Tensor Conductivity in the Ionosphere

180-182The tensor conductivity in the ionosphere was first written by W. G. Baker & D. F. Martin, [Phil. Trans. R. Soc., A246 (1953), 281] as δ = σ1 δij + (σ0- σ1) Bi Bj + σ2 ϵijk Bk where σ0- σ1 and σ2 are parallel, Pederson and Hall conductivities and Bi are the components of the dipole magnetic field in a Cartesian coordinate system. This conductivity has been generalized to include electric fields as well as the intrinsic position vector r. This also gives the components in which the electric and magnetic fields appear together. In any realistic ionosphere system the conductivity should be a function of the electric field besides being an explicit function of r. We have given a general form based on the result of a general theorem proved by N. D. Sen Gupta [Annali Mat. pura appl., Series 4, 68 (1965), 45] on tensors whose elements are functions of vector fields