What we ve learned so far about the Stability of Plasma Confined by a Laboratory Dipole Magnet M. E. Mauel and the CTX and LDX Experimental Teams Annual Meeting of the Division of Plasma Physics Philadelphia, PA October 30 through November 3, 2006
Abstract During the past decade, new experiments with collisionless plasma confined by magnetic dipoles have been built at Columbia University, MIT, and the University of Tokyo. These have resulted in detailed observations of interchange instability, convective mixing, and high-beta toroidal confinement without magnetic shear. This poster discusses these new results with the aim of understanding linear, nonlinear, and turbulent plasma physics due to interchange dynamics. To date, observations show interchange modes to be fixed-boundary modes with broad structures that are easily measured and understood theoretically. Additionally, for a strong dipole magnet, interchange modes create wave-particle kinetics that are essentially one-dimensional. Hence, observations of linear and nonlinear MHD, fast-particle drift-resonances, transport in magnetospheric and fusion systems, and the effects of strong plasma flows are dominated by lowdimensional dynamics and show good agreement between observation, theory, and numerical simulation.
What We ve Learned 1. Robust ECRH start-up 2. Profile control with multiple-frequency ECRH 3. Gas programming yields high beta 4. Fluctuations have Fixed-Boundary MHD structures 5. Wave-particle dynamics are One-Dimensional 6. Turbulence spectrum dominated by machine size 7. Levitation causes dramatic confinement improvement
Acknowledgments Austin Eugenio Ishtak Alex Jen Scott Jeff Dmitry Ben Harry Brian Matt
Acknowledgments Austin Eugenio Ishtak Alex Jen Alex Jeff Dmitry Rick Alex Darren Ben Scott Harry Brian Matt Phil Joe
Dipole Fusion Concept ITER Levitated Dipole Reactor 30 m 60 m 400-600 MW DT Fusion 500 MW DD(He3) Fusion Kesner, et. al. Nucl. Fus. 2002
Dipole Fusion Concept Advanced fusion fuel D-D ( 3 He) with active triton removal No tritium breeding; simplified fusion technology Requires High plasma beta Good plasma energy confinement Poor particle (i.e. triton) confinement High-field, high-temperature superconductors
What We ve Learned #1 to #3: Dipole Plasmas Are Easy to Make and to Control 1. Robust microwave/ecrh plasma start-up 2. Pressure and density profile control is readily obtained using multi-frequency ECRH 3. Controlling the neutral fueling rate stabilizes hot electron interchange mode and produces high beta quasi-steady anisotropic plasma
World-Wide Levitated Dipole Experiments Today s Dipole Experiments CTX (Columbia) 150 ka turns (Not Levitated) 0.15 m Investigate Instability- or Electrostatically-Driven Interchange Mixing Mini-RT (Univ. Tokyo) RT-1 (Univ. Tokyo) LDX (Columbia-MIT) 50 ka turns 17 kg 0.15 m Test Beltrami Physics 250 ka turns 110 kg 0.25 m 1200 ka turns 565 kg 0.34 m Test Fusion-Dipole Physics
ECRH Sustained Dipole Plasmas Artificial Radiation Belt with ECRH Artificial Gravity with Radial Current LDX X-Ray (J. Ellsworth) CTX Mini-RT High-Beta Trapped Electrons RT-1
LDX: High Beta on First Shot! Austin Eugenio Ishtak Alex Jen Scott 1.0 0.6 0.2 Peak pressure in-between 2.45 and 6.4 resonance. 2.45 GHz 50513029 Ishtak Karim, PhD 2006 Pressure Contours 0.2 Anisotropic Pressure p 2-0.2 0.1 0-0.1-0.2 0.6 0.7 0.8 0.9 1 1.1-0.6-1.0 6.4 GHz 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Radius (m) Current Contours
Multi-Frequency ECRH Profile Control Plasma Photos Only 6.4 Ghz, 3.5 s Top View Only 2.45 Ghz, 3.5 s Top View Both Sources, 5.5 s Top View Alex Hansen Side View Side View Side View
DENSITY PROFILE CONTROLLED BY ECRH 6.4GHz only: 2.45GHz & 6.4GHz: 2.45GHz only: 2.45GHz & 6.4GHz: time=[0-2s] and [4-6s] time=[2-4s] and [6-8s] time=[0-2s] and [4-6s] time=[2-4s] and [6-8s] Peaked Shot: 60714033 Shot: 60714034 Steepness Exponent Broad Time(s) Alex Boxer
What We ve Learned #4: Dipole Plasma Dynamics Dominated by MHD-Like Interchange Modes Kinetic and centrifugal/gravity modes have broad radial structures just like fixed-boundary ideal MHD modes. Potential fluctuations constant along B Kinetic effects stabilize higher m modes near marginal stability. m = 1 usually dominates.
