Studying the Microphysics of Magnetic Reconnection in the Earth’s Magnetosphere and the Solar Wind...

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

Collaborators

• Colby Haggerty– Univ of Delaware

• Tai PhanMarit 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

Data from TRACE Spacecraft

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• 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

Auroral Substorms• All Sky Images

– Nishimura et al., GRL, 115, A07222, 2010.

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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

ToSun

Ions (+)

Electrons (-)MHD

MagnetohydrodynamicsCharge Separation Scale

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:

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

Vin

CAδ

Magnetic Reconnection

• Simplistic 2D picture

• Change of magnetic topology– Releases magnetic energy

Diffusion Region

MHD not valid

Magnetic Reconnection

Jz and Magnetic Field Lines

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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)

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

• d

Reconnection drives macroscale flows

Energizes particles Kivelson et al., 1995

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

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

THEMIS-D70 eVheating

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

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⊥

MaxwellianMultiple Species

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

• 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

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

• 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

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

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

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

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

Energy Budget

δ

D

Vin

Vin

B

B

VoutVout

• 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.

12%

5%

ΔTe_max

ΔTe_av

1/2 mi (CAr)2

1/2 mi (CAr)2

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

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

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

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

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⊥

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

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||

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

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 linesVez Te⊥

XX

YY

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

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

Turbulent Reconnection

• This smooth reconnection may be the exception.

Solar Wind is Strongly Turbulent

• What is the nature of reconnection in turbulence?

Solar Turbulence

• Granules– 1000km across– Convection cells across entire sun

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Hinode (G-band 430nm and Ca II H 397nm)

The Solar Wind

• Continuous wind– Supersonic– Magnetic Field

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STEREO Spacecraft

59

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