Magnetic Structures in Electron-scale Reconnection Domain

1. Magnetic Structures in Electron-scaleReconnection Domain Dynamical Processes in Space Plasmas Eyn Bokkek, Israel, 10-17 April 2010 Ilan Roth Space Sciences UC Berkeley, CA Thanks: Forrest Mozer Phil Pritchett

2. Fundamental plasma processes with global implications may occur in a narrow layer Magnetic Reconnection Magnetic shears - electron dominated region What can we learn about electron scale structures without (full) simulations?

3. Symmetric Configuration à la texbook cartoon

4. Classical Symmetric Crossing à la observations- Mozer, 2002 Hall reconnect Hall reconnect

6. Main purpose: assessing the non ideal effects of Ohms Law Environment: electron (current) velocity >> mass velocity Collective plasma scales determine the different (nested) layers: Outer: - Hall effect – ions decouple from B Intermediate: e- inertia (pressure) Inner: break(s) the e- Innermost: frozen-in condition

7. Two Fluid: coupling (B,v) “Ion” fluid Electron fluid

8. Sheared field, Inhomogeneous Plasma General coupling between Shear Alfven Compressional Alfven Slow Magneto-Acoustic modified on short scales by (mainly) electron effects

9. Two (extreme) approaches • Lowest approximation of the electron dynamics + follow ion dynamics • Lowest approximation of the ion dynamics + follow electron dynamics

10. A. Faraday and Ohm’s law couple magnetic and velocity fields MHD: Magnetic field is frozen in the fluid drift

11. Magnetic field – fictitious diagram of lines in R3 satisfying specific rules. MHD – approximate description of magnetic field motion in a plasma fluid. Knot - closed loop of a non-self-intersecting curve, transformed via continuous deformation of R3 upon itself, following laws of knot topology - pushed smoothly in the surrounding viscous fluid, without intersecting itself (stretching or bending). MHD field evolves as a topological transformation of a knot. MHD dynamics forms equivalent knot configurations with a set of knot invariants.

12. All KNOT deformations can be reduced to a sequence of Reidemeister“moves”: (I) twist (II) poke , and (III) slide. Type 3 Type 1 Type 2 Knot topology described through knot diagrams

13. Reidemeister moves

14. Reidemeister moves preserve several invariantsof the knot or link represented by their diagram - topological information. MHD invariants: (cross) helicity, generalized vorticity, Ertel,… Every knot can be uniquely decomposed as a knot sum of prime knots, which cannot themselves be further decomposed - Schubert (1949)

15. Prime knots Characterization based on crossing number – Tait 1877

16. HELIOSPHERE Flux-rope is a KNOT MHD Turbulence forms a LINK- Collection of knots Reconnection is NOT a KNOT: it forms a KNOT SUM

17. MHD (KNOT) can be broken via several physical processes Various physical regions Reconnection: topological transition Diffusion: violation of frozen–in condition Dissipation: conversion of em energy (no consensus on definitions)

18. Parallel electric field is observed in tandem with density gradients Mozer +, 2005 Localized electric field over scale ≤ de=c/ωe – electron inertia effect?

19. Electron diffusion region: filamentary currents on scale ≤ de=c/ωe – dissipation region due to electron inertia effect? ELECTRON PHYSICS COVERS LARGE SPATIAL SCALES.

20. Asymmetric Simulation – Pritchett, 2009 Violation of electron frozen-in condition Elongated Electron Diffusion regions

21. Magnetic field vs Electron Vorticity vs dissipation

22. B. Faraday and Ohm’s law couple magnetic and velocity fields eMHD: Generalized vorticity field is frozen in the electron fluid drift vorticity

23. MHD: “Ion” fluid eMHD: Electron fluid:

24. Homogeneous, incompressible electron fluid Magnetic field slips with respect to the electron fluid Generalized vorticity G is frozen in the electron drift u Electron inertiaHall

25. Inhomogeneous electron fluid

26. Generalized Vorticity – Inhomogeneous fluid Linear homogeneous infinite plasma waves Whistler branch

27. A. Incompressible Homogeneous Plasma; [n(x)=no] Electron inertia effect is manifested on the small spatial scale

28. Inclusion of ion dynamics in the limit Coupling of shear Alfven and compressional Alfven Mirnov+, 2004 eMHD limit:

29. Eigenmodes: two components of the magnetic field bx By=tanh(x/L) de/L=1 Califano, 1999 bz Unstable mode in a whistler regime

30. B. Compressible Homogeneous Plasma Increase in the effective electron skin depth Compressibility - “Guiding” field: enhance the electron inertia effect

31. C. Inhomogeneous, compressible plasma Density dips enhance the electron inertia effect

32. D. Inhomogeneous, compressible plasma – generalized configuration 3D structure may enhance the electron inertia effect

33. E. Kinetic, incompressible, inhomogeneous plasma Attico +, 2002

34. SUMMARY A. MHD satisfies the axioms of knot theory – both evolve preserving various invariants. Knot sum is equivalent to violation of frozen-in condition. B. Density gradients/dips, compressibility, and thermal effects may have a significant effect on the electron vorticity, which determines the slipping of the magnetic field with respect to the electrons. These effects modify the structure of the magnetic field on the short-scale, forming currentfilaments, parallel electric fields, which violate the frozen-in condition and contribute to electron heating. These regions are ubiquitous and are observed outside of the x-points in the reconnection domain.