EFFECT OF PLASMA FLOWS ON TURBULENT TRANSPORT AND MHD STABILITY* by K.H. BURRELL Presented at the Transport Task Force Meeting Annapolis, Maryland April 3 6, 22 *Work supported by U.S. Department of Energy under Contract DE-AC3-99ER54463 94-2/KHB/ci
INTRODUCTION: IMPORTANCE OF PLASMA FLOWS Plasma flows have important effects on tokamak stability and transport on spatial scales ranging from the gyro-orbit scale to the machine size In many interesting cases, these flows are self-generated by the plasma For example, a key topic of present-day research is the effect of gyro-radius-scale zonal flows on micro-turbulence-driven transport Somewhat larger scale flows include the changes in sheared E B flows observed at the L to H transition, the ERS transition and during the spin-up associated with VH mode Sheared toroidal flows have been predicted to affect MHD ballooning mode stability [R.L. Miller, et al., Phys. Plasmas 2, 3676 (1995)] Toroidal flows with scales of the system size have been shown experimentally to stabilize the resistive wall mode 94-2/KHB/ci
GOALS OF PRESENTATION Briefly cover some of the previous results on plasma flows and their effects Pose a series of questions to motivate later discussion 94-2/KHB/ci
STABLE OPERATION WELL ABOVE THE NO-WALL β LIMIT HAS BEEN DEMONSTRATED IN 4 Resistive wall mode stabilized by plasma rotation Theoretically predicted (Bondeson and Ward, 1994) 16521 1763 Ideal wall limit (approx) β N 3 2 1 No-Wall Limit (2.4l i ) 1 15 2 25 3 Time (ms) A.M. Garofalo et al., APS, 21 94-2/rs
PLASMA ROTATION DECREASES MORE SLOWLY WITH DECREASING ERROR FIELD AMPLITUDE 6 4 2 12 11877 13154 13156 13158 Error Field Component at 2/1 Surface (Gauss) Toroidal Rotation (khz) at q = 2 Below a critical rotation value, RWM becomes unstable β N 6 3 2 1 Critical Rotation for Onset of RWM β N no wall (2.4 li ) 12 13 14 15 16 17 Time (ms) A.M. Garofalo et al., APS, 21 94-2/rs
φ
CARBON POLOIDAL ROTATION CHANGE SHOWS CHANGE IN E B FLOW PRIOR TO ERS TRANSITION IN TFTR This precursor occurs at a time before there are changes in pressure and temperature associated with enhanced confinement R.E. Bell P NB (MW) v θ (km/s) 3 2 1 2 2 Li pellet 1.4 P NB #13793, #13794 R = 32 cm 1 RS ERS R = 32 cm RS ERS 1.6 1.8 2. 2.2 2.4 Time (s) Carbon Pressure (a.u.) km/s km/s P Carbon (a.u.) 2 2 4 4 2 2 4 6 8 6 4 2 28 1.77 s 1.81 s Artifact Chordal v θ Location of Shear Layer Inverted v θ Carbon Pressure 6 4 q Safety Factor 2 3 32 34 36 Radius (cm) R.E. Bell et al, Phys. Rev. Lett. 81, 1429 (1998) 94-2/rs
MSE AND SPECTROSCOPY DETERMINE SAME E r CHANGE AT ERS TRANSITION IN TFTR Zero of MSE-determined E r chosen to match spectroscopic value well after ERS transition E r (kv/m) 1 2 E r total p/(ezn) v φ B θ v B φ θ Rapid change in v θ relative to p shows neoclassical v θ is not the whole story E r (kv/m) 1 2 E r (MSE) E r total 1.6 1.8 2. Time (s) 2.2 2.4 R.E. Bell et al, Phys. Rev. Lett. 81, 1429 (1998) 94-2/rs
DENSITY FLUCTUATIONS DECREASE AS CONFINMENT AND Er SHEAR INCREASE AS H MODE GOES TO VH MODE IN.4.3 τ E (s).2.1. ñ/<n> (a.u.) Vϕ (km/s) 1.5 1..5. 2 15 1 5 21 22 23 Time (ms) 24 25 94-2/rs
..5 1. 1.5..5 1. 1.5..5 1. 1.5 ROTATION REVERSES DIRECTION WITH PLASMA CURRENT IN ALCATOR C MOD H MODE PLASMA Core E r > in H mode (MA) (kj) (MW) (km/s) 1..5..5 1. 1 8 6 4 2 1.5 1..5. 2 2 V Tor ICRF Power Plasma Current Plasma Stored Energy..5 1. Time (ms) 1.5 J.E. Rice et al., Nucl. Fusion 41, 277 (21) 94-2/rs
