Studying the Microphysics of Magnetic Reconnection in the Earth’s Magnetosphere and the Solar Wind Electron Heating Michael Shay Department of Physics and Astronomy University of Delaware Precursor: presentations/2012-09-swarthmore-colloquium/presentation.pptx, but I converted to keynote and threw out a huge number of slides.

Collaborators Colby Haggerty Tai Phan Marit Oieroset Masaaki Fujimoto Univ of Delaware Tai Phan Marit Oieroset Berkeley Masaaki Fujimoto Paul Cassak Univ of West Virginia Jim Drake Univ of Maryland

Space Weather The nature of changing environmental conditions in space. Plasma: A gas of charged particles.

A Solar Flare Explosive energy release Data from TRACE Spacecraft Up to 1032 ergs 3 x 1018 kW-hr Takes ~ 20 minutes Equivalent to: 40 billion atomic bombs(!) 2005 human energy consumption: 1.4 x 1014 kW-hr 1 billion mega tons, 40 billion Hiroshima-size atomic bombs Data from TRACE Spacecraft

Auroral Substorms All Sky Images Nishimura et al., GRL, 115, A07222, 2010.

Overview Plasma Physics Primer What is Magnetic Reconnection? Electron Heating due to Magnetic Reconnection

Overview Plasma Physics Primer What is Magnetic Reconnection? Electron Heating due to Magnetic Reconnection

Plasma - Large Scale Behavior To Sun Charge Separation Scale Electrons (- ) Ions (+) MHD Magnetohydrodynamics

MHD - Magnetohydrodynamics Fluid Equations Slow Timescales Large length scales Key Physics Magnetic field lines act like rubber tubes Alfven Speed : Plasma “Frozen-in” to the magnetic field Magnetic Topology is conserved:

Magnetic Topology is Conserved => Magnetic field lines can’t be cut.

Everything Breaks Eventually Formation of Boundary Layers

Boundary Layers Tiny layers that separate distinct regions Plasma Small scales => Different Physics “Effective Larmor Radius:” Inertial Length δ = c/ωp Plasma Different magnetic fields Diffusion region

Overview Plasma Physics Primer What is Magnetic Reconnection? Electron Heating due to Magnetic Reconnection

Magnetic Reconnection Vin δ CA Simplistic 2D picture Change of magnetic topology Releases magnetic energy Diffusion Region MHD not valid

Magnetic Reconnection Jz and Magnetic Field Lines

Reconnection Rate Conservation of Mass D Vin B δ Vout Conservation of Mass mi n Vin D ~ mi n Vout δ Reconnection Rate: Vin ~ (δ/D) cA Last 10 years: δ/D ~ O(0.1) Conservation of Energy Reconnection Rate: Vin Eout-of-plane ~ Vin B

Reconnection in Solar Flares X-class flare: τ ~ 100 sec. τA~ L/cA ~ 10 sec. Fast! Every day analogy: Speed of sound F. Shu, 1992

d Reconnection drives macroscale flows Energizes particles Kivelson et al., 1995

A Multi-Scale Challenge Reconnection Microscale process Macroscale effects Complete description Model Macroscales Resolve Microscales Impossible! Grand Challenge Problem Diffusion region scales: 1 km 300,000 km Kivelson et al., 1995

Unsolved Reconnection Questions What makes it turn on and off? Where does the energy go? Flows, electron or ion heating? What about 3 Dimensions? Turbulence? But you’ve been studying it for 50 years!

Overview Plasma Physics Primer What is Magnetic Reconnection? Electron Heating due to Magnetic Reconnection

Observing Magnetic Reconnection In-situ satellite measurements

MMS Mission Specifically devoted to studying magnetic explosions Cost: $1 billion Launch date: 2014 4 satellite mission MMS Movie

Example of magnetopause reconnection with electron heating THEMIS-D jet jet 70 eV heating THEMIS-D jet

Electron bulk heating seen in some regions, not in others jet jet jet Solar Wind: No heating (Gosling, 2007) Magnetopause: 10s of eV gain in Te (Gosling et al., 1990) Magnetotail: keV heating

Heating in Plasmas H-Theorem Adiabatic Heating Joule Heating Gas/Plasma in thermodynamic equilibrium relaxes to a maxwellian particle distribution. Adiabatic Heating Compression. Does work. Leads to heating. Requires thermodynamic equilibrium. Maxwellian velocity distribution Joule Heating Scatter current. Generate heat. Requires collisions Solar Corona/Solar Wind/Magnetosphere Almost collisionless! Not in thermodynamic equilibrium!

