Understanding and Controlling Turbulent Mixing in a Laboratory Magnetosphere Mike Mauel Department of Applied Physics and Applied Math, Columbia University, New York, NY USA (Acknowledging the work from many former students and collaborators including Darren Garnier,Jay Kesner, Max Roberts, Ben Levitt, Brian Grierson) 58th Annual Meeting of the APS Division of Plasma Physics San Jose, CA Poster Session TP1 (Session VII) November 3, 216 1
With Sincere Apologies Mike Mauel is chair of Invited Session TI3 (now): Non-neutral Plasmas, Fusion, and Beams: The Legacy of Ron Davidson MENT AN INTRODUCTION TO FUSION RESEARCH 29, 1981. AT THE PLASMA FUSION CENTER MASSACHUSETTS INSTITUTE OF TECHNOLOGY PROF. RONALD C. DAVIDSON, DIRECTOR OCTOBER 1981 PFC/RR-81-33 FOR INCLUSION AT THE FUSION ENERGY EDUCATIONAL DEVELOPMENT SEMINAR, Los ALAMOS SCIENTIFIC LABORATORY, OCTOBER 27-29, 1981. FUSION POWER AT MIT MAASSAC - VSETTS (NSTlTVTE OF TECH4NOLo O FUSION POWER AT MIT r Professor of Physics Director, PFC (1978-1991) Director, PPPL (1991-1996) 2 Editor-in-Chief (1991-215)
Abstract In a laboratory magnetosphere, plasma is confined by a strong dipole magnet, and complex nonlinear processes can be studied and controlled in near steadystate conditions. Because a dipole s magnetic field resemble the inner regions of planetary magnetospheres, these laboratory observations are linked to space plasma physics. Unlike many other other toroidal configurations, interchange and entropy modes dominate plasma dynamics, and turbulence causes selforganization and centrally-peaked profiles as the plasma approaches a state of minimum entropy production. We report progress in understanding and controlling turbulent mixing through a combination of laboratory investigation, modeling, and simulation. Topics discussed: (i) Extending the global extent of local regulation of the interchange and entropy mode turbulence through current injection, (ii) Measurement and interpretation of the statistical properties of stationary turbulence, and (iii) Advancements in the nonlinear simulation of turbulence control in a dipole plasma torus. 3
Two Laboratory Magnetospheres: Plasma Experiments without Field-Aligned Currents LDX: High Beta Levitation & Turbulent Pinch Ryan Bergmann Ryan 24 Probes 1 m Radius Max Max Roberts CTX: Polar Imaging, Current Injection. Rotation 4
Toroidal Confinement with Closed-Field Lines: Interchange and Entropy Modes Axisymmetric magnetically dipole guarantees omnigeneous particle drifts. The only high-β toroidal magnetic configuration that satisfies the Palumbo condition: the divergence of the perpendicular plasma current vanishes. Absence of parallel currents in a dipole-confined plasma is significant: many tokamak instabilities are not found in a dipole plasma torus, e.g. kink, tearing, ballooning, and drift modes. Instead, interchange and entropy modes dominate plasma dynamics, and particle and power source profiles determine the level of turbulence. Turbulent transport causes centrally-peaked profiles and self-organization, as the plasma approaches a state of minimum entropy production. Axisymmetric interchange/entropy mode turbulence exhibit 2D inverse cascade at long wavelengths. 5
Closed Field-Line Plasma Dynamics How do we know dynamics is interchange dominated? Direct laboratory measurement of δφ, in all cases, but when ωbe >> ωd What are the consequences of interchange dynamics? 2D inverse cascade couples fluctuations to largest scales Weak gradients with ω* ~ ωd Profile consistency, turbulent pinch, Self-organization toward state of minimum entropy production, η ~ 2/3 6
