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Studying the Microphysics of Magnetic Reconnection in the Earth’s Magnetosphere and the
Solar Wind
Michael Shay
Department of Physics and Astronomy
University of DelawarePrecursor: presentations/2012-09-swarthmore-colloquium/presentation.pptx, but I converted to keynote and threw out a huge number of slides.
Electron Heating
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Collaborators
• Colby Haggerty– Univ of Delaware
• Tai PhanMarit Oieroset– Berkeley
• Masaaki Fujimoto
• Paul Cassak– Univ of West Virginia
• Jim Drake– Univ of Maryland
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Space Weather
• The nature of changing environmental conditions in space.– Plasma: A gas of charged particles.
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A Solar Flare
Data from TRACE Spacecraft
QuickTime™ and aPhoto decompressor
are needed to see this picture.
• Explosive energy release – 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
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Auroral Substorms• All Sky Images
– Nishimura et al., GRL, 115, A07222, 2010.
QuickTime™ and aMotion JPEG OpenDML decompressor
are needed to see this picture.
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Overview
• Plasma Physics Primer
• What is Magnetic Reconnection?
• Electron Heating due to Magnetic Reconnection
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Overview
• Plasma Physics Primer
• What is Magnetic Reconnection?
• Electron Heating due to Magnetic Reconnection
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Plasma - Large Scale Behavior
ToSun
Ions (+)
Electrons (-)MHD
MagnetohydrodynamicsCharge Separation Scale
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MHD - Magnetohydrodynamics
min
d
dtV
BgB
4 nT
B2
8
t
B c E
t
n gnV
E V
cB
• 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:
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Magnetic Topology is Conserved
=>
Magnetic field lines can’t be cut.
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Everything Breaks
Eventually
Formation of Boundary Layers
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Boundary Layers
• Tiny layers that separate distinct regions– Small scales => Different Physics– “Effective Larmor Radius:” Inertial Length
• δ = c/ωp
• Plasma– Different magnetic fields– Diffusion region
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Overview
• Plasma Physics Primer
• What is Magnetic Reconnection?
• Electron Heating due to Magnetic Reconnection
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Vin
CAδ
Magnetic Reconnection
• Simplistic 2D picture
• Change of magnetic topology– Releases magnetic energy
Diffusion Region
MHD not valid
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Magnetic Reconnection
Jz and Magnetic Field Lines
QuickTime™ and aGIF decompressor
are needed to see this picture.
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Reconnection Rate
• Reconnection Rate: Vin
• Eout-of-plane ~ Vin B
δ
D
Vin
Vin
B
B
VoutVout
• Conservation of Mass– mi n Vin D ~ mi n Vout δ• Conservation of Energy• Reconnection Rate: Vin ~ (δ/D) cA
• Last 10 years: δ/D ~ O(0.1)
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Reconnection in Solar Flares
F. Shu, 1992
• X-class flare: τ~100 sec.
• τA~L/cA ~ 10 sec.
• Fast!– Every day analogy: Speed of sound
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• d
Reconnection drives macroscale flows
Energizes particles Kivelson et al., 1995
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Kivelson et al., 1995
A Multi-Scale Challenge• Reconnection
– Microscale process– Macroscale effects
• Complete description– Model Macroscales– Resolve Microscales– Impossible!
• Grand Challenge Problem
300,000 km
Diffusion region scales: 1 km
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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!
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Overview
• Plasma Physics Primer
• What is Magnetic Reconnection?
• Electron Heating due to Magnetic Reconnection
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Observing Magnetic Reconnection
• In-situ satellite measurements
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MMS Mission• Specifically devoted to
studying magnetic explosions– Cost: $1 billion– Launch date: 2014– 4 satellite mission
• MMS Movie
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Example of magnetopause reconnection with electron heating
THEMIS-D
jet
jet
THEMIS-D70 eVheating
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Magnetotail:keV heating
Electron bulk heating seen in some regions, not in others
Solar Wind:No heating
(Gosling, 2007)
Magnetopause:10s of eV gain in Te
(Gosling et al., 1990)
jet
jet
jet
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Heating in Plasmas
• H-Theorem– 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!
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Ion Distribution Function
• Multiple populations
• Non of which are Maxwellian
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Electron Distribution Functions: Simulation
• Chen et al., 2008
T|| > T⊥
MaxwellianMultiple Species
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Fluid Description not Adequate
• Kinetic representation: Boltzmann Equation
• f (x,v)
• Two options– Discretize x and v
• 5 dimensions - Expensive!
