The Many Scales of Collisionless Reconnection in the Earth’s Magnetosphere

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

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

3. Microscale Microscale Microscale The Many Scales of Collisionless Reconnection • A non-exhaustive list Electron Holes Electrons decouple Electrons decouple Electrons Decouple Electrostatic Turbulence (guide field) (fluid case) Pressure tensor, Meandering motion (c/wpe)(cAe/c) re c/wperm Mesoscale Global Scale Guide field No guide field No guide field Solitary x-lines Nearly global Ions decouple Ions decouple O+ decouples scales rs c/wpi c/wpo+ 1 – 4 Re10 – 20 Re

4. Microscale Microscale Microscale The Many Scales of Collisionless Reconnection • A non-exhaustive list Electron Holes Electrostatic Turbulence (c/wpe)(cAe/c) re c/wperm Mesoscale Global Scale No guide field Solitary x-lines O+ decouples rs c/wpi c/wpo+ 1 – 4 Re10 – 20 Re

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

6. 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 By > 0.2

7. 3-D Magnetic Reconnection: with guide field • Particle simulation with 670 million particles • By=5.0Bx, mi/me=100, Te=Ti=0.04, ni=ne=1.0 • Development of current layer with high electron parallel drift • Buneman instability evolves into electron holes Z x

8. 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

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

10. How Large Bz? • By = 5.0 in 3D simulations. • Buneman instability couples with Lower Hybrid wave to produce electron holes: • k ~ pe/(VdCse)1/2 ---  group velocity zero • As By decreases, Vd increases • ky becomes prohibitively small as By ~ 1 • 3D runs too expensive. • Examine 2D runs for electron-ion streams.

11. X-line Structure: Bg = 0, 0.2, 1 z z z Jy Jy Jy z z z

12. Guide Field Criterion • What is the minimum Bg so that the e- excursions are less than de? Reconnection Rate:

13. X-line Distribution Functions Vy Why is this important? Development of x-line turbulence. Why does it happen? Bg means longer acceleration times.

14. 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) • no+ >> ni 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} • mh* = mh/mi • Normalize: t0 = 1/Wi and L0 = di c/wpi • E = Ve B  Pe/ne

15. Vin Vout y x z 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 normalized to lobe proton Alfven speed. • Signatures of reconnection • Quadrupolar Bz out to much larger scales. • Parallel Hall Ion currents • Analogue of Hall electron currents.

16. da = c/wpa Smaller Larger ni = 0.05 cm-3no+/ni = 0.64 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.

17. By with proton flow vectors Z Out-of-plane B • mh* = 1 • Usual two-fluid reconnection. • mh* = 16 • Both light and heavy whistler. • Parallel ion beams • Analogue of electron beams in light whistler. • mh* = 104 • Heavy Whistler at global scales. X Heavy Whistler Z Light Whistler X Z X

18. Reconnection Rate 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.. • Eventually, the heavy whistler is the slowest. mh* = 1mh* = 16mh* = 104 Time Island Width Time

19. symmetry axis Cut through x=55 Key SignaturesO+ Case mh* = 1mh* = 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 proton Vx O+ Vx Velocity Z Heavy Whistler Z Light Whistler X

20. 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, …

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

22. Vin CA z x -y The Simulations • Two fluid simulations • 512 x 64 x 512 grid points, periodic BC’s. • Dx = Dz = 0.1, Dy = (1.0 or 2.0) c/wpi. • Run on 256 processors of IBM SP. • me/mi = 1/25 • w0 = initial current sheet width. • Vary w0 • Initialization: • Random noise • Single isolated x-line Current along y Density Z X X X X

23. Understanding Single X-line Segments • Initially isolated x-line perturbation • w0 strongly affects behavior of the x-line • w0 = 1.0: x-line grows in length very quickly.i w0 = 1.0 Z X

24. Comparing Electron and Ion Velocities • w0 = 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. • Vey ~ J ~ w0-1 • Independent of electron mass. ion velocity vectors Ion end Y X Electron end electron velocity vectors Y X

25. 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.

26. Vin CA z x -y Spontaneous Reconnection: w0 = 2.0 • Initially Random perturbations • Reconnection self-organizes into a strongly 3D process. • Lx , Lz ~ c/wpi • Ly ~ 10 c/wpi • 10 c/wpi  1- 4 Re 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/wpi • Solitary x-lines! Jz greyscale with ion velocity vectors => Reminiscent of a pseudo-breakup or a bursty bulk flow. Y X Z X

27. Spontaneous Reconnection: w0 = 2.0 Jz greyscale with ion velocity vectors • Initially Random perturbations • Reconnection self-organizes into a strongly 3D process. • Lx , Lz ~ c/wpi • Ly ~ 10 c/wpi • 10 c/wpi  1- 4 Re 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/wpi • Solitary x-lines! Y Y => Reminiscent of a pseudo-breakup or a bursty bulk flow. X X Y Y X X

28. Mesoscale 3D: Conclusions • Spontaneous reconnection inherently 3D! • Need Mesoscales: L ~ 10 c/wpi • Global or local energy release • Dependent on w0 => 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. • w0 = 2.0 => Solitary x-line • Length scales • Strong x-line coupled to ions probably has a minimum size • Lz ~ 10 c/wpi ~ 1-4 Re • Consistent with observations!