Tensor Conductivity in the Ionosphere

Abstract

The tensor conductivity in the ionosphere was first written by W. G. Baker &amp; D. F. Martin, [<i>Phil. Trans. R. Soc., </i>A246 (1953), 281] as δ = σ₁ δ<i>_ij </i> + (σ₀- σ₁) <i>B_i B_j </i> + σ₂<i> ϵ_ijk B_k </i> where σ₀- σ₁ and σ₂ are parallel, Pederson and Hall conductivities and <i>Bi </i> are the components of the dipole magnetic field <i>in </i> 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 <i>[Annali Mat. pura appl., </i> Series 4, 68 (1965), 45] on tensors whose elements are functions of vector fields.