Articles | Volume 34, issue 1
Regular paper
 | Highlight paper
19 Jan 2016
Regular paper | Highlight paper |  | 19 Jan 2016

Mapping of steady-state electric fields and convective drifts in geomagnetic fields – Part 1: Elementary models

A. D. M. Walker and G. J. Sofko

Abstract. When studying magnetospheric convection, it is often necessary to map the steady-state electric field, measured at some point on a magnetic field line, to a magnetically conjugate point in the other hemisphere, or the equatorial plane, or at the position of a satellite. Such mapping is relatively easy in a dipole field although the appropriate formulae are not easily accessible. They are derived and reviewed here with some examples. It is not possible to derive such formulae in more realistic geomagnetic field models. A new method is described in this paper for accurate mapping of electric fields along field lines, which can be used for any field model in which the magnetic field and its spatial derivatives can be computed. From the spatial derivatives of the magnetic field three first order differential equations are derived for the components of the normalized element of separation of two closely spaced field lines. These can be integrated along with the magnetic field tracing equations and Faraday's law used to obtain the electric field as a function of distance measured along the magnetic field line. The method is tested in a simple model consisting of a dipole field plus a magnetotail model. The method is shown to be accurate, convenient, and suitable for use with more realistic geomagnetic field models.

Short summary
This paper introduces a new method for mapping electric fields in the magnetosphere along geomagnetic field lines. This is important for conjugate studies of electric fields measured in the ionosphere by SuperDARN radars, and at spacecraft carrying electric field probes. First elementary methods in a dipole field are reviewed and then the theory of of a new method described for general magnetic field models. The method is tested in a dipole model with a Harris magnetotail field.