Introduction
The ionosphere is the region where plasma density is maximum
in the Earth's upper atmosphere.
Its altitude ranges almost from 60 to 1000 km.
It acts not only as the reflection or absorption
layer of the radio wave,
but as an electric current layer.
The ionospheric currents cause large part of the variation of the
geomagnetic field,
although most of the geomagnetic field itself is generated by the dynamo
action in the Earth's core.
The currents flow according to the Ohm's law, but the electric
conductivity is anisotropic because of the effect of
the geomagnetic field, and three conductivities are defined.
Those are parallel, Pedersen and Hall conductivities,
and additionally two dimensional conductivity is used for some purposes.
Unit of these conductivities is S/m (=1/(Ωm)),
and that of the height integrated conductivity is S.
Their meanings are as follows:

Relationship between electric field and current in the ionosphere An example of the daytime height profile of the ionospheric conductivity. An example of the daytime height profile of Black, red and blue lines represent Parallel, Pedersen and Hall conductivities, respectively. The conductivity depends on various parameters such as location, time, season and solar activity. For example, the conductivity at night reduces to one severaltenths of that at noon. 
When we take the coordinate in which X is magnetic north and Y is magnetic east, and horizontal electric field is (E_{X}, E_{Y}), current density (j_{X}, j_{Y}) is expressed as: j_{X} = σ_{XX}E_{X} + σ_{XY}E_{Y}where σ_{XX}, σ_{YY} and σ_{XY} are the elements of the two dimensional conductivity. They can be written using σ_{0}, σ_{1} and σ_{2} and geomagnetic dip angle I as follows: σ_{XX} = (σ_{0}*σ_{1})/(σ_{1}*cos^{2}I + σ_{0}*sin^{2}I) In most cases height integrated values (frequently denoted as Σ_{XX}, Σ_{YY} and Σ_{XY}) of σ_{XX}, σ_{YY} and σ_{XY} are used because of the assumption in the derivation. 