Ion Distribution Function Multiple populations Non of which are Maxwellian

Electron Distribution Functions: Simulation Chen et al., 2008 T|| > T⊥ Multiple Species Maxwellian

Fluid Description not Adequate Kinetic representation: Boltzmann Equation f (x,v) Two options Discretize x and v 5 dimensions - Expensive! Random particles: Follow trajectories

Simulating Kinetic Reconnection Finite Difference Fluid quantities exist at grid points. E,B treated as fluids always Maxwell’s equations Kinetic Particle in Cell E,B fluids Ions and electrons are particles. Stepping fluids: particle quantities averaged to grid. Stepping particles: Fluids interpolated to particle position. Grid cell Macro-particle

Lose the Forest for the Trees Small Scale Reconnection Studies Lose the Forest for the Trees Include all kinetic physics Simplistic simulation geometry Simplistic boundary conditions Basic physics simulations What is the basic physics controlling electron heating during magnetic reconnection? Massively parallel simulations 4000 - 16000 cores 100 billion particles Strong union of simulations/theory Comparisons with observations

Simulation Parameters Normalizations: L0 = di = c/ωpi, t0 = (Ωci)-1 Simulation Size: 204.8 di X 102.4 di Grid: Δ = 0.05 di mi/me = 25, 100, c = 15, 30 Boundary conditions: periodic Equilibrium: Double Harris equilibrium Simulate until quasi-steady Time average over a few (Ωci)-1 Coordinates: “Simulation Coordinates” Outflow: x Inflow: y Out-of-plane: z

Initial Conditions t = 0 t = 1200 Time Z Z X X Z Z X X Basic Reconnection Simulations Double current sheet Reconnects robustly Periodic boundary conditions Initial x-line perturbation Excellent Testbed for studying basic properties of reconnection Does not include many boundary condition effects Current along Z Density Z Y Z t = 0 X X X X Z Y Z Reconnection Rate t = 1200 Reconnected flux Time Time X X X X

Simulation Parameters 3 Observational events are often in a parameter regime not typically simulated β relatively small in simulations Example: GEM Challenge had β ≈ 0.2 ΔTe (eV) ΔTe ∞ 1/βe, rec 0.5 5.0 Ti/Te ~ 5 βe, rec nkTe/(Brec2/2μ0)

Table of All Most Simulations Currently about 50 simulations Simulate a range of: Reconnection B-field: Br = .4 to 2.3 Reconnection Guide Field: Bg = .4 to 2.3 Density: n = .04 to 1.0 Ti/Te = 1 to 10 β = 0.1 to 6 Run # Breconn Bguide ninflow Te Ti B2 β⊥ β⊥e β⊥i βtotal 301 1 0.2 0.25 1.00 0.20 0.10 302 2.00 303 2.25 0.90 304 0.50 305 306 run307 1.0 run311 run308001 0.447 run312001 0.40 run309 0.04 0.02 0.18 run313 run315 run316 run310001 2.236 5.00 run314001 10.00 run317001 run318001 run319 4.50 run320 2.50 run321 run322 run323 1.25 0.60 run324 0.30 run325 0.0625 0.3125 0.15 0.03 0.13 run326 0.08 run327 5 2.40 run328 1.20 run329 2.5 12.5 6.00 run330 3.00

Determination of Heating Vez Y Bx, By, Bz X Bz Y Y Jx, Jy, Jz X Ey Y Y Vix, Viy, Viz X Slice 20 ion inertial lengths downstream of x- line. Y Te||, Te⊥ Y

Effect of β? β = thermal energy/magnetic energy ΔTe βr_tot WARNING: DTetot_max is actually DTepar_max + 2*DTeperp_max

Energy Budget D Vin B δ Vout α = percentage of available energy

Scaling of Electron Heating Energy Conservation Important Questions What is αTe? Is it a constant for a variation of inflow conditions? If αTe is constant:

Scaling with Alfven Speed: Te_tot Scaling evident αTe is independent of inflow parameters! ΔTe_tot (CAr)2

Energy Budget Plot versus 1/2 (CAr)2 Slope of line = 0.12 12% of energy into electron heating? Average heating in exhaust Slope of 5% 5% of magnetic energy converted into heating. ΔTe_max 12% 1/2 mi (CAr)2 ΔTe_av 5% 1/2 mi (CAr)2

Statistical survey of the degree of electron heating at magnetopause Identify reconnection exhausts Determine ΔTe Determine boundary conditions: β, guide field, etc… VA magnetosphere magnetosheath Diffusion region spacecraft

Observations ΔTe (eV) ΔTe (eV) inflow VA,rec (km/s) mi VA,rec2 /2 (eV) Slope= 0.069 ΔTe (eV) ΔTe (eV) inflow VA,rec (km/s) mi VA,rec2 /2 (eV) ΔTe = 0.069 m VA2 /2 = 0.069 Brec2/(2μ0 N) ΔTe ∝ VA,rec 2 Simulations: 5% into electron heating Observations: 7% into electron heating

Degree of heating depends on VA ΔTe (eV) VA,rec (km/s) Solar wind: VA ~ 50 km/s -> practically no heating Magnetopause: inflow VA ~ 50-400 km/s Magnetotail: inflow VA ~ 2000 km/s -> 1.4 keV

Component Reconnection Reconnecting field lines may not be anti-parallel Can think of as: anti-parallel reconnection add a uniform B-field perpendicular to reconnection plane. Guide field. Kivelson and Russel, 1995 Gosling, 1990