Turbulent Intensity is Observed to Peak at Long Wavelengths (Inverse Mode-Mode Cascade) Grierson, M. Worstell, and M. Mauel, Phys Plasmas 16, 5592 (29). Boxer, et al., Nature Phys 6, 27 (21). 7
Measured Interchange Modes in Dipole Torus 6 Measured m 1 Mode 5 5 5 2 5 2 m = 1 m = 2 m = 3 8 ms Convective Structures are Dynamic 4 2 2 4 6 6 4 2 2 4 6 (ɸ ~ Stream function) With Te >> Ti (CTX and LDX) modes (usually) propagate in electron drift direction 8
Induced Field-Aligned Currents in Magnetospheres Figure 3. Dynamo forces, auroral current system, and resulting convection under frictional control by the ionosphere, after Boström (1964). G. Haerendel, Outstanding issues in understanding the dynamics of the inner plasma sheet, Advances in Space Research, 25, 2379 (2). Green, et al., Comparison of large-scale Birkeland currents determined from Iridium and SuperDARN data, Annales Geophysicae 24, 941 (26). 9
Probe-Injected Currents in Laboratory Roberts, et al., Local regulation of interchange turbulence in a dipole-confined plasma torus using currentcollection, Physics of Plasmas, 22, 5572 (215). 1
Interchange Motion is Regulated by Ionosphere, or External Circuits, or Steady MHD Convection in Space Dynamic Drift-like Motion in Lab Ion Inertial Currents Ionospheric Conductivity Integrated Plasma Dielectric Vasyliunas, Mathematical Models of Magnetospheric Convection and Its Coupling to the Ionosphere, in Particles and Fields in the Magnetosphere, edited by B.M. McCormac (D. Reidel, Norwell, MA, 197), pp. 6 71. 11
Entropy & Drift-Interchange Modes (For CTX and LDX with Te >> Ti) ωde flow Collisionless heat flux due to Electron magnetic drift ion-neutral damping Linear Braginskii interchange motion 12
Gradient Drive for Turbulent Transport: Comparing to the Familiar Tokamak (a) Dipole Interchange-Entropy Modes (b) Tokamak ITG-TEM Modes 15 5 Minimum Entropy Production 15 ITG & TEM R d Log(T) 1 5 5 η > 2/3 MHD Interchange Unstable η < 2/3 R d Log(T) 1 5 ITG TEM stable ω < 2 4 6 R d Log(n) 2 4 6 8 Weak gradients: ωp* ~ ωd 8 stable 2 4 6 R d Log(n) Steep gradients: ωp* >> ωd 8 Stable by compressibility and field line tension Stable by average curvature and magnetic shear X. Garbet, Comptes Rendus Physique 7, 573 (26) 13
Quasilinear Flux using 2D Bounce-Averaged Fluid Equations with Drift-Kinetic Closure (a) Particle Flux (b) Temperature Flux (c) Entropy (PδV γ ) Flux Inward Outward Outward.2.6 1. 1.4.2.6 1. 1.4.2.6 1. 1.4 η η η Density 1.2 1..8.6.4.2 1.68 η = {.67.22.. Peaked T Stationary Peaked n Temperature ωd / ρ* 2 ωci. 1.2 1..8.6.4.2. 5 4 3 2 1 1. 1.5 2. 2.5 1. 1.5 2. 2.5 1. 1.5 2. 2.5 Normalized Radius (L/L) Strong or Weak Radial variation of Drift Resonance Kobayashi, Rogers, and Dorland, Phys Rev Lett 15, 2354 (21) 14
Interchange-Entropy Mode Dispersion Agrees with Observations (a) Entropy Mode Dispersion: Wp ~ (PV 5/3 ) ~ Mode Frequency ( /m d) Growth ( /m d) @ p e @t + < 2/3 Outward Particle Flux 2. 1.5 1..5 1.5 1..5. -.5 < 2/3 > 2/3 Electron Drift > 2/3 Inward Particle Flux Reversed Drift -1...5 1. 1.5 1 @ V @ {z } Compressibility (p V )@ @' (b) Warm Core with Electron Drift e - drift apple 2 happle i(t e /e) 2 @ p e @ñ T e @' @' {z } Curvature Heat Flux > 2/3 e - drift e - drift e - drift < 2/3 e - drift e - drift Drift-Kinetic Heat moves toroidally from Warm to Cool Flux-Tubes Entropy Mode Rotation,! 1 ( sm? ) 2/3 (c) Cool Core Reversed Rotation Entropy Mode Rotation 8 < exp(i2 /3) ( 2/3 ) 1/3 if < 2/3 : exp(i /3) ( 2/3) 1/3 if > 2/3 15
