Formation mechanism of the atmospheric ball lightning using the triple   Beltrami equation
  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. 
Ana Marcia Alves Taveira, Paulo Hiroshi Sakanaka