The Many Scales of Collisionless Reconnection in the Earth’s Magnetosphere Michael Shay – University of Maryland

Collaborators Jim Drake – Univ. of Maryland Barrett Rogers – Dartmouth College Marc Swisdak – Univ. of Maryland Cyndi Cattell – Univ. of Minnesota

The Many Scales of Collisionless Reconnection A non-exhaustive list (c/  pe )(c Ae /c)  e c/  pe  m  s c/  pi c/  po+ 1 – 4 R e 10 – 20 R e Electron Holes Electrons decouple Electrons decouple Electrons Decouple Electrostatic Turbulence (guide field) (fluid case) Pressure tensor, Meandering motion Guide field No guide field No guide field Solitary x-lines Nearly global Ions decouple Ions decouple O+ decouples scales Microscale MesoscaleGlobal Scale

The Many Scales of Collisionless Reconnection A non-exhaustive list (c/  pe )(c Ae /c)  e c/  pe  m  s c/  pi c/  po+ 1 – 4 R e 10 – 20 R e Electron Holes Electrostatic Turbulence No guide field Solitary x-lines O+ decouples Microscale MesoscaleGlobal Scale

Outline 1.Microscale: Electron holes/turbulence/anomalous resistivity. Turbulence and anomalous resistivity. Necessary size of guide field: results imply B z > 0.2 B  2.Micro/Mesoscale: O + modified reconnection New hierarchy of scales. New reconnection physics. 3.Mesoscale: Inherently 3D reconnection, solitary x- lines Asymmetry in x-line growth. Solitary x-lines (1-4 R e ).

I: Electron Holes and Anomalous Resistivity In a system with anti-parallel magnetic fields secondary instabilities play only a minor role –current layer near x-line is completely stable Strong secondary instabilities in systems with a guide field –strong electron streaming near x-line and along separatrices leads to Buneman instability and evolves into nonlinear state with strong localized electric fields produced by “electron-holes” strong coupling to lower hybrid waves –resulting electron scattering produces strong anomalous resistivity and electron heating Will this turbulence persist for smaller guide fields? –From 2D simulations: Conditions are favorable for Buneman for B y > 0.2

Particle simulation with 670 million particles B y =5.0 B x, m i /m e =100, T e =T i =0.04, n i =n e =1.0 Development of current layer with high electron parallel drift –Buneman instability evolves into electron holes 3-D Magnetic Reconnection: with guide field Z x

Anomalous drag on electrons Parallel electric field scatter electrons producing effective drag Average over fluctuations along z direction to produce a mean field electron momentum equation –correlation between density and electric field fluctuations yields drag Normalized electron drag

Drag D y has complex spatial and temporal structure with positive and negative values –quasilinear ideas fail badly D y extends along separatrices at late time D y fluctuates both positive and negative in time. Electron drag due to scattering by parallel electric fields Z x

How Large B z ? B y = 5.0 in 3D simulations. Buneman instability couples with Lower Hybrid wave to produce electron holes: –k ~  pe /(V d C se ) 1/2 ---  group velocity zero –As B y decreases, V d increases –k y becomes prohibitively small as B y ~ 1 3D runs too expensive. Examine 2D runs for electron-ion streams.

X-line Structure: B g = 0, 0.2, 1 zzz JyJy JyJy JyJy z z z

Guide Field Criterion What is the minimum B g so that the e - excursions are less than d e ? Reconnection Rate:

Why is this important? Development of x-line turbulence. Why does it happen? B g means longer acceleration times. X-line Distribution Functions VyVy

II: Three Species Reconnection 2-species 2D reconnection has been studied extensively. Magnetotail may have O + present. –Due to ionospheric outflows: CLUSTER CIS/CODIF (kistler) –n o+ >> n i sometimes, especially during active times. What will reconnection look like? –What length scales? Signatures? –Reconnection rate? Three fluid theory and simulations –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

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 normalized to lobe proton Alfven speed. 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

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 

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

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, …

III: Inherently 3D Reconnection Angelopoulos et al., 1997 Bursty Bulk Flows: Sudden flow events in the magnetotail. Significant variation in convection of flux measured by satellites only 3 R e apart. –E ~ v B = Convection of flux –Slavin et al., 1997, saw variation in satellites 10 R e apart. Reconnection process shows strong 3D variation along GSM y –Mesoscales.

The Simulations Two fluid simulations 512 x 64 x 512 grid points, periodic BC’s.  x =  z = 0.1,  y = (1.0 or 2.0) c/  pi. Run on 256 processors of IBM SP. m e /m i = 1/25 w 0 = initial current sheet width. Vary w 0 Initialization: –Random noise –Single isolated x-line V in CACA z x -y X X X X Z Current along y Density

Initially isolated x-line perturbation w 0 strongly affects behavior of the x-line –w 0 = 1.0: x-line grows in length very quickly. i Understanding Single X-line Segments w 0 = 1.0 Z X

Comparing Electron and Ion Velocities w 0 = 1.0 Electrons initially carry all of the current X-line grows preferentially in the direction of electron flow. X-line perturbation is carried along y by frozen-in electron flow Hall Physics. X-line perturbation has a finite size, so its velocity is the average equilibrium electron velocity. –V ey ~ J ~ w 0 -1 –Independent of electron mass. ion velocity vectors electron velocity vectors X Y X Y Electron end Ion end

Direction of Propagation Magnetotail: Assume something like a Harris equilibrium. –Ions carry most of the current, not electrons. Shift reference frames so the ions are nearly at rest. –X-line segments should propagate preferentially in the dawn to dusk direction: Westward. If auroral substorm is directly linked to reconnection: –Stronger westward propagation during expansion phase. –Consistent with Akasofu, 1964.

Spontaneous Reconnection: w 0 = 2.0 => Reminiscent of a pseudo-breakup or a bursty bulk flow. X X Y Z Initially Random perturbations Reconnection self-organizes into a strongly 3D process. –L x, L z ~ c/  pi –L y ~ 10 c/  pi –10 c/  pi  1- 4 R e in magnetotail X-lines only form in limited regions. –Local energy release –Marginally stable? –Nearly isolated x-lines form. X-line length along GSM y stabilizes around 10 c/  pi –Solitary x-lines! J z greyscale with ion velocity vectors V in CACA z x -y

Spontaneous Reconnection: w 0 = 2.0 => Reminiscent of a pseudo-breakup or a bursty bulk flow. XX XX Y Y Y Y J z greyscale with ion velocity vectors Initially Random perturbations Reconnection self-organizes into a strongly 3D process. –L x, L z ~ c/  pi –L y ~ 10 c/  pi –10 c/  pi  1- 4 R e in magnetotail X-lines only form in limited regions. –Local energy release –Marginally stable? –Nearly isolated x-lines form. X-line length along GSM y stabilizes around 10 c/  pi –Solitary x-lines!

Mesoscale 3D: Conclusions Spontaneous reconnection inherently 3D! –Need Mesoscales: L ~ 10 c/  pi Global or local energy release –Dependent on w 0 => Implications for substorms. Behavior of isolated x-line –Electron and ion x-line “ends” behave differently. –Grows preferentially along electron flow direction. –Equilibrium current the key to understanding behavior. –w 0 = 2.0 => Solitary x-line Length scales –Strong x-line coupled to ions probably has a minimum size L z ~ 10 c/  pi ~ 1-4 R e Consistent with observations!