ROTATION AND STORED ENERGY CHANGE TOGETHER IN ICRF AND OHMIC H MODES IN ALCATOR C MOD 14 12 1 1.2 MA 1. MA.8 MA ICRF and Ohmic H modes V (km/s) Tor 8 6.6 MA Ohmic 4 2 2 4 6 8 1 12 14 W/I P (kj/ma) J.E. Rice et al, Nucl. Fusion 41, 277 (21) 94-2/rs
.6.8 1. 1.2 1.4.6.8 1. 1.2 1.4.6.8 1. 1.2 1.4 CORE E r > IN H MODE AND E r < IN H MODE + ITB IN ALCATOR C-MOD (kev) (1 2 m 3 ) (km/s) 12 8 4 (kj) WPICRF 1.5 1..5. 6 4 2 2 2 V Tor Ion Temperature Central Electron Density 4.5 T 4.7 T.6.8 1. 1.2 1.4 Time (s) 4 2 (MW) J.E. Rice et al., Nucl. Fusion 41, 277 (21) 94-2/rs
3.5 4. 4.5 5. 5.5 CORE BARRIER FORMS IN ALCATOR C MOD WITH OFF-AXIS ICRF BOTH INSIDE AND OUTSIDE MAGNETIC AXIS 7 MHz P ICRF = 1.5 MW, I P =.8 MA 4 Resonance Location (r/a).6.4.2..2.4.6 3 V Tor (km/s) 2 1 1 2.2 n e ()/n e (.7) 2. 1.8 1.6 1.4 1.2 1. 3.5 4. 4.5 5. 5.5 B T (T) J.E. Rice et al, Nucl. Fusion 42 (22) (to be published) 94-2/rs
ZONAL FLOWS SHEAR APART RADIAL TURBULENCE STRUCTURES Gyro kinetic code (Gyro), toroidal geometry, shaped plasma J. Candy, R.E. Waltz, J. Comp. Phys. (submitted) 13-2/rs
ENERGETICS OF TURBULENCE/ZONAL FLOW INTERACTION Free Energy Turbulence Reynolds Stress Drive Zonal Flow n T e Drift Waves d dr v r ṽ θ v θ (r) t Flow shear decorrelation P. Diamond et al., Phys. Fluids B 3, 1626 (1991) UNIVERSITY OF WISCONSIN M A DIS O N Department of Engineering Physics 13-2/rs
ADDITIONAL ZONAL FLOW DRIVE IN EDGE-CORE TRANSITION REGION Stringer-Windsor drive owing to magnetic field curvature plus poloidal asymmetry P Poloidal Variation t Psin θ n T Drift Waves B Field Curvature d dr v r ṽ θ t v θ Flow shear decorrelation Hallatschek and Biskamp, PRL 86, 1223 (21) 13-2/rs
PHYSICAL CHARACTERISTICS OF ZONAL FLOWS: TESTABLE PREDICTIONS Fluctuating poloidal Er BT flows, vθ(t) Toroidally and poloidally symmetric: n=, m= Low frequency (<< ambient ~ n, 1 khz) Radially localized (k ρ i ~.1) RMS amplitude predicted to be small, v ZF /v th,i 1% [T.S. Hahm, et al., PPCF 42, A25 (22)] Geodesic acoustic mode (GAM) frequency f c s /2πR [Hallatschek and Biskamp, Phys. Rev. Lett. 86, 1223 (21)] 94-2/KHB/ci
2D TURBULENCE FLOW-FIELD CONSTRUCTED FROM 2D ñ MEASUREMENTS Poloidal Cross Section of Tokamak.2 Two radial ñ(t) channels v r.2.6.1 2. 2.1 2.2 2.3 Two poloidal ñ(t) channels v θ Correlation Coefficient (ρ(t)) 1..5..5 1. 6 time delay τ Z=1.1 cm 4 2 2 4 6 Time (µs) Eddies convect past spatial channels: z v z (t) = τ(t) delay between two observation points Jakubowski, McKee, Fonck APS, 21 SAN DIEG O UNIVERSITY OF WISCONSIN M A DIS O N Department of Engineering Physics 13-2/rs
ñ, AND v θ COHERENCY SPECTRA ARE DISTINCTLY DIFFERENT Frequency distributions distinct; frequency range similar 1..5. r/a=.91 <ñ 1 ñ 2 > θ z=1.1 cm Density Coherency.3.2.1 <v θ,1 v θ,2 > θ z=1.1 cm Strong zonal flow Poloidal velocity ~ feature in v θ (f). 1 2 Frequency (khz) 3 Jakubowski, McKee, Fonck APS, 21 UNIVERSITY OF WISCONSIN M A DIS O N Department of Engineering Physics 13-2/rs
ZONAL FLOW FEATURE EXHIBITS EXPECTED SPATIAL STRUCTURE ~ v θ,zf correlations have long poloidal, short radial length Poloidal Radial 1. ṽ θ.8 Correlation for ñ and v θ in zonal flow frequency range (1-2 khz) ρ ().5.4 n ñ.. r/a=.91 -.4 ṽ θ 2 4 6 1 2 3 4 z (cm) z (cm) ~ v θ, pol very long wavelength in the poloidal direction Contrasts with L c,ñ ~3 cm (poloidal) ~ In contrast, v θ, rad L c,v 3.3 cm in the radial direction Comparable to the L c,ñ 2.3 cm (radial) Jakubowski, McKee, Fonck APS, 21 UNIVERSITY OF WISCONSIN M A DIS O N Department of Engineering Physics 13-2/rs
