The Many Scales of Collisionless Reconnection in the Earth’s

Magnetosphere

Michael Shay – University of Maryland

Collaborators

• Jim Drake – Univ. of Maryland

• Barrett Rogers – Dartmouth College

• Marc Swisdak – Univ. of Maryland

• Cyndi Cattell – Univ. of Minnesota

The Many Scales of Collisionless Reconnection

• A non-exhaustive list

(c/pe)(cAe/c) e c/pe m

s c/pi c/po+ 1 – 4 Re 10 – 20 Re

Electron Holes Electrons decouple Electrons decouple Electrons Decouple

Electrostatic Turbulence (guide field) (fluid case) Pressure tensor, Meandering motion

Guide field No guide field No guide field Solitary x-lines Nearly global Ions decouple Ions decouple O+ decouples scales

Microscale Microscale

Microscale Mesoscale Global Scale

The Many Scales of Collisionless Reconnection

• A non-exhaustive list

(c/pe)(cAe/c) e c/pe m

s c/pi c/po+ 1 – 4 Re 10 – 20 Re

Electron Holes Electrostatic Turbulence

No guide field Solitary x-lines O+ decouples

Microscale Microscale

Microscale Mesoscale Global Scale

Outline1. Microscale: Electron holes/turbulence/anomalous

resistivity.• Turbulence and anomalous resistivity.

• Necessary size of guide field: results imply Bz > 0.2 B

2. Micro/Mesoscale: O+ modified reconnection• New hierarchy of scales.

• New reconnection physics.

3. Mesoscale: Inherently 3D reconnection, solitary x-lines

• Asymmetry in x-line growth.

• Solitary x-lines (1-4 Re).

I: Electron Holes and Anomalous Resistivity

• In a system with anti-parallel magnetic fields secondary instabilities play only a minor role– current layer near x-line is completely stable

• Strong secondary instabilities in systems with a guide field– strong electron streaming near x-line and along separatrices leads to

Buneman instability and evolves into nonlinear state with strong localized electric fields produced by “electron-holes”

• strong coupling to lower hybrid waves

– resulting electron scattering produces strong anomalous resistivity and electron heating

• Will this turbulence persist for smaller guide fields?– From 2D simulations: Conditions are favorable for Buneman

for By > 0.2

• Particle simulation with 670 million particles

• By=5.0 Bx, mi/me=100, Te=Ti=0.04, ni=ne=1.0

• Development of current layer with high electron parallel drift– Buneman instability evolves into electron holes

3-D Magnetic Reconnection: with guide field

Z

x

Anomalous drag on electrons

• Parallel electric field scatter electrons producing effective drag

• Average over fluctuations along z direction to produce a mean field electron momentum equation

– correlation between density and electric field fluctuations yields drag

• Normalized electron drag

0

eyy y

pen E e nE

t

0 0

yy

A

c nED

n v B

• Drag Dy has complex spatial and temporal structure with positive and negative values

– quasilinear ideas fail badly

• Dy extends along separatrices at late time

• Dy fluctuates both positive and negative in time.

Electron drag due to scattering by parallel electric fields

Z

x

How Large Bz?

• By = 5.0 in 3D simulations.

• Buneman instability couples with Lower Hybrid wave to produce electron holes:

– k ~ pe/(VdCse)1/2 --- group velocity zero

– As By decreases, Vd increases

– ky becomes prohibitively small as By ~ 1• 3D runs too expensive.

• Examine 2D runs for electron-ion streams.

X-line Structure: Bg = 0, 0.2, 1

z z z

J y J y

J y

z z z

Guide Field Criterion

• What is the minimum Bg so that the e- excursions are less than de?

in0

0

0.1vv 0.1

( / )Ae

L gce ce g pe

cB B

B B

edid Aec Ac0.1 Aec

0.1 Ac Reconnection Rate:

0

z

A

cE

t c B

ExBv

~ 0.1Ac

Why is this important? Development of x-line turbulence.Why does it happen? Bg means longer acceleration times.

1gB

0gB

Ions

0.2gB

X-line Distribution Functions

Vy

II: Three Species Reconnection

• 2-species 2D reconnection has been studied extensively.

• Magnetotail may have O+ present.– Due to ionospheric outflows: CLUSTER CIS/CODIF (kistler)

– no+ >> ni sometimes, especially during active times.

• What will reconnection look like?– What length scales? Signatures?

– Reconnection rate?

• Three fluid theory and simulations– Three species: {e,i,h} = {electrons, protons, heavy ions}

– mh* = mh/mi

– Normalize: t0 = 1/i and L0 = di c/pi

– E = Ve B Pe/ne

Effect on Reconnection• Dissipation region

– 3-4 scale structure.

• Reconnection rate– Vin ~ /D Vout

– Vout ~ CAt

• CAt = [ B2/4(nimi + nhmh) ]1/2

– nhmh << nimi • Slower outflow, slower reconnection normalized

to lobe proton Alfven speed.

• Signatures of reconnection– Quadrupolar Bz out to much larger scales. – Parallel Hall Ion currents

• Analogue of Hall electron currents.

VinVout

y

xz

3-Species Waves: Magnetotail Lengths

• Heavy whistler: Heavy species are unmoving and unmagnetized.

• Electrons and ions frozen-in => Flow together.

• But, their flow is a current. Acts like a whistler.

• Heavy Alfven wave

• All 3 species frozen in.

