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

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?

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

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

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

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.

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

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

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

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 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

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

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

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

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

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

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

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

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

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

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 = [ B2/4p(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.