Dipole Interchange Modes have Broad Radial Structures Centrifugal Interchange Hot Electron Interchange 1.2 0.8 m=1 0.4 Normmalized Correlation Amplitude 0.0 1.6 1.2 0.8 0.4 0.0 1.2 m=2 0.8 m=3 0.4 Ben Levitt, PhD 04 0.0 10 20 30 40 50 60 70 r (cm) (Computed, self-consistent, mode structures shown with solid lines.)
Measured Centrifugal Mode Structure (A Fixed Boundary MHD Mode) 60 Measured m 1 Mode 40 20 0 20 40 Ben Levitt, PhD 04 60 60 40 20 0 20 40 60 (ɸ ~ Stream function)
Measured Kinetic Interchange Mode: Structure of Driven Polar Losses (A Kinetic MHD Mode) Brian Grierson
Relative Strength of Centrifugal and Curvature Drives Determine Nonlinear Mode Structure
Ideal MHD The ideal MHD equations are P t where γ = 5/3. dv nm i = P + J B dt n t + nv = 0 E + V B = 0 J = 0 + (P V) = (γ 1)P V Rosenbluth and Langmuir, 1957
E B = 0, E = Φ, axial symmetry, B = ϕ ψ, and the electric potential, Φ(ψ, ϕ), is constant along a field line. The plasma flow is two-dimensional, V = E B B 2 = ˆϕR Φ ψ + ˆψ Φ RB ϕ Low-frequency (ω < ω B ) plasma dynamics is well described by flux-tube averaged motion!! Interchange '' motion ( ballooning more stable than interchange.)
Typical Ideal Interchange Eigenmodes 2 1 Unstable LDX 0-1 -2 2 1 0-1 -2-2 -1 0 1 2-2 -1 0 1 2 UnStable m 1: Γ 0.31, 0.14, 0.093 0.15 0.1 0.05 0.75 1.25 1.5 1.75 2 2.25-0.05-0.1-0.15-0.2 Pressure Peak (Radial structure variation always slows mode.)
What We ve Learned #5: Wave-Particle Dynamics in a Laboratory Dipole is One-Dimensional (at least for kinetic-interchange modes) (µ, J) remains invariant even during chaotic radial transport. Phase-space holes have long lifetimes during frequency sweeping. Holes can be destroyed with low-power RF scattering. High beta electron transport can be very small or rapid and disruptive.
Drift-Resonances: Phase-Space Holes Harry Warren, PhD 1994 Chaotic, drift-resonant transport induced by a beautiful chorus of fastelectron interchange instabilities with frequency sweeping (Warren, PRL, 1995) Dmitry Maslovsky, PhD 2003 Fast-electron, gyrokinetic interchange instability creates inward-propagating phase-space holes (bubbles) and a chorus of rising tones. (Maslovsky, PRL, 2003)
this induces global chaos. Nonlinear Simulation Reproduces Measured Frequency Sweeping Suppression A! eff /" =0.45 that limits resonance with the 2.45 GHz microwaves. Frequency sweeping is only observed 0.4 0.4 after the outward expansion of the energetic electrons when the radially-broadened energetic Simulated Simulated electron disk can support RF pulse phase-space holes that do not experience RF pulse RF scattering from the B = 875 G cyclotron resonance. 0.2 0.2 We have modified a nonlinear, self-consistent numerical simulation in order to interpret the observed frequency sweeping suppression. This simulation is described fully elsewhere[12, 13] and reproduces the observed frequency sweeping. The simulation explicitly solves for the 0 0 evolution 0.02 of cold ion and energetic electron number 0.02densities and the electrostatic potential, Φ, on the (ψ, ϕ) plane. (ψ, ϕ) are simultaneously the canonical coordinates of the electrons 0.00-0.02 0 200 400 The energetic electrons (heated by the 2.45 GHz microwaves and localized near the equatorial position where B = 875 G) are expelled radially by the HEI bursts while preserving µ and J [19, 20]. As the electrons move outward, no further cyclotron resonance is possible because of the magnetic mirror effect. The collisionless, outward radial transport therefore creates an energetic electron disk at the dipole s equator 0.00-0.02 B! eff /" =1.7 guiding-center drift Hamiltonian (i.e. the electron phase-space) and the magnetic coordinates of the dipole, B = ψ ϕ [21]. Plasma E B drifts, ion polarization drifts, and energetic electron magnetic drifts determine particle dynamics, and Poisson s equation in magnetic ~ 14 W coordinates determines the nonlinear evolution of the potential. Cyclotron resonance due to the applied microwave and RF fields is modeled as causing diffusion of energetic electrons in µ-space according to: ~ 50 W 0 200 400 Dmitry Maslovsky, PhD 2003 2 F (µ, ψ, ϕ, t) = D(ψ, t) t µ (F F ) (1) 2
