M. Austin, H.L. Berk, UT Austin R. Fischer, M.A. Van Zeeland, GA Presented at the IAEA Technical Meeting on Energetic Particles Austin, TX Sept. 7, 2011

2 Geodesic Acoustic Modes in Turbulence and Energetic Particle Physics Geodesic Acoustic Modes are Zonal Flows n=0 finite frequency zonal flows, scaling with the sound speed: ω GAM C s /R In the last decade the importance of localized zonal flows (including GAMs) in the self regulation of turbulence has taken center stage in transport theory More recently there has been the discovery of macroscopic zonal flows in energetic particle driven instabilities (a) Linear nonperturbative instability, the E-GAM (b) Nonlinear coupling of Alfven eigenmodes to n=0 zonal component and self regulation (Todo, ) Measurement of intense macroscopic GAMs driven by energetic particles provides a validation platform for advanced nonlinear simulation

3 What is the E-GAM? The E-GAM is a super sized Geodesic Acoustic Mode - dominant m=0, n=0 Er oscillation, couples to m=+/- 1, n=0 sidebands - mode radial scale determined by poloidal orbit width of energetic (not thermal) particles ~ B Interferometer - mode frequency determined by poloidal bounce frequency, must be close to GAM frequency for resonance ~ n n Hybrid sim. G. Fu

4 Outline Mode excitation condition Nonlinear E-GAM structure ~ n n Hybrid sim. G. Fu Zonal Flow Measurements Interferometer ~ B

5 Recipe for E-GAM Excitation in DIII-D: Counter Tangential Beam Injection into High q min Plasma EAE 80 kev q min > 3 T i, T e < 2 kev, typically. Why? 80 kev bounce frequency GAM frequency at high q in DIII-D Ion Landau damping minimized at high-q through sideband resonance Note: co beams can drive modes, but typically much weaker, shorter

6 Example of Intense E-GAM Excitation in DIII-D with Counter Beam Injection Interferometer Interferometer Strong RSAE/TAE Weak E-GAMs can be observed in co beam injection plasmas Intense E-GAM: 2-5 % density fluctuation near midplane Why should direction matter so much?

7 Mode Particle Resonance is Well Aligned with Counter Beam Injected Ions Resonance condition for E- GAM is given by ω E-GAM =pω pol r/a 0.5 Most energetic co injected particles miss the resonance p=1,2 co-injection Counter injected particles are well aligned with the resonance at all energies; p=-1, -2 Note: Proximity of counter going resonances to loss boundary suggests that large enhanced losses should occur due to E-GAM

8 Fast Ion Distribution With Slowing Down and Scattering Shows Good Alignment With Counter Resonances 50 ms simulation using actual beam injection geometry in SPIRAL (Kramer) Shadow of loss boundary and low intensity of counter injected ions due to enhanced first orbit loss Note: Resonant interaction with the E-GAM should push particles over the edge for counter injection over a broad energy range.

9 SPIRAL Code Simulations Are in Good Agreement with of Fast Ion Loss Detector For Pitch and Energy of Loss FILD1: Pace, Fisher Note: No E-GAM losses observed for co-injected particles SPIRAL: Kramer

10 Outline Mode excitation condition Nonlinear E-GAM structure ~ n n Hybrid sim. G. Fu Zonal Flow Measurements Interferometer ~ B

11 Up/Down Standing Wave Prediction Confirmed Using Vertical BES : Validation of Linear theory ~ n n Hybrid sim. G. Fu BES _ +

12 Strong Outward Radial Propagation of E-GAM Observed in Simulation and BES Measurement Fu, Hybrid simulation Er Time (ms) 0.4 BES, DIII-D qmin 0 0 Normalized Minor Radius 1 q Major Radius (cm)

13 However, Experimental Observations Indicate Very Large Second Harmonic Component Interferometer Interferometer Strong RSAE/TAE E-GAM - second harmonic E-GAM - Fundamental

14 Nonlinear Analytic Theory of the Second Harmonic Density Fluctuation G. Fu, J. Plasma Phys δρ ρ = r R [2 ˆ E r sin(θ)sin(ωt) Where E r is the normalized radial electric field. ˆ E r 2 cos(θ)(1 cos(2ωt))]] - Note that the second term is always nega9ve and the first term can have either sign. ~ B Interferometer sin(θ)>0; above midplane sin(θ)<0; below midplane

15 Hybrid Simulation of E-GAM Burst Consistent Analytic Theory and Observations on DIII-D G. Fu, J. Plasma Phys Experiment BES Density Fluctuation above on Ch 34, +2.3 cm Ch 09, 0.0 cm below Ch 22, -4.4 cm Time (msec) DC density component is negative on midplane Second harmonic peaks on midplane, while fundamental goes through zero

16 DC and Second Harmonic Stay in Phase, Fundamental Flips Phase, Across Midplane BES Density Fluctuation No fundamental Above Midplane, ch. 34 On Midplane, ch. 09 Below Midplane, ch. 22 Time (msec) Some third harmonic is also contributing

17 Analytic Theory Predicts Amplitude of Electric Field From Second Harmonic Midplane Density Fluctuation δρ ρ = r R [2 ˆ E r sin(θ)sin(ωt) ˆ E r 2 cos(θ)(1 cos(2ωt))] δρ 2ω ρ θ =0 = r 2R ˆ E r 2 ˆ E r : normalized radial electric field NOTE: Direct Measurement of E r Would Be A Major Breakthrough in model validation

18 Outline Mode excitation condition Nonlinear E-GAM structure ~ n n Hybrid sim. G. Fu Zonal Flow Measurements Interferometer ~ B

19 Doppler Back Scatter can infer the ExB velocity from the Doppler shift of high-k turbulence V=ExB

20 Spectrum of ExV Velocity Fluctuation Induced by E- GAM Is Resolved using DBS on DIII-D

21 NOTE: Zonal Component of RSAE/TAE may also be resolved, can tie into nonlinear theory of saturation RSAE/TAE

22 Summary E-GAM is a remarkable instability for detailed understanding of nonlinear dynamics of wave-particle interactions - large scale, large amplitude, low frequency, large losses Directional sensitivity of mode excitation confirmed from Hybrid simulation, orbit analysis and resonance condition - prediction of large losses over a broad energy range observed Theoretical prediction of nonlinear structure of second harmonic validated using BES, can be used to infer E r Detection of zonal flow oscillations from ExB Doppler shift of high-k turbulence will allow for detailed validation of theory of E-GAM and RSAE/TAE saturation mechanism