### NITheP cordially invites you to a seminar by:

### Professor Dave Walker

### School of Chemistry and Physics, UKZN

### Dates: Friday, 23October 2015

Time: 11h30 – 12h30

Venue: NITheP Seminar Room, H-Block, 3rd Floor

### Title: Electric field mapping in geomagnetic field models

In magnetospheric plasmas the conductivity parallel to the field lines is effectively infinite. As a consequence the field lines coincide with electric equipotentials: all electric fields are normal to magnetic field lines. A consequence of this is that, in principle, electric fields can be mapped along magnetic field lines by using Faraday’s law. SuperDARN radars such as the South African radar at Sanae Antarctica measure electric fields in the ionosphere over a large geographic region. It is important to be able to compare these fields with those in the conjugate hemisphere or at the position of conjugate spacecraft. The usual method of estimating the electric field involves tracing magnetic field lines from one location to a conjugate point and to use their potential difference and their calculated separation to estimate the electric field. This is a crude numerical differentiation involving the small differences of large quantities and is inherently inaccurate. We describe a new accurate method that has been developed to compute the electric fields. Our method finds analytic expressions for the spatial derivatives of the magnetic field. These form a second rank tensor – the magnetic gradient tensor – which is used to deduce three simultaneous first order differential equations for the components of the normalized elementary field separation between two closely separated field lines. This must be done for two different directions of separation. There are thus nine simultaneous first order differential equations to be integrated: three for the field line coordinates, and three for the components of each of the separations. From this Faraday’s law can be used to find the covariant components of the electric field. From these, in turn, the contravariant components and hence the resultant electric field can be found at each point along the field line trace. A Python package has been developed to carry out this process for the International Geomagnetic Reference Field (IGRF), a spherical harmonic representation of 13th order and 13th degree of the geomagnetic field. A variety of tests have been carried out to confirm the accuracy of the method. The next stage will be to add routines to incorporate the Tsyganenko model of the external field. The validity of using external field models for electric field mapping at times of high magnetic activity will be discussed. It is intended that a Python package for the complete model will eventually be made available to the SuperDARN community.

Coffee and biscuits will be served before the talk