Structure of the Magnetic Reconnection Diffusion Region from Four-Spacecraft Observations

Magnetic reconnection leads to energy conversion in large volumes in space but is initiated in small diffusion regions. Because of the small sizes of the diffusion regions, their crossings by spacecraft are rare. We report four-spacecraft observations of a diffusion region encounter at the Earth's magnetopause that allow us to reliably distinguish spatial from temporal features. We find that the diffusion region is stable on ion time and length scales in agreement with numerical simulations. The electric field normal to the current sheet is balanced by the Hall term in the generalized Ohm's law, $E_n\sim \mathbf{j}\times \mathbf{B}/ne·\widehat{\mathbf{n}}$, thus establishing that Hall physics is dominating inside the diffusion region. The reconnection rate is fast, $\sim 0.1$. We show that strong parallel currents flow along the separatrices; they are correlated with observations of high-frequency Langmuir/upper hybrid waves.

Figure 1

Location of the four Cluster spacecraft (red circle) and the magnetic field lines of the Earth's magnetosphere from the Tsyganenko 2001 model (interplanetary magnetic field IMF in GSE $(B_X,B_Y,B_Z)=(0,7,-2)\mathrm{n}\mathrm{T}$, and solar wind pressure $3.5\mathrm{n}\mathrm{P}\mathrm{a}$ are observed averages from the ACE spacecraft). Assuming that reconnection occurs in regions with antiparallel magnetic fields, the varying IMF $B_Z$ (from $+3$ to $-7\mathrm{n}\mathrm{T}$ within 10 min) is consistent with a diffusion region occurring duskward and tailward of the cusp, as observed by Cluster.

Figure 2

Left: The structure of the diffusion region from a numerical simulation. The magnetic field lines are shown, and the out-of-plane magnetic field is color coded (white is positive and black is negative). Also shown is the projection of the Cluster configuration and the approximate location relative to the diffusion region (C1: black square; C2: red diamond; C3: green circle; C4: blue triangle). Right: Cluster observations; simulation results are shown with gray thick lines. (a) Reconnecting magnetic field component. (b) Out-of-plane magnetic field component. (c) Normal magnetic field component. (d) Electric field normal to the magnetopause, directly observed $E_n$ (solid lines), $\mathbf{j}\times \mathbf{B}/ne·\widehat{\mathbf{n}}$ (dotted lines). (e) Tangential electric field; the average value is about $-1\mathrm{m}\mathrm{V}/\mathrm{m}$. (f) plasma density from the satellite potential. At the bottom the spatial scale obtained from the four-spacecraft magnetopause velocity estimate is given. The observations are consistent with fast collisionless reconnection.

Figure 3

Observations of field-aligned currents and Langmuir/upper hybrid waves at the separatrices. The same time interval as in Fig. 2, for Clusters 2, 3, and 4 the time series have been shifted $-0.09$, $-0.3$, and $+0.55\mathrm{s}$ so that the observations are in the magnetopause frame. (a) Out-of-plane magnetic field component. (b) Current parallel to the magnetic field; the direction is away from the $X$ line. (c) Total spectral density in the frequency range $2–80\mathrm{k}\mathrm{H}z$ (integration from several times the electron gyrofrequency up to several times the electron plasma frequency). (d) Wave spectrum; strong emissions are seen observed near the plasma frequency, $f_p\sim 28\mathrm{k}\mathrm{H}\mathrm{z}$.