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

*

and

, { , }

( )

( )

( ),

e e i i h h h e i h h

i ii h h e h i e

e

h h hh h h h h e h e

e

e

n n z n n n z n

nn i h

td n

n z n P Pdt n

d z nm n z n P P

dt n

t

V V V J

V

VV V B J B

VV V B

BV B J B

• Three species: {e,i,h} = {electrons, protons, heavy species}

• mh* = mh/mi

• Normalize: t0 = 1/i and L0 = di c/pi

• E = Ve B Pe/ne

1D Linear waves

• Examine linear waves– Assume k || Bo

– Compressional modes decouple.

-Z

Y

X

Vin

Vou

t

Dispersion Relation

Slow Alfven

• h

• 2nd and 4th terms

3 22 2 2 2 2 2

3 2

2

1 0

/

h h h h h h h hs s s

i i i i i i i i i

s i i e

z n z nk d k d k d

n n

d d n n

2

2

4

At

Ath h i i

k c

Bc

m n m n

Fast Waves

• h, i >> h

22 2 2 2

20h h

s si i

z nk d k d

n

3-Species Waves: Magnetotail Lengths

• 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.

2 22000kmi e

ih h

n nd

z n800kmi

ie

nd

n 5000kmhd

Heavy Alfve

=

n

Ahk c2

Heavy Whistler

= h Ahk d c

Light A

=

lfven

iAi

e

nk c

n

2

Light Whis

=

tler

ii Ai

e

nk d c

n

Smaller Larger

ni = 0.05 cm-3

no+/ni = 0.64

d = c/p

Heavy Whistler

• Assume:– Vh << Vi,Ve

– Ignore ion inertia => Vi Ve

( ) ( )eh hnt t z

B JV B B

B

hi h hi

h e hz znt

nd

nd

V JB VV

B B

22 2i e

iz h

n ndz n 1 dh

The Nature of Heavy Whistlers1. Heavy species is unmagnetized and almost unmoving.

2. 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.

Z

Y

-X

Frozen-in Ion/Electron current

Z

Y

-X

Effect on Reconnection?• Dissipation region

– 3-4 scale structure.

• Reconnection rate– Vin ~ /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.

VinVout

y

xz

Simulations: Heavy Ions

• Initial conditions:– No Guide Field.– Reconnection plane: (x,y) => Different from GSM– 2048 x 1024 grid points

• 204.8 x 102.4 c/pi.

• x = y = 0.1

• Run on 64 processors of IBM SP.

• me = 0.0, 44B term breaks frozen-in, 4 = 5 • 10-5

• Time normalized to i-1, Length to di c/pi.

• Isothermal approximation, = 1

VinCA

z

xy

Reconnection Simulations• Double current sheet

– Reconnects robustly

• Initial x-line perturbation

X

X X

X

Y

Y

Current along Z Density

t = 0

t = 1200

Equilibrium• Double current sheet

– 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

Z

Z

Jz

Bx

dens

ity Electrons

Ions

Heavy Ions

nVz

2-Fluid case mh* = 1

• Quadrupolar By

– about di scale size.

• Vix = Vhx

By with proton flow vectors

Vix with B-field lines.

Vhx

X

Z

X

Z

X

Z

• Quadrupolar By

– Both light and heavy whistler.

• Vi participates in Hall currents.

• Vhx acts like Vix in two-fluid case.

X

Z

Z

Light Whistler

Heavy Whistler

By with proton flow vectors

Vix with B-field lines.

Vhx

O+ Case: mh* = 16

• Quadrupolar By

– System size heavy whistler.

• Vix – Global proton hall

currents.

• Vhx basically immovable.

By with proton flow vectors

Vix with B-field lines.

Vhx

Whistler dominated mh* = 104

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.

mh* = 1mh* = 16mh* = 104

Reconnection Rate

Island WidthTime

Time

Key SignaturesO+ Case

• 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?

By

Cut through x=55

Cut through x=55

Vel

ocit

y

mh* = 1mh* = 16

proton Vx

O+ Vx

mh* = 16

Z

Z

symmetry axis

X

ZLight Whistler

Heavy Whistler

Physical Regions

• Cuts through x-line along outflow direction.– Inner regions substantially

compressed for mh* = 104.

– Vix minimum.

light whistler

light Alfven

heavy whistler heavy Alfven

Vex

Vix

Vhx

X

X

Z

Z

Z

X

Vex

Vix

light whistler light Alfven

heavy whistler

mh* = 1

mh* = 16

mh* = 104

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 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 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.