The Laboratory Magnetosphere: Studying space physics in plasmas confined by a levitated dipole magnet Darren Garnier and Mike Mauel THE UNIVERSITY IDENTITY Columbia University The design of the Columbia identity incorporates the core elements of well- Pantone 286 thought-out branding: name, font, representing results of Jay Kesner, Masaki Nishiura, Barrett color, and visual mark. The logo was designed using the official University Rogers, Zensho Yoshida, and the students and scientists font, Trajan Pro, and features specific conducting research in support of the CTX, LDX, and RT-1 proportions of type height in relation @ MIT to the visual mark. The official Colum- bia color is Columbia Blue, or Pantone Black 290. On a light color background, the Bring Space Down To Earth logo can also be rendered in black, grey (60% black), Pantone 280, or Pantone University of California, Los Angeles, April 12, 2017 286; on a darker color background, the logo can be rendered in Pantone 290, 291, or 284, depending on which color works best with the overall design of your product, the media in which it will 4-color Process be reproduced, and its intended use. 100% Cyan 72% Magenta White or Pantone 290 (Columbia Blue) Background: Pantone 286 For photographs, use the logo in white against a darker area, posi- tioning it either at top left/right or bottom left/right. 3 Birkeland and assistant Devik with his largest chamber and terrella (1913) The first laboratory plasma physicist! Laboratory Magnetospheres (Space) Plasma Physics started with the terrella ‣ From Birkeland to the present, much has been studied in the dipole magnetic configuration “Laboratory Magnetospheres” have been built to study a particular process in magnetospheric physics ‣ Hasegawa’s question: Can fluctuations drive particles and energy to steep radial profiles in the laboratory as seen in space? ‣ Spoiler: Yes. However, they are much more generic platforms, capable of studying other processes in laboratory Reliable, steady state plasmas, with high beta, large size, lower collisionality Opportunity to build a new facility with higher density and warm ions Akira Hasegawa invited to Voyager 2’s encounter with Uranus January 24, 1986 12 Hour Flyby 10 Newly Discovered Moons Large, Tilted Magnetosphere Long, Twisted Magnetotail Substorm Injection Inward diffusion and convection Energetic Particles Centrally-peaked Profiles Plasma - Moon Interactions … Ed Stone, JGR 92, 14,873 (1987) Inward Transport of Energetic Particles Inward Transport Lunar Loss Source F(µ, J, ψ) ∂F(µ, J)/∂ψ ~ 0 Increasing Fixed (µ, J) J Fixed µ = Low-Energy-Charged Particles (LECP) = R/Ru Protons: 10 keV – 150 MeV Chen, et al., JGR 92, 15,315 (1987) Inwardβ 0.18 Transport (mWb 1Creates,Peak-local) Centrally-Peaked Pressure ⇡ − Inward transport of @F magnetospheric plasma 0 @ ⇡ compresses and heats… (µ,J) B 1 P ? / V ⇠ L7 1 1 P 2 6 || / L V ⇠ L ∂F(µ, J)/∂ψ ~ 0 Increasing Fixed (µ, J) ds 4 J V = L Fixed µ = Z B / Low-Energy-Charged Particles (LECP) = R/Ru Protons: 10 keV – 150 MeV Chen, et al., JGR 92, 15,315 (1987) dl Flux-tube Volume = V = L4 Z B / 4 1 1 1 V L results in n , T ,P ⇠ h i⇠L4 h i⇠L8/3 ⇠ L20/3 ∆(nV ) 0 2/3 ⇡ ∆(TV ) 0⌘ n V constant ds ⇡ ⌘h i ⇡ V = L4 5/3 3/4 ∆(PV ) λ 0 E V constant Z B / Convection⇡ ⌘hof Thermali Plasma⇡ Creates Regions with 5/3 Constant Flux-TubeP V Content constantand Invariant Temperature h i ⇡ dl ∆(nV ) ⌘ 0 n V Flux-tubeconstant Volume = V = L4 ⇡ ⌘h i ⇡ B / ∆(TV2/3) 0 3/4 Z λ⇡ E V constant ⌘h i⌘ nV ⇡ ~ 1 keVconstant Protons 5 3 ⌘/2/3 ⇡ ∆λ(PnVVTV) 0 constantconstant h ⌘i ⇡⇡ 2/3 5⇡/3 4 1 1 1 ∆(TV P )V 0 VconstantL results2/3 in n , T ,P Constant ⇠ Invariant (TV ) h i⇠L4 h i⇠ 8/3 ⇠ 20/3 1 1 5h/3i ⇡ ⇡ L L P ∆(PV ) 0 Constant Flux-Tube (nV) / V 5/3 ⇠ L20/3 ⇡ ⌘ nV constant ⌘ 2/3 ⇡ λ ∆(TV ) 0 constant ⌘ nV ⇡ 5/3⇡ = R/Ru ∆(TVP 2V/3) 0 constant h i ⇡ ⇡ Plasma Science Experiment (PLS) Selesnick and McNutt, JGR 92, 15,249 (1987) Ions and Electrons: 10 eV – 5.9 keV 1 1 P / V 5/3 ⇠ L20/3 Magnetospheres are Nature’s Laboratories for Magnetic Confinement Physics Voyager 2 Encounters: Jupiter (1979), Saturn (1981), Uranus (1986), Neptune (1989) Observations of magnetospheric radial transport and stability… ➡ Inward transport of energetic particles preserve (µ, J) creating centrally-peaked pressure ➡ Interchange motion of thermal plasma preserves flux-tube content (n V) and invariant temperature (T V2/3) creating centrally peaked profiles ➡ Marginally stable profiles Δ(P V5/3) ~ 0 at high beta, β ≥ 1 Stone and Lane, Science, 206, 925 (1979) Stone, JGR 88, 8639 (1983) Stone, JGR 92, 14,873 (1987) Stone and Miner, Science, 246, 1417 (1989) Hasegawa: Does magnetospheric physics apply to magnetic confinement in the laboratory? • Levitate a small, high-current superconducting current ring within a very large vacuum vessel • Inject heating power and a source of plasma particles at outer edge • Somehow drive low-frequency fluctuations that create radial transport, preserve (μ, J), and sustain “centrally-peaked” profiles at marginal stability • Achieve high beta, β ≥ 1, steady-state, and link space and fusion studies Akira Hasegawa, Comments on Plasma Physics and Controlled Fusion 11, 147 (1987) Much is already understood from non-levitated laboratory dipole experiments like CTX… Measured m " 1 Mode 60 Auroral Spatial structure and temporal 40 ✓ Imager dynamics of gradient and 20 centrifugally-driven interchange 0 and entropy mode turbulence !20 !40 !60 !60 !40 !20 0 20 40 60 ✓ “Artificial radiation belts” show complex nonlinear particle dynamics and drift-resonant transport understood without adjustable parameters ✓ Turbulent mixing is 2D (flute-like) with inverse cascade of scales Turbulent Transport of Magnetized Plasma are at the Intersection of Laboratory and Space Physics • Turbulence in magnetized plasma involves anisotropic fluctuations, which interact nonlinearly and couple energy, momentum, and particle number through spectral cascades spanning many length scales: • The global plasma size, L • The ion inertial length, λi • The particle (sound) gyroradius, ρs • Dipole plasma must be large: L >> λi ~ ρs ★Technical challenges: • Create conditions to study magnetized plasma turbulence across extreme range of scales while also at the very low collisionality characteristic of space plasma. • Create and