Isolated Relaxation Events and Rapid Beta Collapse at High Beta 6 ECRH (kw) S50318014 Eugenio Ortiz, PhD 2006 At high β, periodic relaxation events occur a few times per second. Outward motion of ring currrent. (Also, x-ray and µwave bursts!) Depending upon neutral fueling and heating power, relaxation events can be small or fully disrupt high-beta regime. HEI can appear in (nearly?) all cases LDX is the first to observe the HEI in a high-beta dipole plasma! 4 2 0 6 4 2 0 0.15 0.10 0.05 0.00 3 2 1 0 0.90 0.85 0.80 0.75 0.02 0.01 0.00-0.01 X-Ray (A.U.) PhotoDet (A.U.) Ip (ka) Rc (m) Relaxation Events Mirnov 2 (A.U.) 5.0 6.0 7.0 8.0 time (s)
Three Types of Fast Electron Interchange Spectra Eugenio Ortiz, PhD 2006 Chaotic Radial Transport Intermittent Bursts Chaotic Radial Transport Nonlinear Frequency Sweeping ± 20 V ± 80 V Frequency (MHz) 1.2 0.8 0.4 0.0 Edge Potential Fluctuations 0.804 0.805 0.806 0.807 0.808 Low-Beta Continuous 0 0.804 0.805 0.806 0.807 0.808 time (s) 100 50 Drift Resonant Energy (kev) Frequency (MHz) 60.79 0.791 0.792 0.793 0.794 5 4 3 2 1 Edge Potential Fluctuations Disruption 0 0.790 0.791 0.792 0.793 0.794 time (s) 400 200 0 Drift Resonant Energy (kev) Instability behavior determined by beta and by gas fueling history! (Hysteresis) Frequency (MHz) Volts Top Probe Floating Potential Weak Relaxation Burst 400 µsec
What We ve Learned #6: Turbulence in a Laboratory Dipole has Length Scales Dominated by the System Size Power-law spectrum for convective turbulence. Low-frequencies (in the rotating plasma frame) characterize the dominant long wavelengths. Transients and phase-transitions mediated by large m = 1 rotating perturbations.
Causes a trend dynamic change in floating potential fluctuations. towards power-law like spectra. Evolution of Spectrum with Gas Fueling Rate Change Power Spectrum Brian Grierson Matt Worstell 1µ s Low Density High Density 2µ s 3µ s Gas Puff 10µ s 5,40µ s 0.1 1.0 10.0 Freq (khz) 100.0 1000.0 9
10 8 6 4 2 0 Vacuum (E-6 Torr) Gas Puff PhotoDet (A.U.) Gas Puff S60714009 Coherent Fluctuations Suppressed with Flatter Gradient 0.8 0.4 0.0 Outer Flux (mv s) 1.0 0.5 0.0 30 Line Density (R = 0.77m, 0.96m) (E16/m2) 20 10 0 0.0020 Mirnov RMS Fluctuations (A.U.) Reduced Gradient 0.0010 0.0000 0.010 Mirnov Fluctuations (A.U.) 0.000-0.010 0 2 4 6 time (s)
What We ve Learned #7: Levitation Causes Dramatic Confinement Improvement Mini-RT
Still Many Unanswered Questions What (and why) are the particle and energy transport rates? How do these rates depend upon the convective turbulence? What are the characteristics of the convective/ turbulent transport as profiles are adjusted? Why? Is thermal transport adiabatic in a dipole plasma?
Summary Dipoles provide magnetic confinement for hot plasma in nature and in the laboratory (and dipole physics may help fusion energy!) The dipole has a unique field structure for study of confined plasma: unmatched diagnostic access, well-characterized magnetic geometry, and fascinating (and musical) wave-particle interactions. Two types of global interchange instabilities excited/modeled: Hot electron interchange (fast) modes illustrate collisionless dynamics with phase-space mixing and bubbles. Centrifugal interchange (slow) modes illustrate MHD mass flows and convective mixing. The world s first high-beta (β > 20%) dipole-confined plasma has been created in LDX by stabilization of the fast-electron interchange instability with programmed gas fueling.