– Random particles: Follow trajectories
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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
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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
Small Scale Reconnection Studies
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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
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Initial Conditions• 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
Time
Rec
onne
cted
flu
x
X
X X
X
Y
Y
Current along Z Density
t = 0
t = 1200
X
X
X
X
Z Z
Z Z
Time
Reconnection Rate
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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)
βe, rec nkTe/(Brec2/2μ0)
ΔTe ∞ 1/βe, rec
0.5 5.0
Ti/Te ~ 5
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Table of All Most SimulationsRun # Breconn Bguide ninflow Te Ti B2 β⊥ β⊥e β⊥i βtotal
301 1 0 0.2 0.25 0.25 1.00 0.20 0.10 0.10 0.20
302 1 1 0.2 0.25 0.25 2.00 0.20 0.10 0.10 0.10
303 1 0 0.2 0.25 2.25 1.00 1.00 0.10 0.90 1.00
304 1 1 0.2 0.25 2.25 2.00 1.00 0.10 0.90 0.50
305 1 0 0.2 2.25 0.25 1.00 1.00 0.90 0.10 1.00
306 1 1 0.2 2.25 0.25 2.00 1.00 0.90 0.10 0.50
run307 1 0 1.0 0.25 0.25 1.00 1.00 0.50 0.50 1.00
run311 1 1 1.0 0.25 0.25 2.00 1.00 0.50 0.50 0.50
run308001 0.447 0 0.2 0.25 0.25 0.20 1.00 0.50 0.50 1.00
run312001 0.447 0.447 0.2 0.25 0.25 0.40 1.00 0.50 0.50 0.50
run309 1 0 0.04 0.25 2.25 1.00 0.20 0.02 0.18 0.20
run313 1 1 0.04 0.25 2.25 2.00 0.20 0.02 0.18 0.10
run315 1 0 0.04 2.25 0.25 1.00 0.20 0.18 0.02 0.20
run316 1 1 0.04 2.25 0.25 2.00 0.20 0.18 0.02 0.10
run310001 2.236 0 0.2 0.25 2.25 5.00 0.20 0.02 0.18 0.20
run314001 2.236 2.236 0.2 0.25 2.25 10.00 0.20 0.02 0.18 0.10
run317001 2.236 0 0.2 2.25 0.25 5.00 0.20 0.18 0.02 0.20
run318001 2.236 2.236 0.2 2.25 0.25 10.00 0.20 0.18 0.02 0.10
run319 0.447 0 0.2 0.25 2.25 0.20 5.00 0.50 4.50 5.00
run320 0.447 0.447 0.2 0.25 2.25 0.40 5.00 0.50 4.50 2.50
run321 1 0 1.0 0.25 2.25 1.00 5.00 0.50 4.50 5.00
run322 1 1 1.0 0.25 2.25 2.00 5.00 0.50 4.50 2.50
run323 1 0 0.2 0.25 1.25 1.00 0.60 0.10 0.50 0.60
run324 1 1 0.2 0.25 1.25 2.00 0.60 0.10 0.50 0.30
run325 1 0 0.2 0.0625 0.3125 1.00 0.15 0.03 0.13 0.15
run326 1 1 0.2 0.0625 0.3125 2.00 0.15 0.03 0.13 0.08
run327 1 0 0.2 1 5 1.00 2.40 0.40 2.00 2.40
run328 1 1 0.2 1 5 2.00 2.40 0.40 2.00 1.20
run329 1 0 0.2 2.5 12.5 1.00 6.00 1.00 5.00 6.00
run330 1 1 0.2 2.5 12.5 2.00 6.00 1.00 5.00 3.00
• 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
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Determination of Heating
• Slice 20 ion inertial lengths downstream of x-line.
Bx, By, Bz
Jx, Jy, Jz
Vix, Viy, Viz
Te||, Te⊥
Y
Y
Y
Y
Y
Y
Y
X
X
X
Vez
Bz
Ey
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Effect of β?
• β = thermal energy/magnetic energy
ΔTe
βr_tot
WARNING: DTetot_max is actually DTepar_max + 2*DTeperp_max
WARNING: DTetot_max is actually DTepar_max + 2*DTeperp_max
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Energy Budget
δ
D
Vin
Vin
B
B
VoutVout
• α = percentage of available energy
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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:
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Scaling with Alfven Speed: Te_tot
• Scaling evident– αTe is independent of inflow
parameters!
ΔTe_tot
(CAr)2
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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.
