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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
– Univ of Delaware
• Tai Phan
Marit Oieroset
– Berkeley
• Masaaki Fujimoto
• Paul Cassak
– Univ of West Virginia
• Jim Drake
Space Weather
• The nature of changing environmental
conditions in space.
– Plasma: A gas of charged particles.
A Solar Flare
• Explosive energy release
– Up to 1032 ergs
3 x 1018 kW-hr
– Takes ~ 20 minutes
– Equivalent to:
QuickTime™ and a
Photo decompressor
are needed to see this picture.
40 billion atomic bombs(!)
2005 human energy
consumption:
1.4 x 1014 kW-hr
Data from TRACE Spacecraft
Auroral Substorms
• All Sky Images
– Nishimura et al., GRL, 115, A07222, 2010.
QuickTime™ and a
Motion JPEG OpenDML decompressor
are needed to see this picture.
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
Electrons ()
Ions (+)
MHD
Magnetohydrodynamics
Charge Separation Scale
MHD - Magnetohydrodynamics
• Fluid Equations
– Slow Timescales
– Large length scales
• Key Physics
– Magnetic field lines act like rubber tubes
• Alfven Speed :
mi n
d
V 
B g B
dt

t

t
B  c   E
n   gnV
E  
– Plasma “Frozen-in” to the magnetic field
• Magnetic Topology is conserved:
4
2

B 
   nT 

8 

V
c
B
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
– 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