One Stark Effect: Guide Field Bg = Br Almost no perpendicular heating! Bx, By, Bz Y Te|| Vix, Viy, Viz Y X Y Te⊥ Te||, Te⊥ Y X Y

Anisotropy Striking In General: ΔTe|| ≳ ΔTe⊥ Guide field Case: No ΔTe⊥ Guide field has larger ΔTe||? Bg = 0 All Bg ΔTe|| ΔTe|| ΔTe|| Bg = Br (CAr)2 (CAr)2 (CAr)2 All Bg ΔTe⊥ ΔTe⊥ Bg = 0 ΔTe⊥ Bg = Br (CAr)2 (CAr)2 (CAr)2

Observations: Guide field suppresses perpendicular heating ΔTe⊥ (eV) ΔTe⊥ < ΔTe|| ΔTe|| (eV) magnetic shear > 150o (guide field < 0.3) magnetic shear < 120o (guide field > 0.6) ΔTe⊥~ 0.75ΔTe|| ΔTe⊥ << ΔTe|| ΔTe⊥ (eV) ΔTe⊥ (eV) ΔTe|| (eV) ΔTe|| (eV)

Magnetotail guide field ~ 0 Conflicting findings on anisotropy of electron heating: Guide field effect Magnetosheath: Te|| heating only Guide field ~ 1 Magnetotail: ~Isotropic heating [Chen et al., 2008] jet Magnetotail guide field ~ 0

Unanswered Question What if Te/Ti > 5? May effect heating What is the physical mechanism behind the heating? Acceleration at x-line (e.g. Pritchett et al., 2006, Ashour- Abdalla et al.) Acceleration in high field regions (e.g. Birn et al., 2000, 2004, Hoshino et al. 2001) Contracting Islands (e.g. Drake et al., 2006) Turbulent electric fields (e.g. Dmitruck et al., 2004) Parallel Electric Fields (e.g. Egedal et al., 2012) What if there are many x-lines? (Solar Flares) Turbulent Reconnection?

Conclusions Magnetic Reconnection Magnetic Energy Release in Plasma Multiscale problemf Satellite Observations and PIC Simulations Range of inflow parameters, guide field Simulation/Observations Find Similar Scaling ΔTe scales with (CAr)2 for wide range of parameters Universal process Guide Field Effect ΔTe⊥ shut off for guide field. Physics: Isotropization? Electron Thermal Heating is Generic

Physics? Now comes the hard part. Focus is on exhaust region No strong compression at dipole fields, etc. Easier to create Te|| Contracting Island Model E|| near x-line and separatrices Important issue: Isotropization Example: Scattering at strongly curved field lines Vez Te⊥ Y Y X X

What Controls Electron Bulk (Thermal) Heating in Reconnection? Answer: VA2 and guide field VA Tai Phan, Mike Shay, Masaki Fujimoto, et al. Reconnection converts magnetic energy into: Kinetic energy (plasma jetting) Ion heating Electron heating -> Thermal and Supra-Thermal Diffusion region assumed to always happen, but not true

Electron bulk heating seen in some regions, not in others jet jet jet Solar Wind: No heating (Gosling, 2007) Magnetopause: 10s of eV gain in Te (Gosling et al., 1990) Magnetotail: keV heating The degree of electron bulk heating must depend on plasma regime

Turbulent Reconnection This smooth reconnection may be the exception.

Solar Wind is Strongly Turbulent What is the nature of reconnection in turbulence?

Hinode (G-band 430nm and Ca II H 397nm) Solar Turbulence Granules 1000km across Convection cells across entire sun Hinode (G-band 430nm and Ca II H 397nm) Taken from: http://solarb.msfc.nasa.gov/news/movies.htmlThese are high resolution movies in G-band (430nm) and Ca II H (397nm) showingthe motion of granules and small magnetic fluxGranulesGranules are small (about 1000 km across) cellular features that coverthe entire Sun except for those areas covered by sunspots. Thesefeatures are the tops of convection cells where hot fluid rises upfrom the interior in the bright areas, spreads out across the surface,cools and then sinks inward along the dark lanes. Individual granuleslast for only about 20 minutes. The granulation pattern is continuallyevolving as old granules are pushed aside by newly emerging ones (470kB MPEG movie from the Swedish Vacuum Solar Telescope). The flowwithin the granules can reach supersonic speeds of more than 7 km/s(15,000 mph) and produce sonic "booms" and other noise that generateswaves on the Sun's surface. supergranules_sm.jpg (18400 bytes)SupergranulesSupergranules are much larger versions of granules (about 35,000 kmacross) but are best seen in measurements of the "Doppler shift" wherelight from material moving toward us is shifted to the blue whilelight from material moving away from us is shifted to the red. Thesefeatures also cover the entire Sun and are continuallyevolving. Individual supergranules last for a day or two and have flowspeeds of about 0.5 km/s (1000 mph). The fluid flows observed insupergranules carry magnetic field bundles to the edges of the cellswhere they produce the chromospheric network.

The Solar Wind Continuous wind Supersonic Magnetic Field STEREO Spacecraft Continuous wind Supersonic Magnetic Field