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) n o+ >> n i 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 Three species: {e,i,h} = {electrons, protons, heavy ions} m h* = m h /m i Normalize: t 0 = 1/  i and L 0 = d i  c/  pi E =  V e  B   P e /n e

1D Linear waves Examine linear waves –Assume k || B o –Compressional modes decouple. -Z Y X V in V out 

3-Species Waves: Magnetotail Lengths 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. SmallerLarger n i = 0.05 cm -3 n o+ /n i = 0.64 d   = c/  p 

Effect on Reconnection Dissipation region –3-4 scale structure. Reconnection rate –V in ~  /D V out –V out ~ C At C At = [ B 2 /4  (n i m i + n h m h ) ] 1/2 –n h m h << n i m i Slower outflow, slower reconnection. Signatures of reconnection –Quadrupolar B z out to much larger scales. –Parallel Hall Ion currents Analogue of Hall electron currents. V in V out y x z

The Simulations Initial conditions: –No Guide Field. –Reconnection plane: (x,y) => Different from GSM – 2048 x 1024 grid points x c/  pi.  x =  y = 0.1 Run on 64 processors of IBM SP. m e = 0.0,  4  4 B term breaks frozen-in,  4 = Time normalized to  i -1, Length to d i  c/  pi. Isothermal approximation,  = 1 V in CACA y x z

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 –T e = T i –Ions and electrons carry current. Background heavy ion species. –n h = –T h = 0.5 –m h = {1,16,10 4 } –d h = {1,5,125} Seed system with x-lines. Y Y Y JzJz BxBx density Electrons Ions Heavy Ions nV z

Out-of-plane B m h* = 1 –Usual two-fluid reconnection. m h* = 16 –Both light and heavy whistler. –Parallel ion beams Analogue of electron beams in light whistler. m h* = 10 4 –Heavy Whistler at global scales. X X Z Z Z B y with proton flow vectors Light Whistler Heavy Whistler X

Reconnection Rate Reconnection rate is significantly slower for larger heavy ion mass. –n h same for all 3 runs. This effect is purely due to m h.. Eventually, the heavy whistler is the slowest. m h* = 1 m h* = 16 m h* = 10 4 Reconnection Rate Island Width Time

Key Signatures O + Case Heavy Whistler –Large scale quadrupolar B y –Ion flows Ion flows slower. Parallel ion streams near separatrix. Maximum outflow not at center of current sheet. –Electric field? ByBy Cut through x=55 Velocity m h* = 1 m h* = 16 proton V x O + V x m h* = 16 Z Z symmetry axis X Z Light Whistler Heavy Whistler

Outflow shows all 4 wave regions Outflow region –4 different physics regions Maximum outflow speed –m h* = 1: V out1  1.0 –m h* = 16: V out16  0.35 Expected scaling: –V out  c At C At = [ B 2 /4  (n i m i + n h m h ) ] 1/2 –V out1 /V out16  2.9 –c At1 /c At16  2.6 light whistler light Alfven heavy whistler heavy Alfven V ex V ix V hx X Cut through x-line along outflow

Consequences for magnetotail reconnection When n o+ m o+ > n i m i –Slowdown of outflow normalized to upstream c Ai –Slowdown of reconnection rate normalized to upstream c Ai. However: –Strongly dependent on lobe B x. –Strongly active times: c Ai may change dramatically.

Specific Signatures: O + Modified Reconnection O + outflow at same speed as proton outflow. –Reduction of proton flow. Larger scale quadrupolar B y (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, …