maintain plasma for the long time required to observe cross-field transport ➡ Technical solution: magnetically levitate a high-field superconducting dipole magnet Laboratory Magnetospheres 2 m 3.6 m 1.8 m Levitated Dipole Experiment (LDX) Ring Trap 1 (RT-1) (1.2 MA ⋅ 0.41 MA m2 ⋅ 550 kJ ⋅ 565 kg) (0.25 MA ⋅ 0.17 MA m2 ⋅ 22 kJ ⋅ 112 kg) Nb3Sn ⋅ 3 Hours Float Time Bi-2223 ⋅ 6 Hours Float Time 24 kW ECRH 50 kW ECRH High β, SteadyLDX State,(MIT/Columbia) Self-Organized, Very- Large Plasma Torus RT-1 (U Tokyo) Laboratory Magnetospheric Devices LDX (MIT - USA) Components of a Laboratory Nb3Sn Dipole 1.2 MA Magnetosphere Inductively Charged 3 Hour Float Time 25 kW CW ECRH • Strong superconducting dipole for 5 m long-pulse, quasi-steady-state experiments • Large vacuum chamber for unequalled diagnostic access and large magnetic compressibility • Upper levitation coil for robust axisymmetric magnetic levitation • Lifting/catching fixture for re-cooling, coil safety, and physics studies • ECRH for high-temperature, high-beta 2 m plasmas Measurement of Density Profile and Turbulent Electric Field Gives Quantitative Verification of Bounce-Averaged Drift-kinetic Pinch 5 m Interferometer Array Measured Density Profile Evolution Measured Turbulent Electric Field Plasma in Supported vs Levitated Dipole Levitated Supported • 5 kW ECRH power and ~ 300 J 6 ECRH Power (kW) stored energy (levitated) 4 • Peak local beta ~ 40% 2 0 • Supported plasma has stored Vacuum Pressure (E-6 Torr) energy in energetic electron 1.0 0.8 population 0.6 0.4 • 2-3 x stored energy when levitated 0.2 0.0 Outer Flux Loop (mV sec) • Levitation increases ratio of 2.0 diamagnetism-to-cyclotron 1.5 emission indicating higher thermal 1.0 pressure. 0.5 0.0 V-Band Emission (A.U.) • Supported long afterglow 3 confinement indicative of energetic 2 particle confinement 1 0 • Long, higher-density levitated Interferometer (Radian) afterglow shows improved bulk 4 plasma confinement. 2 0 0 5 10 15 time (s) Pressure and Density Profiles During Levitation Indicate Marginally Stable Pressure (PV5/3) and Flux-Tube Content (nV) Decreasing Inward Inner Inward Transport Edge Loss Source 11 19 S100805046 8•10 1•10 Density (Particles/cc) Flux-Tube Content (Particles/Wb) �� Entropy Density 18 11 8•10 6•10 �� 18 6•10 �� Central Energy 11 γ 4•10 Source �� 18 �� 4•10 11 2•10 18 � 5/3 2•10 Edge Particle Δ(PV ) ≥ 0 Δ(nV) > 0 Source � 0 5/3 0 2/3 ∆ (0.6nV )���0.8 ���01.0 ��� and1.2 ���1.4∆��� 1.6PV��� 1.8��� 0.6 00.8 and1.0 ∆1.2 TV1.4 1.6 1.8 0 ⇠ Radius������ (m) (�) ⇠ Radius (m) ⇠ ⇣ ⌘ ⇣ ⌘ “warm core” Warm Core: Δ(nV) > 0 and Δ(TV2/3) < 0 η > 2/3 η > 2/3 ∆ ln T 2 ∆ (nV ) 0 and ∆ TV2/3 0 and ⌘ = = ⇠ ⇠ ∆ ln n 3 Alex Boxer, et al., “Turbulent inward pinch of plasma confined by a levitated dipole magnet,”⇣ Nat Phys⌘ 6, 207 (2010). Matt Davis, et al., "Pressure profiles of plasmas confined in the field of a magnetic dipole," PPCF 56, 095021 (2014). 2/3 ∆ ln T 2 ∆ TV 0 and ⌘ = = ⇠ ∆ ln n 3 ✓ ◆ h i ∆ PV5/3 = 0 (MHD stability) ⇣ ⌘ Quantitative Verification of Inward Turbulent Pinch Thomas Birmingham, “Convection Electric Fields and the Diffusion of Trapped Magnetospheric Radiation,” JGR, 74, (1969).