Transcript Three Species Collisionless Reconnection: Effect of O+ on Magnetotail Reconnection Michael Shay – Univ.

Three Species Collisionless
Reconnection: Effect of O+ on
Magnetotail Reconnection
Michael Shay – Univ. of Maryland
Preprints at: http://www.glue.umd.edu/~shay/papers
Overview
• 3-species reconnection
– What length scales?
– Signatures?
– Reconnection rate?
• Examples and background
• Linear theory of 3-species waves
• 3-Fluid simulations
Magnetospheric O+
• Earth’s magnetosphere
– ionospheric outflows can lead to
significant O+ population.
– Active Times
• Oct. 1, 2001: Geomagnetic storm
–
–
–
–
CLUSTER, spacecraft 4
CIS/CODIF data
More O+ than protons.
Chicken or Egg?
March 18, 2002
Astrophysical Plasmas
• Star and planet forming regions
– Molecular clouds and
protoplanetary disks.
– Lots of dust.
– Wide range of conditions.
• Dust
– negatively charged
– mass >> proton mass.
• Collisions with neutrals
important also.
Hubble Orion Nebula
Panorama
Previous Computational Work
• Birn et al. (2001, 2004)
– Global MHD magnetotail simulations.
– Test particle O+ to examine acceleration and beam
generation.
• Winglee et al. (2002, 2004)
– Global MHD 2-fluid magnetospheric simulations.
– Reduction of cross polar cap potential.
– Did not resolve inner reconnection scales.
• Hesse et al., 2004
– 3-species full particle simulations.
– O+ had no effect on reconnection, although an increase
in proton density did.
– Simulation size not large enough to fully couple O+.
Three-Fluid Equations
•
•
•
•
Three species: {e,i,h} = {electrons, protons, heavy species}
mh* = mh/mi
Normalize: t0 = 1/Wi and L0 = di  c/wpi
E = Ve  B  Pe/ne
ne Ve  ni Vi  zh nh Vh  J and ne  ni  zh nh
n
   n V  ,   {i, h}
t
dVi
ni
ni
 zh nh (Ve  Vh )  B  J  B  Pi  Pe
dt
ne
dVh
zh nh
mh*nh
 zh nh (Vh  Ve )  B  Ph 
Pe
dt
ne
B
   (Ve  B),
t
J  B
Vout
1D Linear waves
X
Vin
Y
-Z
• Examine linear waves
d
– Assume k || Bo
– Compressional modes decouple.
Dispersion Relation
Wh zh nh Wh
w 2 2  Wh  2 2 Wh
2 2
 2


 k ds  
k d s 1 
0
 k ds
3
Wi Wi  ni
Wi ni
Wi
Wi
 Wi
 Wi 
w3
w 2  zh nh
d s2  di ni / ne
Slow Alfven
• w << Wh
• 2nd and 4th terms
w   k cAt
2
B
c 
4  mh nh  mi ni 
2
At
Fast Waves
• w >> Wh, Wi >> Wh
 zh nh
2 2
2 2


k
d

k
ds  0

s 
2
Wi  ni

w2
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
• Previous Astrophysical Work.
• Heavy dust whistler (nh << ni, mhnh >> mini) has been
examined but not in the context of reconnection.
• Shukla et al, 1997.
• Rudakov et al., 2001.
• Ganguli et al., 2004.
ni = 0.05 cm-3
no+/ni = 0.64
Heavy Whistler
di2
ni ne
z z2 nh2
1
dh
dVi
ni
 zh nh Ve  B  J  B  zh nh Vh  B
dt
• Assume:
– Vh << Vi,Ve
– Ignore ion inertia => Vi  Ve
B
  (Ve  B)
t

B
J
  (
 B)
t
zh nh
The Nature of Heavy Whistlers
1.
2.
Heavy species is unmagnetized and almost unmoving.
Primary current consists of frozen-in ions and electrons E B drifting.
Ions+Electron fluid has a small net charge: charge density = e zh nh.
3.
This frozen-in current drags the magnetic field along with it.
Y
Z
-X
Frozen-in Ion/Electron current
Y
Z
-X
D
Effect on Reconnection?
• Dissipation region
– 3-4 scale structure.
• Reconnection rate
– Vin ~ d/D Vout
– Vout ~ CAt
• CAt = [ B2/4(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
Simulations: Heavy Ions
Vin
• Initial conditions:
CA
y
– No Guide Field.
– Reconnection plane: (x,y) => Different from GSM
– 2048 x 1024 grid points
•
•
•
•
•
•
204.8 x 102.4 c/wpi.
Dx = Dy = 0.1
Run on 64 processors of IBM SP.
me = 0.0, 44B term breaks frozen-in, 4 = 5 • 10-5
Time normalized to Wi-1, Length to di  c/wpi.
Isothermal approximation, g = 1
z
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.
Z
– Te = Ti
– Ions and electrons carry
current.
• Background heavy ion species.
nh = 0.64.
Th = 0.5
mh = {1,16,104}
dh = {1,5,125}
• Seed system with x-lines.
• Note that all differences in cAt is
due to mass difference.
Electrons
Ions
Heavy Ions
Z
nVz
–
–
–
–
density
• Harris equilibrium
Z
2-Fluid case
mh* = 1
Z
By with proton flow vectors
• Quadrupolar By
– about di scale size.
• Vix = Vhx
X
Z
Vix with B-field lines.
X
Z
Vhx
X
O+ Case:
mh* = 16
Z
By with proton flow vectors
Light
Whistler
Heavy
Whistler
• Quadrupolar By
– Both light and heavy
whistler.
X
Z
Vix with B-field lines.
• Vi participates in Hall
currents.
• Vhx acts like Vix in twofluid case.
Vhx
Whistler dominated
mh* = 104
By with proton flow vectors
• Quadrupolar By
– System size heavy
whistler.
Vix with B-field lines.
• Vix
– Global proton hall
currents.
• Vhx basically
immovable.
Vhx
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
Slowdown in mh* = 104?
Time
•
System size scales:
Island Width
– Alfven wave: V  cAh
– Whistler: V  k dh cAh
V  dh cAh/L
=> As island width
increases, global speed
decreases.
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
light
whistler
Physical Regions
light Alfven
Z
Vex
Vix
mh* = 1
• Cuts through x-line along
outflow direction.
– Inner regions substantially
compressed for mh* = 104.
– Vix minimum.
X
light
Alfven
light
whistler
heavy
whistler
Z
heavy Alfven
Vex
Vix
Vhx
mh* = 16
X
Z
heavy
whistler
mh* = 104
X
Scaling of Outflow speed
• Maximum outflow speed
– mh* = 1: Vout1  1.0
– mh* = 16: Vout16  0.35
• Expected scaling:
– Vout  cAt
CAt = [ B2/4(nimi + nhmh) ]1/2
• Vout1/Vout16  2.9
• cAt1/cAt16  2.6
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, …
Conclusion
• 3-Species reconnection: New hierarchy of scales.
– 3-4 scale structure dissipation region.
– Heavy whistler
• Reconnection rate
– Vin ~ d/D Vout
– Vout ~ CAt
• CAt = [ B2/4(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.