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, 1z 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( / )

AeL g

ce ce g pe

c B BB B

edid Aec Ac0.1 Aec

0.1 Ac Reconnection Rate:

0

z

A

cEt 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.

Vin Vout 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 2 2000 kmi ei

h h

n ndz n

800 kmii

e

ndn

5000kmhd

Heavy Alfve

=

n

Ahk c2

Heavy Whistler

= h Ahk d c

Light A

=

lfven

iAi

e

nk cn

2

Light Whis

=

tler

ii Ai

e

nk d cn

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

ocity

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

Vin CAz

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

Vin CAz

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!