CA
• Simplistic 2D picture
• Change of magnetic topology
– Releases magnetic energy
Diffusion Region
MHD not valid
Magnetic Reconnection
Jz and Magnetic Field Lines
QuickTime™ and a
GIF decompressor
are needed to see this picture.
Reconnection Rate
D
Vin
B
Vout
Vout
Vin
••
•
–
••
B
Conservation
of
Mass
Conservation Rate:
Reconnection
of
Rate:
Energy
Vinin ~ (δ/D) cA
Reconnection
V
mi n Vin D ~ mi n Vout δ
Last 10 years:
~ O(0.1)
Eδ/D
out-of-plane ~ Vin B
δ
Reconnection in Solar Flares
• X-class flare: ~ 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
Diffusion region scales: 1 km
– Microscale process
– Macroscale effects
• Complete description
300,000 km
– Model Macroscales
– Resolve Microscales
– Impossible!
• Grand Challenge
Problem
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
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
– 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
SmallLose
Scale
theReconnection
Forest for theStudies
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
•
•
Basic Reconnection
Simulations
– Periodic boundary
conditions
Reconnected flux
Density
Double current sheet
– Reconnects robustly
•
Initial x-line perturbation
•
Excellent Testbed for
studying basic properties of
reconnection
•
Current along Z
Does not include many
boundary condition effects
Reconnection Rate
Time
Y
Z
Z
t=0
X
X
XX
Y
Z
Z
t = 1200
Time
X
X
XX
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
Te
Te ∞ 1/e, rec
(eV)
0.5
Ti/Te ~ 5
e, rec 5.0
nkTe/(Brec2/2 0)
Table of All Most Simulations
• Currently about 50 simulations
• Simulate a range of:
Run #
301
Breconn
Bguide
ninflow
Te
B2
Ti
β⊥
β⊥e
β⊥i
βtotal
1
0
0.2
0.25
0.25
1.00
0.20
0.10
0.10
0.20
1
1
0.2
0.25
0.25
2.00
0.20
0.10
0.10
0.10
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
306
1
run307
1
run311
1
302
303
–
–
–
–
–
run308001 0.447
run312001 0.447
run309
1
run313
1
run315
1
run316
1
run310001 2.236
run314001 2.236
run317001 2.236
run318001 2.236
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
0
0.2
2.25
0.25
1.00
1.00
0.90
0.10
1.00
1
0.2
2.25
0.25
2.00
1.00
0.90
0.10
0.50
0
1.0
0.25
0.25
1.00
1.00
0.50
0.50
1.00
1
1.0
0.25
0.25
2.00
1.00
0.50
0.50
0.50
0
0.2
0.25
0.25
0.20
1.00
0.50
0.50
1.00
0.447
0.2
0.25
0.25
0.40
1.00
0.50
0.50
0.50
0
0.04
0.25
2.25
1.00
0.20
0.02
0.18
0.20
1
0.04
0.25
2.25
2.00
0.20
0.02
0.18
0.10
0
0.04
2.25
0.25
1.00
0.20
0.18
0.02
0.20
1
0.04
2.25
0.25
2.00
0.20
0.18
0.02
0.10
0
0.2
0.25
2.25
5.00
0.20
0.02
0.18
0.20
2.236
0.2
0.25
2.25
10.00
0.20
0.02
0.18
0.10
0
0.2
2.25
0.25
5.00
0.20
0.18
0.02
0.20
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
Determination of Heating
Vez
Y
Bx, By, Bz
Bz
X
Y
Y
Jx, Jy, Jz
Ey
X
Y
Y
Vix, Viy, Viz
X
• Slice 20 ion inertial
lengths downstream of xline.
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
Vout
Vout
Vin
B
• α = percentage of available energy
δ
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
ΔTe_tot
– αTe is independent of inflow
parameters!
(CAr)2
Energy Budget
• Plot versus 1/2 (CAr
• Slope of line = 0.12
)2
ΔTe_max
12%
– 12% of energy into electron
heating?
1/2 mi (CAr)2
• Average heating in exhaust
– Slope of 5%
• 5% of magnetic energy
converted into heating.
ΔTe_av
5%
1/2 mi (CAr)2
Statistical survey of the degree of electron heating at magnetopause
1. Identify reconnection exhausts
2. Determine Te
• Determine boundary conditions: ,
guide field, etc…
magnetosphere
Diffusion region
VA
magnetosheath
spacecraft
Te (eV)
Te (eV)
Observations
inflow VA,rec (km/s)
Te  VA,rec 2
Slope= 0.069
mi VA,rec2 /2 (eV)
Te = 0.069 m VA2 /2
= 0.069 Brec2/(2 0 N)
• Simulations: 5% into electron heating
• Observations: 7% into electron heating
Te (eV)
Degree of heating depends on VA
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
45
One Stark Effect: Guide Field
• Bg = Br
Y
– Almost no
perpendicular
heating!
Bx, By, Bz
Te||
Vix, Viy, Viz
Y
X
Y
Te⊥
Y
Te||, Te⊥
X
Y
Anisotropy
• Striking
– In General: ΔTe|| ≳ ΔTe⊥
– Guide field Case: No ΔTe⊥
– Guide field has larger ΔTe||?
ΔTe||
ΔTe||
All Bg
ΔTe⊥
All Bg
(CAr)2
Bg = Br
(CAr)2
(CAr)2
ΔTe⊥
ΔTe||
Bg = 0
Bg = 0
(CAr)2
ΔTe⊥
(CAr)2
Bg = Br
(CAr)2
Te (eV)
Observations: Guide field suppresses perpendicular heating
Te < Te||
Te|| (eV)
Te~ 0.75Te||
Te|| (eV)
magnetic shear < 120o (guide field > 0.6)
Te (eV)
Te (eV)
magnetic shear > 150o (guide field < 0.3)
Te << Te||
Te|| (eV)
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, AshourAbdalla 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
Vez – Example: Scattering at strongly
Te⊥ curved field lines
Y
Y
X
X
What Controls Electron Bulk (Thermal) Heating in Reconnection?
Answer: VA2 and guide field
Diffusion region
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
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
Magnetotail:
keV heating
(Gosling et al., 1990)
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?
Solar Turbulence
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Hinode (G-band 430nm and Ca II H 397nm)
• Granules
– 1000km across
– Convection cells across entire sun
The Solar Wind
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
• Continuous wind
– Supersonic
– Magnetic Field
STEREO Spacecraft
QuickTime™ and a
GIF decompressor
are needed to see this picture.
59
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