ZONAL FLOW MAGNITUDE CONSISTENT WITH PREDICTIONS v θ, ZF /v th,i ~ 1% 5x1 2 4 v θ,zf ~.8 km/s <v 1 v 2 > θ z=1.1 cm Cross Phase (p) Cross Power 3 2 1 1 v turb ~ v th,i = 15 km/s ~ v θ, ZF /v th,i ~.5 Consistent with Hahm ~ v/v th,i ~.1 Broadband v turb exists in addition to ~15 khz peak ~ ~ ~ L c,v turb 2 cm 1 5 1 15 f (khz) 2 25 ρ=.91 3 Jakubowski, McKee, Fonck APS, 21 UNIVERSITY OF WISCONSIN M A DIS O N Department of Engineering Physics 13-2/rs
BICOHERENCE SHOWS ñ AND v θ PHASE COUPLING Three-wave interactions with drift waves zonal flows (Diamond 91) max =.3 Zonal flow generation mechanism should be evident in the cross-bispectrum < * (k z ) v r (k 1 ) (k 2 ) > v θ v θ zonal flow scale turbulent scales f 1 (khz) 25 We observe a nonzero bicoherency at low frequency < v θ * (f 1 f 2 ) ñ (f 1 ) ñ (f 2 ) > 5 25 f 2 (khz) 5 Peak ~.3 at f 2 f 1 15 khz = f ZF Coupling of ñ to the zonal flow feature Jakubowski, McKee, Fonck APS, 21 UNIVERSITY OF WISCONSIN M A DIS O N Department of Engineering Physics 13-2/rs
SIMILARITY WITH 3D BRAGINSKII SIMULATION OF EDGE TURBULENCE Recent work by Klaus Hallatschek (PRL 86, 1223 (21)) simulating turbulence in the edge/core transition region: Zonal flows here are Geodesic Acoustic Modes (GAMs) Driven by pressure asymmetry on flux surface, rather than by Reynold s Stress couple to pressure perturbations (m/n=1/) by magnetic field inhomogeneity Experimental indications Nearly coherent zonal flows (radially and temporally) f ~ 1 khz for DIII-D edge parameters Suggests experimental tests: Dependence on ion temperature Dependence on plasma shaping/curvature Jakubowski, McKee, Fonck APS, 21 UNIVERSITY OF WISCONSIN M A DIS O N Department of Engineering Physics 13-2/rs
HEAVY ION BEAM PROBE MEASUREMENTS OF POSSIBLE ZONAL FLOWS As was pointed out by P. Schoch (APS, 21), HIBP systems on many devices (TEXT, JIPP TII-U, ISX-B) have long seen fluctuations in the 2 to 5 khz range which were not understood TEXT data indicate these may be geodesic acoustic modes Retrospective analysis of TEXT results from 199 show E r fluctuations are consistent with m= poloidal structure Correlation of these E r fluctuations with density fluctuations is weak Frequency is consistent with GAM frequency over a range of radii E r fluctuations seen only for.6 r/a =.95 in discharges studied No E r significant fluctuations at smaller or larger radii Correlation length is short, about the sample volume size 94-2/KHB/ci
~ FREQUENCY OF E r FLUCTUATIONS IN TEXT AGREES WITH GAM FREQUENCY 6 5 Frequency (khz) 4 3 2 1 Curve is estimate of GAM frequency ~ Vertical bars show range of measured E r frequency Horizontal bars show radial spacing of sample locations.6.65.7.75.8 r/a.85.9.95 1. P. Schoch, APS 21 13-2/rs
ZONAL FLOW QUESTIONS Do the theoretically predicted zonal flows really exist? What criteria do we use to decide that zonal flows have been observed? Do detailed zonal flow properties really agree with theory? Why is the geodesic acoustic mode experimentally so obvious compared to the f zonal flow? How do we best measure the zonal flow s properties experimentally? Can we distinguish f zonal flows from mean flows? What are the relative roles of Reynold s stress and Stringer-Windsor drive in various plasma regions? 94-2/KHB/ci
