Transcript Document
Magnetic Reconnection in Multi-Fluid
Plasmas
Michael Shay – Univ. of Maryland
Magnetic Reconnection in Multi-Fluid
Plasmas
General Theory and Simulations of O+
Modified Reconnection.
Michael Shay – Univ. of Maryland
Background
• 2-species 2D reconnection has been substantially studied.
• Many plasma have 3 or more charged species.
– Magnetotail:
• O+ due to ionospheric outflows: CLUSTER CIS/CODIF (kistler)
• no+ >> ni sometimes, especially during active times.
– Astrophysical plasmas
• Dust species present
• Neutrals also.
• What will reconnection look like?
– What length scales? Signatures?
– Reconnection rate?
• Previous work
– Global 3-fluid magnetospheric codes (Winglee).
– Tracer particle stepping in global MHD models (Birn).
– Full particle codes (Hesse).
Three-Fluid Equations
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•
•
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Three species: {e,i,h} = {electrons, protons, heavy ions}
mh* = mh/mi
Normalize: t0 = 1/Wi and L0 = di c/wpi
E = Ve B Pe/ne
n
n V , {i, h}
t
dVi
ni
ni
zh nh (Ve Vh ) B Pi Pe
dt
ne
dVh
zh nh
mh*nh
zh nh (Vh Ve ) B Ph
Pe
dt
ne
B
(Ve B), J B
t
ne Ve ni Vi zh nh Vh and ne ni zh nh
Vout
1D Linear waves
X
Vin
Y
-Z
• Examine linear waves
d
– Assume k || Bo
– Compressional modes decouple.
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
d = c/wp
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.
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.
• Signatures of reconnection
– Quadrupolar Bz out to much larger scales.
– Parallel Hall Ion currents
• Analogue of Hall electron currents.
Vin
Vout
z
y
x
The Simulations
Vin
• Initial conditions:
CA
z
– No Guide Field.
– Reconnection plane: (x,y) => Different from GSM
– 2048 x 1024 grid points
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204.8 x 102.4 c/wpi.
Dx = Dy = 0.1
Run on 64 processors of IBM SP.
me = 0.0, 44B term breaks frozen-in, 4 = 5 • 10-5
Time normalized to Wi-1, Length to di c/wpi.
Isothermal approximation, g = 1
y
x
Reconnection Simulations
• Double current sheet
– Reconnects robustly
Current along Z
• Initial x-line
perturbation
Density
Y
t=0
X
X
Y
t = 1200
X
X
Equilibrium
Bx
Jz
• Double current sheet
– Double tearing mode.
Y
• Background heavy ion species.
–
–
–
–
nh = 0.64.
Th = 0.5
mh = {1,16,104}
dh = {1,5,125}
• Seed system with x-lines.
Electrons
Ions
Heavy Ions
Y
nVz
– Te = Ti
– Ions and electrons carry
current.
density
• Harris equilibrium
Y
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
Outflow shows all 4 wave regions
• Outflow region
– 4 different physics regions
Cut through x-line along outflow
• Maximum outflow speed
– mh* = 1: Vout1 1.0
– mh* = 16: Vout16 0.35
• Expected scaling:
– Vout cAt
light
Alfven
light
whistler
heavy
whistler
heavy Alfven
Vex
Vix
Vhx
CAt = [ B2/4p(nimi + nhmh) ]1/2
– Vout1/Vout16 2.9
– cAt1/cAt16 2.6
X
Consequences for magnetotail
reconnection
• When no+mo+ > ni mi
– Slowdown of outflow normalized to upstream cAi
– Slowdown of reconnection rate normalized to upstream
cAi.
• However:
– Strongly dependent on lobe Bx.
– Strongly active times: cAi may change dramatically.
Specific Signatures: O+ Modified
Reconnection
• O+ outflow at same speed as proton outflow.
– Reduction of proton flow.
• Larger scale quadrupolar By (GSM).
• Parallel ion currents near the separatrices.
– Upstream ions flow towards x-line.
• The CIS/CODIF CLUSTER instrument has
the potential to examine these signatures.
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, …