A model for the formation of the fireball arc or spark discharge, sometimes called a fireball plasma, is developed based on the nonlinearity of the voltage‐current characteristics of a high‐current arc discharge. A nonlinear transmission line equation for the discharge current is obtained which is solved in terms of the Jacobi elliptic functions. Under certain prescribed conditions the current field collapses into a small region. This collapse of the current field is taken to be the fireball. It is additionally pointed out that nonlinearities other than the voltage‐current characteristics of the high‐current arc could produce similar results. Finally, it is suggested that Ball Lightning may have the same origin.