POLOIDAL FLOW QUESTIONS What physics governs the mean poloidal flows in the plasma? What is the role of the physics described by neoclassical theory? May need to include collisions with fast ions (W. Houlberg, 22) What additional physics, if any, is needed to understand how the spontaneously generated poloidal rotation arises, for example, at the ERS transition? G.M. Staebler, Phys. Rev. Lett. 84, 361 (2) How can we best test the neoclassical theory? 94-2/KHB/ci
IN H MODE EDGE IN, MAIN ION AND CARBON POLOIDAL ROTATION DISAGREE WITH NEOCLASSICAL PREDICTION Helium plasma [I p = 1 MA, B T = 2T, n e = (1 4) 1 19 m 3 ] Poloidal Rotation (km/s) 5 4 3 2 1 1 2 Theory for He 2+ He 2+ (75594) He 2+ (75595) Theory for C 6+ C 6+ (75592) C 6+ (75593) ω *i ω *e 3 2.25 2.26 2.27 Major Radius (m) LCFS 2.28 2.29 2.3 J. Kim et al, Phys. Rev. Lett. 72, 2199 (1994) 94-2/rs
TOROIDAL ROTATION QUESTIONS What physics governs the mean toroidal flow in the plasma? Does neoclassical theory play any role here? Even in ITB cases where the ion thermal diffusivity is neoclassical, the toroidal angular momentum diffusivity exceeds neoclassical by about a factor of 5 What physics must be added to that in neoclassical theory to understand this? How do we understand toroidal flow generation in the core of C-Mod plasmas in the apparent absence of toroidal torque? What role do MHD modes play in governing the toroidal plasma rotation? Are MHD modes only important near beta limits? How do we isolate the effects of MHD modes experimentally? 94-2/KHB/ci
TURBULENCE AND TRANSPORT CONTROL TECHNIQUES What new tools can we develop to locally reduce turbulence-driven transport by altering plasma flows? Present control tools (e.g. NBI) are crude and act over broad regions Control is the ultimate demonstration of understanding 94-2/KHB/ci
DIAGNOSTIC DEVELOPMENT ISSUES AND QUESTIONS How can we best use synthetic diagnostics from modeling codes? Need to develop improved experimental techniques to measure the zonal flow over wider regions of the plasma Need larger poloidal and radial range Improved signal-to-noise Must refine the analysis techniques needed to compute the gyro-orbit cross section effect on poloidal rotation measurements and then verify the calculations experimentally in order to test neoclassical poloidal rotation theory properly Improve techniques to measure MHD modes (e.g., resistive wall modes and Alfvén modes) which can affect rotation 94-2/KHB/ci
FREQUENCY SPECTRUM IN ALFVEN FREQUENCY RANGE IS EXTREMELY RICH ` 15 QDB phase FIR Scattering Data 171 k = 1 cm -1 Frequency (khz) 1 5-5 Core localized quasi-coherent modes } Edge modes (EHO) 4. -1 1. 2. 3. 4. NBI initiation Time (s). UCLAUCLA UCLA 13-2/rs
REFLECTOMETER DATA INDICATE THE CORE QUASI-COHERENT MODES ARE LOCALIZED TO ρ..4 Frequency (khz) 2 15 1 5 2 15 1 5 6 4 2 Frequency spectrum evolution of fixed frequency reflectrometer data 32 GHz, refelected at ρ =.85 4 GHz, refelected at ρ =.55 5 GHz, refelected at ρ =.3 26 27 28 29 3 31 Time (ms) 171 Core quasi-coherent modes UCLAUCLA UCLA 13-2/rs
CONCLUSION Plasma flows have important effects on tokamak stability and transport on spatial scales ranging from the gyro-orbit scale to the machine size In many interesting cases, these flows are self-generated by the plasma Key open questions include theory and experimental measurements in the areas of Zonal flows Poloidal and toroidal rotation Coupling of rotation and MHD modes 94-2/KHB/ci