Charge balance and ionospheric potential dynamics in time dependent global electric circuit model

Abstract:

We have developed a time-dependent model of global electric circuit (GEC)
in spherical coordinates. The model solves time-dependent charge continuity equation coupled
with Poisson's equation. An implicit time stepping is used to avoid strict dielectric
relaxation time step condition, and boundary conditions for Poisson's equation
are implemented to allow accurate description of time evolution of the ionospheric potential.
The concept of impulse response of GEC is introduced that allows effective representation
of complex time dynamics of various physical quantities in the circuit using
model results obtained for instantaneous deposition of a point charge.
The more complex problems, like continuous charging of thunderstorms and different types
of lightning discharges
are then reconstructed using convolution and linearity principles.
It is shown that for a thundercloud charging phase, typically
represented by a current dipole, the ionospheric potential can be determined from the difference
of time integrals of two ionospheric potential impulse responses
corresponding to charge locations at the opposite ends of the current dipole.
During a cloud to ground lightning discharge,
the ionospheric potential changes instantaneously by a value proportional
to the charge moment change produced by lightning and then relaxes to zero.
We will also discuss processes involving transient conductivity perturbations in GEC associated with
extraterrestrial gamma ray bursts and sprites.