## 1. Introduction

[2] Magnetic reconnection in the Earth's magnetotail accelerates fast plasma jets. On the front edge of the earthward propagating jet a discontinuity forms, called the dipolarization front (DF). DFs have a typical scale comparable to the ion inertial length (*c*/*ω*_{pi}). They are characterized by the sharp increase of *Bz*, decrease of density and increase of plasma flow velocity [e.g., *Runov et al.*, 2009]. Strong gradients of *Bz* and density at the DF as well as the pileup of magnetic field behind the DF generate strong DC electric fields as well as electromagnetic waves in a broad frequency range [e.g., *Sergeev et al.*, 2009; *Zhou et al.*, 2009; *Deng et al.* 2010; *Khotyaintsev et al.*, 2011]. DFs are also associated with the acceleration of energetic electrons [e.g., *Fu et al.*, 2011; *Asano et al.* 2010]. Understanding the electric structure of DFs is one of the keys to understanding the DF dynamics and the associated particle acceleration.

[3] According to the generalized Ohm's law [e.g., *Khotyaintsev et al.* 2006],

the convection, **V**_{i} × **B**, Hall, **j** × **B**/*ne*, and electron pressure, ∇ ⋅ P_{e}/*ne*terms all balance the electric field at the sub-proton scale (*L* ≤ *c/ω*_{pi}). The electron inertia term is neglected in equation (1) as it becomes important only at scales comparable to the electron inertial length (*L*∼*c/ω*_{pe}) [e.g., *Birn and Priest*, 2007]. While it is straightforward to compute the convection term from the spacecraft measurements, in order to estimate the Hall and electron pressure terms, one should use some simplifying assumptions. For instance, *Zhou et al.* [2009] and *Zhang et al.* [2011] calculated the current as using single-spacecraft data and assuming constant DF speed. This is reasonable when one is crossing the central part (subsolar point) of a DF, where normal to the DF is along*X*_{GSM} [*Runov et al.*, 2009, Figure 4b] and the largest change is in the *Bz.* However, this assumption clearly does not work at the flank of a DF. *Zhang et al.* [2011] estimated *j*_{y} as a sum of contributions from the bulk ion motion, **E** × **B** drift and the electron diamagnetic current, for which the electron pressure term ∇ ⋅ P_{e} was computed using the two THEMIS probes which are separated mainly in the *Z*_{GSM} direction. This approach works well away from the DF, however, it will not work at the DF where plasma parameters are changing fast during a spacecraft spin period (several sec) which results in unreliable particle moments. Alternatively, one can estimate the current ** j**at a DF using the multi-spacecraft curlometer technique [

*Dunlop et al.*, 1988, 2002], as done for example by

*Schmid et al.*[2011] and

*Hwang et al.*[2011]. This method gives reliable results only in case the current sheet thickness exceeds the separation between the spacecraft, and thus can be applied only to some of the thickest DFs observed by Cluster.

[4] Since computation of ** j** in the previous studies depends on the location of a spacecraft relative to the DF [e.g.,

*Zhou et al.*, 2009;

*Zhang et al.*, 2011] or cannot resolve the small-scale structure of DF [e.g.,

*Schmid et al.*, 2011;

*Zhang et al.*, 2011], we re-compute

**and ∇ ⋅ P**

*j*_{e}using two different techniques: single-spacecraft and multi-spacecraft technique (using 4 Cluster SC), and then compare the results from them. We perform the analysis in the local

*lmn*coordinates, which is valid for both the center (subsolar point) and the flank of DF. Then we use the obtained

**and ∇ ⋅ P**

*j*_{e}to examine which terms in the generalized Ohm's law (equation (1)) balance the electric field throughout the DF.