On 3D Potential Field Solutions for Atmospheric Charge Distributions

Abstract

For atmospheric electricity including space charge we obtain static 3D solutions from quaternion space. From standard functions we calculate regular quaternion potentials val- idated by inductive proofs. We check plots of their iso-surfaces with parametric plots from the inverse function. Quaternion arctangens models thundercloud electriflcation by equi-potential spheres sharing a dipolar ring source. Nested iso-surfaces for space charge converge on this ring as tangent tori. Intersecting iso-surfaces draw circular fleld lines around the same ring as Hopf links. Quaternion inversion converges tangent iso-spheres for space charge on a central dipole source. Its alignment with a uniform fleld plots stable fleld equilibria as for dielectric or paramagnetic spheres. Opposed far and near fleld sources plot cusped iso-surfaces as for the Earth's magne- tosphere or for Meissner states in superconductors. Meissner-type fleld cusps explain why ball lightning usually avoids metallic or dielectric objects.