CHAPTER 3
THE MODEL
Hager et al. [6] were the first to use Maxwell's equations to develop a three-
dimensional electric model for a thunderstorm. We first establish the model based
on Maxwell's equations.
3.1 Formulation of the Equations
According to Hager et al. [6], the curl of the magnetic field strength H is given
based on Maxwell's equations:
9E
Vx H = e- + E + J, (3.1)
where e is the permittivity, a is the conductivity, E is the electric field, and J is the
current density associated with the influence of the wind. In this model, we have
the following assumptions:
Assumption 1: The time derivative of the magnetic field is zero, i.e.,
B B_
=0 VxE- 0
> E=V0
Therefore E is the gradient of a potential q.
Assumption 2: Let EB be the breakdown field strength. Then the electric
field magnitude is always less than or equal to the breakdown threshold EB
That is, El < EB.
Assumption 3: When the electric field reaches the breakdown threshold EB at
some point, the conductivity tends to infinity in a small neighborhood at that
point. That is, if IE(x, y, z) = EB, then a(x, y, z) = +oc.