Magnetospheric electric convection field

The impact of the solar wind onto the magnetosphere generates an electric field within the inner magnetosphere (r < 10 a; with a the Earth's radius) - the convection field-. Its general direction is from dawn to dusk. The co-rotating thermal plasma within the inner magnetosphere drifts orthogonal to that field and to the geomagnetic field B_o. The generation process is not yet completely understood. One possibility is viscous interaction between solar wind and the boundary layer of the magnetosphere (magnetopause). Another process may be magnetic reconnection. Finally, a hydromagnetic dynamo process in the polar regions of the inner magnetosphere may be possible. Direct measurements via satellites have given a fairly good picture of the structure of that field. A number of models of that field exists.

A widely used model is the Volland-Stern model

It is based on two simplifying assumptions: first, a coaxial geomagnetic dipole field B is introduced. Its magnetic field lines can be represented by the shell parameter

${\displaystyle L={\frac {r}{a\sin ^{2}\theta }}}$

 

 

 

 

()

with r the distance from the Earth, a the Earth's radius, and θ the co-latitude. For r = a, θ is the co-latitude of the foot point of the line on the ground. L = const is the equation of a magnetic field line, and r = a L is the radial distance of the line at the geomagnetic equator (θ = 90°). Second, it is assumed that the electric field can be derived from an electrostatic potential Φ_c. Since in a highly conducting electric plasma like the magnetosphere, the electric fields must be orthogonal to the magnetic fields, the electric potential shell is parallel to the magnetic shell. The relation

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