2 22000kmi e

ih h

n nd

z n800kmi

ie

nd

n 5000kmhd

Heavy Alfve

=

n

Ahk c2

Heavy Whistler

= h Ahk d c

Light A

=

lfven

iAi

e

nk c

n

2

Light Whis

=

tler

ii Ai

e

nk d c

n

Smaller Larger

ni = 0.05 cm-3

no+/ni = 0.64

d = c/p

Out-of-plane B• mh* = 1

– Usual two-fluid reconnection.

• mh* = 16 – Both light and heavy whistler.

– Parallel ion beams• Analogue of electron beams in

light whistler.

• mh* = 104

– Heavy Whistler at global scales.

X

X

Z

Z

Z By with proton flow vectors

Light Whistler

Heavy Whistler

X

Reconnection Rate• Reconnection rate is

significantly slower for larger heavy ion mass.

– nh same for all 3 runs. This effect is purely due to mh..

• Eventually, the heavy whistler is the slowest.

mh* = 1mh* = 16mh* = 104

Reconnection Rate

Island WidthTime

Time

Key SignaturesO+ Case

• Heavy Whistler– Large scale quadrupolar By

– Ion flows • Ion flows slower.

• Parallel ion streams near separatrix.

• Maximum outflow not at center of current sheet.

– Electric field?

By

Cut through x=55

Cut through x=55

Vel

ocit

y

mh* = 1mh* = 16

proton Vx

O+ Vx

mh* = 16

Z

Z

symmetry axis

X

ZLight Whistler

Heavy Whistler

Questions for the Future

• How is O+ spatially distributed in the lobes?– Not uniform like in the simulations.

• How does O+ affect the scaling of reconnection?– Will angle of separatrices (tan D) change?

• Effect on onset of reconnection?• Effect on instabilities associated with substorms?

– Lower-hybrid, ballooning,kinking, …

III: Inherently 3D Reconnection

Angelopoulos et al., 1997

• Bursty Bulk Flows: Sudden flow events in the magnetotail.

• Significant variation in convection of flux measured by satellites only 3 Re apart.

– E ~ v B = Convection of flux

– Slavin et al., 1997, saw variation in satellites 10 Re apart.

• Reconnection process shows strong 3D variation along GSM y– Mesoscales.

The Simulations

• Two fluid simulations

• 512 x 64 x 512 grid points, periodic BC’s.

• x = z = 0.1, y = (1.0 or 2.0) c/pi.

• Run on 256 processors of IBM SP.

• me/mi = 1/25

• w0 = initial current sheet width.

• Vary w0

• Initialization:– Random noise

– Single isolated x-line

VinCA

z

x-y

X X

Z

Current along y Density

• Initially isolated x-line perturbation

• w0 strongly affects behavior of the x-line

– w0 = 1.0: x-line grows in length very quickly.i

Understanding Single X-line Segments

w0 = 1.0

Z

X

Comparing Electron and Ion Velocities

• w0 = 1.0

• Electrons initially carry all of the current

• X-line grows preferentially in the direction of electron flow.

• X-line perturbation is carried along y by frozen-in electron flow

• Hall Physics.

• X-line perturbation has a finite size, so its velocity is the average equilibrium electron velocity.

– Vey ~ J ~ w0-1

– Independent of electron mass.

ion velocity vectors

electron velocity vectors

X

Y

X

Y

Electron end

Ion end

Direction of Propagation• Magnetotail: Assume something like a Harris equilibrium.

– Ions carry most of the current, not electrons.

• Shift reference frames so the ions are nearly at rest.– X-line segments should propagate preferentially in the dawn to dusk

direction: Westward.

• If auroral substorm is directly linked to reconnection:– Stronger westward propagation during expansion phase.

– Consistent with Akasofu, 1964.

Spontaneous Reconnection: w0 = 2.0

=> Reminiscent of a pseudo-breakup or a bursty bulk flow.

X

X

Y

Z

• Initially Random perturbations• Reconnection self-organizes into

a strongly 3D process. – Lx , Lz ~ c/pi

– Ly ~ 10 c/pi

– 10 c/pi 1- 4 Re in magnetotail

• X-lines only form in limited regions.– Local energy release– Marginally stable?– Nearly isolated x-lines form.

• X-line length along GSM y stabilizes around 10 c/pi

– Solitary x-lines!

Jz greyscale with ion velocity vectors

VinCA

z

x-y

Spontaneous Reconnection: w0 = 2.0

=> Reminiscent of a pseudo-breakup or a bursty bulk flow.

X X

X X

Y Y

YY

Jz greyscale with ion velocity vectors • Initially Random perturbations• Reconnection self-organizes into

a strongly 3D process. – Lx , Lz ~ c/pi

– Ly ~ 10 c/pi

– 10 c/pi 1- 4 Re in magnetotail

• X-lines only form in limited regions.– Local energy release– Marginally stable?– Nearly isolated x-lines form.

• X-line length along GSM y stabilizes around 10 c/pi

– Solitary x-lines!

Mesoscale 3D: Conclusions• Spontaneous reconnection inherently 3D!

– Need Mesoscales: L ~ 10 c/pi

• Global or local energy release– Dependent on w0 => Implications for substorms.

• Behavior of isolated x-line– Electron and ion x-line “ends” behave differently.

– Grows preferentially along electron flow direction.

– Equilibrium current the key to understanding behavior.

– w0 = 2.0 => Solitary x-line

• Length scales– Strong x-line coupled to ions probably has a minimum size

• Lz ~ 10 c/pi ~ 1-4 Re

• Consistent with observations!