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

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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?

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Symmetric Configuration à la texbook cartoon

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

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Non-symmetric crossing

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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 Main purpose: assessing the non ideal effects of Ohms Law Environment: electron (current) velocity >> mass velocity

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

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

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

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

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Magnetic field – fictitious diagram of lines in R 3 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 R 3 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.

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

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Reidemeister moves

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Reidemeister moves preserve several invariants of 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)

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Prime knots Characterization based on crossing number – Tait 1877

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

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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)

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Parallel electric field is observed in tandem with density gradients Localized electric field over scale ≤ d e =c/ω e – electron inertia effect? Mozer +, 2005

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

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Electron diffusion found NOT at the null of magnetic field: β<1 Localized electric field – scale – electron inertia effect?

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

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Asymmetric PIC simulation – Pritchett, 2009

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Magnetic field vs Electron Vorticity vs dissipation

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Electron Diffusion vs Dissipation

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

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eMHD: Electron fluid: MHD: “Ion” fluid

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

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Inhomogeneous electron fluid

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

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The eigenmodes evolve from linear perturbations

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A. Incompressible Homogeneous Plasma; [n(x)=n o ] Electron inertia effect is manifested on the small spatial scale

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

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Eigenmodes: two components of the magnetic field Unstable mode in a whistler regime Califano, 1999 B y =tanh(x/L) d e /L=1 bxbx bzbz

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B. Compressible Homogeneous Plasma

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Lowest order : Increase in the effective electron skin depth Compressibility - “Guiding” field: enhance the electron inertia effect

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

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

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

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E. Kinetic, incompressible, inhomogeneous plasma

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Calculation of σ +, σ - requires integration over electron trajectories in an inhomogeneous magnetic field; choose the magnetic field in y (parallel) direction and include both k y and k z.

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For k z =0, n=0

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

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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 current filaments, 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.

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