Transcript Document

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
Microscale
Electron Holes
Electrostatic Turbulence
Microscale
Electrons decouple
(guide field)
Electrons decouple
Electrons Decouple
(fluid case)
Pressure tensor, Meandering motion
re
(c/wpe)(cAe/c)
Microscale
Guide field
Ions decouple
rs
No guide field
Ions decouple
c/wpi
rm
c/wpe
Mesoscale
No guide field
O+ decouples
c/wpo+
Global Scale
Solitary x-lines
Nearly global
scales
1 – 4 Re
10 – 20 Re
The Many Scales of Collisionless Reconnection
• A non-exhaustive list
Microscale
Microscale
Electron Holes
Electrostatic Turbulence
re
(c/wpe)(cAe/c)
Microscale
rs
c/wpi
rm
c/wpe
Mesoscale
No guide field
O+ decouples
Solitary x-lines
c/wpo+
1 – 4 Re
Global Scale
10 – 20 Re
Outline
1. Microscale: Electron holes/turbulence/anomalous
resistivity.
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Turbulence and anomalous resistivity.
Necessary size of guide field: results imply Bz > 0.2 B
2. Micro/Mesoscale: O+ modified reconnection
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New hierarchy of scales.
New reconnection physics.
3. Mesoscale: Inherently 3D reconnection, solitary xlines
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•
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
3-D Magnetic Reconnection: with guide field
• 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
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
 pey
t
 en0 Ey  e  nE y 
– correlation between density and electric field fluctuations yields
drag
• Normalized electron drag
Dy 
c  nE y 
n0 v A B0
Electron drag due to scattering by parallel
electric fields
• Drag Dy has complex
spatial and temporal
structure with positive
and negative values
Z
– quasilinear ideas
fail badly
• Dy extends along
separatrices at late time
• Dy fluctuates both
positive and negative in
time.
x
How Large Bz?
• By = 5.0 in 3D simulations.
• Buneman instability couples with Lower
Hybrid wave to produce electron holes:
– k ~ wpe/(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.
z
z
Jy
Jy
Jy
z
z
X-line Structure: Bg = 0, 0.2, 1
z
z
Guide Field Criterion
• What is the minimum Bg so that the eexcursions are less than de?
0.1c A
di
c Ae
de
cA
Reconnection Rate:
 cEz
v ExB

~ 0.1
t cA B0
cA
0.1cAe
0.1v Ae
vin
c
rL 


ce ce ( Bg / B0 ) w pe
 Bg  0.1B0
X-line Distribution Functions
Ions
Bg  0
Bg  0.2
Bg  1
Vy
Why is this important? Development of x-line turbulence.
Why does it happen? Bg means longer acceleration times.
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
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–
–
–
Three species: {e,i,h} = {electrons, protons, heavy ions}
mh* = mh/mi
Normalize: t0 = 1/i and L0 = di  c/wpi
E = Ve  B  Pe/ne
Effect on Reconnection
• Dissipation region
– 3-4 scale structure.
• Reconnection rate
– Vin ~ d/D Vout
– Vout ~ CAt
• CAt = [ B2/4p(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
z
y
x
3-Species Waves: Magnetotail Lengths
Light
Whistler
w = k 2 d i c Ai
Light
Alfven
ni
ne w = k c Ai
ni
ne
Heavy
Whistler
Heavy
Alfven
w = k 2 dh cAh
w = k cAh
Smaller
da = c/wpa
Larger
di
ni
 800 km
ne
di
ni ne
 2000 km
zh2 nh2
dh  5000km
ni = 0.05 cm-3
no+/ni = 0.64
• 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.
Out-of-plane B
Z
By with proton flow vectors
• mh* = 1
– Usual two-fluid reconnection.
X
• mh* = 16
Z
Light
Whistler
Heavy
Whistler
– Both light and heavy whistler.
– Parallel ion beams
• Analogue of electron beams in
light whistler.
X
Z
• mh* = 104
– Heavy Whistler at global
scales.
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..
•
Reconnection Rate
mh* = 1
mh* = 16
mh* = 104
Eventually, the heavy
whistler is the slowest.
Time
Island Width
Time
symmetry axis
Key Signatures
Cut through x=55
O+ Case
mh* = 1
mh* = 16
By
• Heavy Whistler
Z
– Large scale quadrupolar By
– Ion flows
Cut through x=55
mh* = 16
Velocity
• Ion flows slower.
• Parallel ion streams near separatrix.
• Maximum outflow not at center of
current sheet.
proton Vx
O+ Vx
– Electric field?
Z
Z
Light
Whistler
Heavy
Whistler
X
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 q  d/D) change?
• Effect on onset of reconnection?
• Effect on instabilities associated with substorms?
– Lower-hybrid, ballooning,kinking, …
III: Inherently 3D Reconnection
• 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.
Angelopoulos et al., 1997
The Simulations
Vin
• Two fluid simulations
• 512 x 64 x 512 grid points, periodic
BC’s.
• Dx = Dz = 0.1, Dy = (1.0 or 2.0) c/wpi.
• Run on 256 processors of IBM SP.
• me/mi = 1/25
• w0 = initial current sheet width.
• Vary w0
• Initialization:
CA
-y
Current along y
z
x
Density
Z
– Random noise
– Single isolated x-line
X
X
Understanding Single X-line Segments
• Initially isolated x-line perturbation
• w0 strongly affects behavior of the x-line
– w0 = 1.0:
x-line grows in length very quickly.i
w0 = 1.0
Z
X
Comparing Electron and Ion Velocities
ion velocity
vectors
Ion end
Y
• w0 = 1.0
• Electrons initially carry all of
the current
• X-line grows preferentially in
the direction of electron flow.
•
X
electron velocity
vectors
Electron end •
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.
Y
X
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
Jz greyscale with ion velocity vectors
• Initially Random perturbations
• Reconnection self-organizes into
a strongly 3D process.
– Lx , Lz ~ c/wpi
– Ly ~ 10 c/wpi
– 10 c/wpi  1- 4 Re in magnetotail
Y
X
• X-lines only form in limited
regions.
Z
– Local energy release
– Marginally stable?
– Nearly isolated x-lines form.
Vin
X
CA
-y
z
• X-line length along GSM y
stabilizes around 10 c/wpi
– Solitary x-lines!
x
=> Reminiscent of a pseudo-breakup or a bursty bulk flow.
Spontaneous Reconnection: w0 = 2.0
Jz greyscale with ion velocity vectors
Y
• Initially Random perturbations
• Reconnection self-organizes into
a strongly 3D process.
Y
– Lx , Lz ~ c/wpi
– Ly ~ 10 c/wpi
– 10 c/wpi  1- 4 Re in magnetotail
X
Y
X
Y
• X-lines only form in limited
regions.
– Local energy release
– Marginally stable?
– Nearly isolated x-lines form.
X
X
• X-line length along GSM y
stabilizes around 10 c/wpi
– Solitary x-lines!
=> Reminiscent of a pseudo-breakup or a bursty bulk flow.
Mesoscale 3D: Conclusions
• Spontaneous reconnection inherently 3D!
– Need Mesoscales: L ~ 10 c/wpi
• Global or local energy release
– Dependent on w0 => Implications for substorms.
• Behavior of isolated x-line
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–
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–
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/wpi ~ 1-4 Re
• Consistent with observations!