1. Three Species Collisionless Reconnection: Effect of O+ on Magnetotail Reconnection
Michael Shay – Univ. of Maryland
Preprints at:

2. Overview 3-species reconnection Examples and background
What length scales?
Signatures?
Reconnection rate?
Examples and background
Linear theory of 3-species waves
3-Fluid simulations

3. Magnetospheric O+ March 18, 2002 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?

4. 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

5. 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+.

6. 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

7. 1D Linear waves Examine linear waves Assume k || Bo
Vin
Vout d -Z Y X
Examine linear waves
Assume k || Bo
Compressional modes decouple.

8. Dispersion Relation Slow Alfven w << Wh 2nd and 4th terms
Fast Waves
w >> Wh, Wi >> Wh

9. 3-Species Waves: Magnetotail Lengths
Smaller
Larger
ni = 0.05 cm-3 no+/ni = 0.64
da = c/wpa
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.

10. Heavy Whistler 1 dh Assume: Vh << Vi,Ve
Ignore ion inertia => Vi  Ve

11. The Nature of Heavy Whistlers
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.
This frozen-in current drags the magnetic field along with it. Z Y -X
Frozen-in Ion/Electron current Z Y -X D

12. 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 y x z

13. Simulations: Heavy Ions
Vin CA z x y
Initial conditions:
No Guide Field.
Reconnection plane: (x,y) => Different from GSM
2048 x 1024 grid points
204.8 x 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

14. Reconnection Simulations
Double current sheet
Reconnects robustly
Initial x-line perturbation
Current along Z
Density Y
t = 0 X X Y
t = 1200 X X

15. Equilibrium Bx Jz density nVz Double current sheet Harris equilibrium
Double tearing mode.
Harris equilibrium
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. Z
Electrons
density
Ions
Heavy Ions Z
nVz Z

16. 2-Fluid case mh* = 1 Quadrupolar By Vix = Vhx about di scale size.
By with proton flow vectors Z
Quadrupolar By
about di scale size.
Vix = Vhx X
Vix with B-field lines. Z X
Vhx Z X

17. O+ Case: mh* = 16 Quadrupolar By Vi participates in Hall currents.
By with proton flow vectors Z
Heavy Whistler
Light Whistler
Quadrupolar By
Both light and heavy whistler.
Vi participates in Hall currents.
Vhx acts like Vix in two-fluid case. X
Vix with B-field lines. Z
Vhx

18. Whistler dominated mh* = 104
By with proton flow vectors
Quadrupolar By
System size heavy whistler.
Vix
Global proton hall currents.
Vhx basically immovable.
Vix with B-field lines.
Vhx

19. 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..
Slowdown in mh* = 104?
System size scales:
Alfven wave: V  cAh
Whistler: V  k dh cAh
V  dh cAh/L
=> As island width increases, global speed decreases.
Reconnection Rate
mh* = 1 mh* = 16 mh* = 104
Time
Island Width
Time

20. Key Signatures O+ Case Heavy Whistler Cut through x=55
symmetry axis
Key Signatures O+ Case
Cut through x=55
mh* = 1 mh* = 16 By
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? Z
Cut through x=55
mh* = 16
Velocity
proton Vx O+ Vx Z
Heavy Whistler Z
Light Whistler X

21. Physical Regions Cuts through x-line along outflow direction.
light whistler
Physical Regions
light Alfven Z
mh* = 1
Vex Vix
Cuts through x-line along outflow direction.
Inner regions substantially compressed for mh* = 104.
Vix minimum. X
light Alfven
light whistler
heavy whistler
heavy Alfven Z
Vex Vix Vhx
mh* = 16 X
heavy whistler Z
mh* = 104 X

22. Scaling of Outflow speed
Maximum outflow speed
mh* = 1: Vout1  1.0
mh* = 16: Vout16  0.35
Expected scaling:
Vout  cAt CAt = [ B2/4p(nimi + nhmh) ]1/2
Vout1/Vout16  2.9
cAt1/cAt16  2.6

23. 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.

24. 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.

25. 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, …

26. 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 = [ B2/4p(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.