  Ball lightning, also known as fire ball, is a luminous globe which occurs in
the course of a thunderstorm. Taking as model of fire ball, the two fluid
plasma consisting of electrons and one species ions, and considering that the
plasma flow is a finite quantity, we can derive the equation of relaxed energy
state, maintaining the helicity constant, in the form of triple
Beltramiequations for the magnetic field: s curl x curl x curl x B + p curl x
curl x B +q curl xB +r B = 0. Where B is the magnetic field s, p, q, and r are
constants to be determined through boundary conditions. This equation is
coupled with an equation which describes the hydrodynamic vortex. The problem
of the formation of an isolated luminous mass in the sky and the moderate
persistence of the resulting form combined with observations of ball lightning
describing hollow globes, surface coronas and rapid rotation led to theories
depicting ball lightning as a vortex. We explore the solutions of this equation
using the method of Chandrasekhar-Kendall eigenfunctions and appropriate
boundary conditions similar, but more extensive, to the description given by
Shukla, Dasgupta and Sakanaka. We will show solutions which might explain the
fire ball configurations.Supported by FAPESP-Fundacao de Amparo a Pesquisa do
Estado de Sao Paulo.