12%
5%
ΔTe_max
ΔTe_av
1/2 mi (CAr)2
1/2 mi (CAr)2
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Statistical survey of the degree of electron heating at magnetopause
Diff
usio
n re
gion
VA
1. Identify reconnection exhausts2. Determine ΔTe• Determine boundary conditions: β,
guide field, etc…
spacecraft
magnetosphere magnetosheath
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ObservationsΔT
e (e
V)
inflow VA,rec (km/s)
ΔTe
(eV
)
mi VA,rec2 /2 (eV)
ΔTe ∝ VA,rec 2
ΔTe = 0.069 m VA2 /2
= 0.069 Brec2/(2μ0 N)
Slope= 0.069
• Simulations: 5% into electron heating
• Observations: 7% into electron heating
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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
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45
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, 1995Gosling, 1990
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One Stark Effect: Guide Field
• Bg = Br
– Almost no perpendicular heating!
Bx, By, Bz
Vix, Viy, Viz
Te||, Te⊥
Y
Y
Y
Y
Y
X
X
Te||
Te⊥
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Anisotropy • Striking– In General: ΔTe|| ΔT≳ e⊥
– Guide field Case: No ΔTe⊥ – Guide field has larger ΔTe||?
ΔTe|| All Bg
(CAr)2
ΔTe|| Bg = 0
(CAr)2
ΔTe|| Bg = Br
(CAr)2
ΔTe⊥ All Bg
(CAr)2
ΔTe⊥ Bg = 0
(CAr)2
ΔTe⊥ Bg = Br
(CAr)2
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Observations: Guide field suppresses perpendicular heating
ΔTe⊥
(eV)
ΔTe|| (eV)
ΔTe⊥
(eV)
ΔTe⊥
(eV)
ΔTe|| (eV)
ΔTe|| (eV)
ΔTe⊥ < ΔTe||
magnetic shear > 150o (guide field < 0.3) magnetic shear < 120o (guide field > 0.6)
ΔTe⊥ << ΔTe||ΔTe⊥~ 0.75ΔTe||
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Conflicting findings on anisotropy of electron heating: Guide field effect
Magnetotail:~Isotropic heating[Chen et al., 2008]
Magnetosheath:Te|| heating onlyGuide field ~ 1
jet
Magnetotail guide field ~ 0
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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?
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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
![Page 52: Studying the Microphysics of Magnetic Reconnection in the Earth’s Magnetosphere and the Solar Wind Michael Shay Department of Physics and Astronomy University](https://reader037.vdocuments.mx/reader037/viewer/2022110206/56649cec5503460f949b8135/html5/thumbnails/52.jpg)
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 linesVez Te⊥
XX
YY
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What Controls Electron Bulk (Thermal) Heating in Reconnection?
Tai Phan, Mike Shay, Masaki Fujimoto, et al.
Diff
usio
n re
gion
VA
Reconnection converts magnetic energy into:- Kinetic energy (plasma jetting)- Ion heating- Electron heating -> Thermal and Supra-Thermal
assumed to always happen, but not true
Answer: VA2 and guide field
![Page 54: Studying the Microphysics of Magnetic Reconnection in the Earth’s Magnetosphere and the Solar Wind Michael Shay Department of Physics and Astronomy University](https://reader037.vdocuments.mx/reader037/viewer/2022110206/56649cec5503460f949b8135/html5/thumbnails/54.jpg)
Magnetotail:keV heating
Solar Wind:No heating
(Gosling, 2007)
Magnetopause:10s of eV gain in Te
(Gosling et al., 1990)
jet
jet
jet
The degree of electron bulk heating must depend on plasma regime
Electron bulk heating seen in some regions, not in others
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Turbulent Reconnection
• This smooth reconnection may be the exception.
![Page 56: Studying the Microphysics of Magnetic Reconnection in the Earth’s Magnetosphere and the Solar Wind Michael Shay Department of Physics and Astronomy University](https://reader037.vdocuments.mx/reader037/viewer/2022110206/56649cec5503460f949b8135/html5/thumbnails/56.jpg)
Solar Wind is Strongly Turbulent
• What is the nature of reconnection in turbulence?
![Page 57: Studying the Microphysics of Magnetic Reconnection in the Earth’s Magnetosphere and the Solar Wind Michael Shay Department of Physics and Astronomy University](https://reader037.vdocuments.mx/reader037/viewer/2022110206/56649cec5503460f949b8135/html5/thumbnails/57.jpg)
Solar Turbulence
• Granules– 1000km across– Convection cells across entire sun
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Hinode (G-band 430nm and Ca II H 397nm)
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The Solar Wind
• Continuous wind– Supersonic– Magnetic Field
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STEREO Spacecraft
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59
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