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A theoretical model is proposed which describes the influence of non-uniform ionospheric height-integrated conductivity distributions on VLF-pulsations. The assumption is made that the field-aligned currents carried by the wave-field are closed by polarisation currents in the magnetosphere and by the irrotational part of the height-integrated ionospheric currents. Current continuity at the magnetosphere-ionosphere boundary provides for a differential equation governing the reflected electric field for arbitrary non-uniform conductivity distributions. Model calculations for simple, but realistic conductivity and electric field distributions show that local shifts of the ionospheric field maximum against that of the magnetic field below the ionosphere as well as double-peak distributions of the electric field can occur. Strong electric field anomalies i.e. significant deviations of the electric field distribution as compared with the uniform case occur in conductivity gradient zones and fall off rapidly outside. The previously predicted 90° rotation between the magnetic field below and above the ionosphere does not hold generally because the rotation angle depends strongly on the conductivity gradients.
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