Presentation on theme: "Magnetic Structures in Electron-scale Reconnection Domain"— Presentation transcript:
1 Magnetic Structures in Electron-scale Reconnection Domain Dynamical Processes in Space PlasmasEyn Bokkek, Israel, April 2010Ilan RothSpace SciencesUC Berkeley, CAThanks: Forrest MozerPhil PritchettElectron compressibility n(x); far from answering all these questions
2 Fundamental plasma processes with global implications may occur in a narrow layerMagnetic ReconnectionMagnetic shears - electron dominated regionWhat can we learn aboutelectron scale structures without (full) simulations?
3 Symmetric Configuration à la texbook cartoon Nonsymmetric!
4 Classical Symmetric Crossing à la observations- Mozer, 2002 HallreconnectHallClassical , large scale; Ey – inductive field;reconnect
7 Main purpose: assessing the non ideal effects of Ohms Law Environment: electron (current) velocity >> mass velocityCollective plasma scales determine the different (nested) layers:Outer: Hall effect – ions decouple from BIntermediate: e- inertia (pressure)Inner: break(s) the e-Innermost: frozen-in conditionElectron diffusion region controls the global structure. Note: resistive time absent NOTE: density fluctuations <d_e
8 Two Fluid: coupling (B,v) “Ion” fluidElectron fluidTwo approaches: simplify electron(ion) fluid and concentrate on ions(electrons)
9 Sheared field, Inhomogeneous Plasma General coupling between Shear AlfvenCompressional AlfvenSlow Magneto-Acousticmodified on short scales by(mainly) electron effectsTwo approaches: simplify electron(ion) fluid and concentrate on ions(electrons)9
10 Two (extreme) approaches Lowest approximation of the electron dynamics + follow ion dynamicsLowest approximation of the ion dynamics + follow electron dynamics
11 A. Faraday and Ohm’s law couple magnetic and velocity fields MHD:Magnetic field is frozen in the fluid driftAlfven vs Whistler(Helicon); few manipulations
12 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.Invatriant of link - + or- .NOTE: MHD Turbulence is a great example for knots
13 All KNOT deformations can be reduced to a sequence of Reidemeister “moves”: (I) twist (II) poke , and (III) slide.Type 3Type 1Type 2Knot topology described through knot diagrams
14 Reidemeister movesInvariants: assign to each crossing specific value, o 1 –1, t and form determinant polynomial
15 MHD invariants: (cross) helicity, generalized vorticity, Ertel,… 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)Diagram- projection of 3D 0n 2D. Link – set of knots. Franz Peter Schubert – composer; Ertel – curlv . Grad s
16 Prime knotsCharacterization based on crossing number – Tait 1877
17 Flux-rope is a KNOT MHD Turbulence forms a LINK- HELIOSPHEREFlux-rope is a KNOT MHD Turbulence forms a LINK-Collection of knotsReconnection is NOT a KNOT:it forms a KNOT SUMSchubert (1949) showed that every knot can be uniquely decomposed (up to the order in which the decomposition is performed) as a knot sum of a class of knots known as prime knots, which cannot themselves be further decomposed. Knots that are the sums of prime knots are known as composite knots.17
18 MHD (KNOT) can be broken via several physical processes Various physical regionsReconnection: topological transitionDiffusion: violation of frozen–in conditionDissipation: conversion of em energy(no consensus on definitions)Topological transition: fields from different regions encounter themselves. Dissipation : < ion skin; diffusion – filamentary current, dens gradients…Interesting physics NOT in reconnection;most energy conversion – to electrons.Important: parts of electron diffusion has also strong currents.
19 Parallel electric field is observed in tandem with density gradients Mozer +, 2005Localized electric field overscale ≤ de=c/ωe – electron inertia effect?
20 Electron diffusion region: filamentary currents on scale ≤ de=c/ωe –dissipation region due to electron inertia effect?ELECTRON PHYSICS COVERS LARGE SPATIAL SCALES.Tangential E field – reconnection rate5. Note” pressure terms scales - ion skin; el inertia – electron skin depth.
21 Electron diffusion found NOT at the null of magnetic field: β<1 Large localized electric field spikes – electron inertia? Small fluctuations in B – large in E; U different from ExBLocalized electric field – scale – electron inertia effect?
22 Asymmetric Simulation – Pritchett, 2009 Violation of electron frozen-in conditionElongated Electron Diffusion regions
26 B. Faraday and Ohm’s law couple magnetic and velocity fields eMHD:Generalized vorticity field is frozen inthe electron fluid driftvorticityAlfven vs Whistler(Helicon); few manipulations26
27 MHD: “Ion” fluid eMHD: Electron fluid: Alfven vs Whistler(Helicon); few manipulations
28 Homogeneous, incompressible electron fluid Magnetic field slips with respect to the electron fluidGeneralized vorticity G is frozen in the electron drift uElectrons can slip with respect to the mag field; the role of Alfven helicon waveElectron inertia Hall
30 Generalized Vorticity – Inhomogeneous fluid Electrons can slip with respect to the mag field; the role of Alfven helicon wave; can add resistivity and viscosityLinear homogeneous infinite plasma wavesWhistler branch
31 The eigenmodes evolve from linear perturbations
32 A. Incompressible Homogeneous Plasma; [n(x)=no] Electron inertia effect is manifested on the small spatial scaleExpress the perturbed velocity with the help of the magnetic field components
33 Inclusion of ion dynamics in the limit Coupling of shear Alfven and compressional AlfvenMirnov+, 2004eMHD limit:Express the perturbed velocity with the help of the magnetic field components33
34 Eigenmodes: two components of the magnetic field bxBy=tanh(x/L)de/L=1bzCalifano, 1999Unstable mode in a whistler regime
43 E. Kinetic, incompressible, inhomogeneous plasma Attico +, 2002
44 SUMMARYA. 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.