Entropy Modes Reverse with η (Pellet Injection) (a) (a) Line Density and Photodiode Array t1 t2 t3 t4 Profile Times Pellet Trajectory (b) Probe Array 3.6 m µwave Interferometer Interferometer (Radian) 6 4 2 S1452916 Probe Array Pellet Trajectory R 2.5 m Photodiode Array (A.U.) 1 8 6 4 2 6.15 6.2 6.25 6.3 6.35 6.4 6.45 time (s) η > 2/3 η < 2/3 η > 2/3 16
Entropy Modes Reverse with Pellet Injection (a) Cross Phase Before Pellet 1 (b) Cross Phase and Cross Coherence During Pellet 1 Increasing Coherence 8 8 Frequency (Hz) 6 4 ω/2π ~ m 7 Hz δi(sat) Cross-Phase 6 4 ω/2π ~ - m 55 Hz δi(sat) Cross-Coherence δφ Cross-Coherence 2 δφ Cross-Phase 2 5 1 15 2 25 Cross Phase <α> (Degree) -25-2 -15-1 -5 Cross Phase <α> (Degree).2.4.6.8 1. Cross Coherence <κ 2 > η > 2/3 η < 2/3 17
Global Entropy Eigenmodes Temperature Density ωd / ρ* 2 ωci 1.2 1..8.6.4.2. 1.2 1..8.6.4.2. 5 4 3 2 1 1.68 η = {.67.22 1. 1.5 2. 2.5 1. 1.5 2. 2.5 1. 1.5 2. 2.5 Normalized Radius (L/L).. Mode Growth Rate (γ/mωd) Growth (γ/mω d ) 2. 1.5 1..5. Global Eigenvalues for m = 1, 2, 8 η ~.22 η ~.67 m = 1 m = 2 m = 8 η ~ 1.7-1.5-1. -.5..5 1. 1.5 Rotation (ω/mω d ) Mode Toroidal Rotation (ω/mωd) 18
Global Entropy Eigenmodes (a) η = 1.68.2.15.1.5. -.5 ω/mωd ~ 1.8 + i 1.4 Inward Outward 1. 1.5 2. 2.5 Normalized Radius (L/L) (b) η =.67.1. ω/mωd ~.51 + i 1.9 Mode Growth Rate (γ/mωd) (c) η =.22. Growth (γ/mω d ) 2. 1.5 1..5. ω/mωd ~ -1.9 + i 3.2 Global Eigenvalues for m = 1, 2, 8 η ~.22 m = 1 m = 2 m = 8 η ~ 1.7 η ~.67-1.5-1. -.5..5 1. 1.5 Rotation (ω/mω d ) Mode Toroidal Rotation (ω/mωd) Inward -.1 -.2 Outward -.2 -.4 -.3 -.4 -.6 -.5 1. 1.5 2. 2.5 Normalized Radius (L/L) -.8 1. 1.5 2. 2.5 Normalized Radius (L/L) 19
Summary and Applications Global flux-tube averaged gryo-fluid description of flute-type instabilities describes driftinterchange and entropy modes Long wavelength eigenmodes and real frequencies like observations in CTX and LDX Quasilinear theory describes up-gradient turbulent pinches Linear theory can model local current-injection feedback (Roberts, PoP 215) Li pellet injection reduces η and reverses toroidal propagation of fluctuations Need to include bounce-averaged drift-resonances, like Maslovsky, Levitt, and Mauel, Phys Rev Lett 9, 1851 (23) Beer and Hammett, Phys Plasmas 3, 418 (1996) Mode-mode and 2D interchange cascade may explain the discrepancy between observations dominated with low-m eigenmodes and linear high-m eigenmodes with large growth rates. Flux-tube averaging makes possible whole-plasma nonlinear turbulence simulations. 2
Single-Point Regulation of Interchange Turbulence with Current-Collection Feedback Roberts, et al., Local regulation of interchange turbulence in a dipole-confined plasma torus using currentcollection, Physics of Plasmas, 22, 5572 (215). 21
Local Regulation of Interchange Turbulence with Current-Collection Feedback (Roberts, Phys. Plasmas, 215) Measurement Linear Theory 22
Application: Toroidal Confinement without Bt may Speed Fusion Development using much smaller Superconducting Coils (QDT ~ 1 Magnet Systems Compared at Same Scale) Toroidal and Poloidal Magnets Kesner, et al., Nuclear Fusion 44, 193 (24) Small Levitated Magnet Plasma Volume = 837 m 3 Plasma Volume = 42, m 3 Pfus = 41 MW Wp = 1.1 GJ Wb = 51 GJ It = 164 MA Pfus = 39 MW Wp =.6 GJ Wb = 1.6 GJ Id = 25 MA (a) Conventional Fusion Experiment (Gain = 1) (b) Dipole Fusion Experiment (Gain = 1) 3-fold size/energy reduction (!) 23