1. 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/ swarthmore-colloquium/presentation.pptx, but I converted to keynote and threw out a huge number of slides.

2. 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

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

4. 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

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

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

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

8. Plasma - Large Scale BehaviorTo
Sun
Charge Separation Scale
Electrons (- )
Ions (+)
MHD Magnetohydrodynamics

9. 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:

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

11. Everything Breaks Eventually
Formation of Boundary Layers

12. 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

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

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

15. Magnetic Reconnection
Jz and Magnetic Field Lines

16. Reconnection Rate Conservation of MassD
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

17. 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

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

19. 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

20. 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!

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

22. Observing Magnetic Reconnection
In-situ satellite measurements

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

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

25. 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

26. 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!

27. Ion Distribution Function
Multiple populations
Non of which are Maxwellian

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

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

30. 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

31. 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
cores
100 billion particles
Strong union of simulations/theory
Comparisons with observations

32. Simulation Parameters
Normalizations: L0 = di = c/ωpi, t0 = (Ωci)-1
Simulation Size: di X 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

33. 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

34. 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)

35. 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

36. 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

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

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

39. 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:

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

41. 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

42. 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

43. 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 = m VA2 /2
= Brec2/(2μ0 N)
ΔTe ∝ VA,rec 2
Simulations: 5% into electron heating
Observations: 7% into electron heating

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

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, 1995
Gosling, 1990

46. 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

47. 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

48. 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)

49. 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

50. 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?

51. 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

52. 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

53. 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

54. 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

55. Turbulent Reconnection
This smooth reconnection may be the exception.

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

57. 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: 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.

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