Michael Hesse NASA GSFC

Michael Hesse NASA GSFC

Collisionless Magnetic Reconnection: Part 1: Basic force balance in electron diffusion region (guide field example) Part 2: Currents in the electron outflow jet (anti-parallel example) Part 3: Summary Ackn.: S. Zenitani, A. Klimas, J. Birn, and K. Schindler

E How is the parallel electric field generated?

Basic question: Which mechanism balances the parallel electric field acceleration? - - - - E B Parallel E accelerates particles Force balance should involve inertial effects How are these related to the electron dynamics?

Reconnection Evolution

magnetic field and current density Ω i t = 16 z x

Electric Field Equations z B y x At reconnection site E = E y = 1 n e e E = v e B 1 P e m e en e e P xye x + P yze z + P yye y Pressure tensor is candidate v e t m e e + v e v e v ey t + v e v ey Major contributor in anti-parallel reconnection -Vasyliunas, 1975, Hesse et al., 1999; Pritchett, 2001; Ricci et al., 2003; Schmitz and Grauer, 2006

0.1 ~20-80km -0.1 P xye 13.0 13.4 0.1-0.1 P yze relevant z-gradient E y = 1 n e e P xye x + P yze z Hesse et al., 2002, 2004 Ricci et al., 2004 Pritchett, 2005

log F F(v y,v z ) 20 V z /V A -20-20 Note: T > T V y /V A 20 small asymmetry, origin?

Localization of Parallel Electric Field z x E

v z These particles are from below (more E acceleration) and moving up v y These particles are from above (less E acceleration) and moving down

Localization of Parallel Electric Field z x E

F(v x,v y ) log F 20 leaving entering V y /V A -20-20 V x /V A 20 loss of accelerated particles

Concept Reconnection involves a mixing on Larmor scales between accelerated and not (yet) accelerated particles. The diffusion region population is composed of slower particles that have just entered and faster particles, which are about to leave. This means that, in the absence of a reconnection electric field, the current density should evolve diffusively (leading order): Postulate: n e m e v y t κ 2 ( n e m e v ) y κ = L2 τ

The role of the reconnection electric field is to minimize the time change of the current (momentum) density: n e m e v y t en e E y +κ 2 ( n e m e v ) y 0 or: E y 1 en e κ 2 ( n e m e v ) y v ey Consistent with analytical results?

Pressure tensor approximation, leading order: P yze Q P v v 1 xyze xx x y 2 e z y x z Ω Ω Implies: E y1 = 1 P yze en e z 1 en e P xx Ω y 2 v x x 2 v y z 2 Similar argument for P xye

Weak density variation: en e E y 1 2 r v 2 x L x 2 ( n e m e v ) y with: κ = 1 2 r v 2 x L x r L 2 τ c -> The electric field acceleration balances the loss of accelerated particles. -> Scales are electron Larmor radius, typical convection time. -> This process provides effective inertia Hesse, 2006

..emerging picture of diffusion region dynamics Incoming particles: preferentially lower energy, v y Outgoing particles: preferentially higher energy, v y Mixing, acceleration, parallel heating

Super-Alfvenic Electron Outflow Jet

Large Variation of Electron Pressure Component P yze Dissipative?

Electron Flow Velocity Larger Than ExB Note: E y * = E y v ex B z + v ez B x = 1 en P yze z < 0

Electron Fluxes, Bx ~ By

Transform into rotated coordinate system:

Magnetic fields and electron velocities in rotated coordinate system:

Comparison total and convection electric fields:

Force balance in z direction: v ey' B x' = E z + 1 P zze en e z v iy' B x' = E z 1 P zzi en i z v ey' B x' 1 en P zzi z + P zze z

Velocities in the y direction:

Velocities in x direction: Ions and electrons appear coupled

Force balance in x direction: v ey' B z 1 en P x'ze z

Force Balance in x direction: Pressure well matched by gyrotropic model Fit to: p p B 2 B B

SUMMARY - Magnetic reconnection in the presence of a finite B y show dominance of quasi-viscous dissipation in the electron dissipation region - Scale size is Larmor scale ( β e < 1) - Larmor radius-scale mixing leads to nongyrotopic distributions and it provides effective inertia - Mixing likely source of irreversibility - Universality is promising but TBD - Electron outflow jet does not appear to be a dissipative structure - Electron diffusion region identified by E * j = E + v e B ( ) j > 0

Happy Birthday! Russell Kulsrud