Consider the physical process that leads to the formation of the corona current
through the neutralization process. The neutralization process takes place when
the channel core changes its potential from cloud to ground value. If this change
is instantaneous, then in principle, the corona decay time constant could be very
small and the shape of the corona current can be replaced by a Dirac delta function.
However, when the ground is finitely conducting, the ground potential cannot be
transferred to the channel faster than the relaxation time of the finitely conducting
ground. Thus the relaxation time limits the rapidity with which the channel potential
can be changed. In other words, the neutralization time and hence the corona
decay time constant depend on the ground conductivity. Assume that the ground is
perfectly conducting. The ground potential cannot then be transferred in a time less
than 10 ns, which is the time necessary for the heating and transfer of electron
energy to the ions and neutrals in the central core. This sets a lower limit to the
value of the corona decay time constant. When the ground is finitely conducting
and the relaxation time is larger than the thermalization time, then the minimum
value of the corona decay time constant, t0, is determined by the relaxation
time. Thus one can write