Abstract
Recent analytical studies of ULF electromagnetic fields in the atmosphere are reviewed. These fields have their origin in the discharge of thunderclouds. The problem for a vertical electrical dipole source played in an atmosphere where the conductivity increases exponentially with altitude is described. The analytical expressions for the electric and magnetic field, which vary in time and space, are approximately obtained by a vector potential. It is seen that the amplitudes of the pulse decrease with both increases of the horizontal distance and the gradient of the conductivity. However, the shapes of the pulse are almost constant.
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