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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.
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!
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