Abstract:

A plasmoid model for ball lightning is examined. The usual virial theorem shows that confinement by self-field alone is inconsistent with conservation laws for energy and momentum; a generalization shows that the presence of air pressure removes this inconsistency and gives an upper bound to the stored energy. This upper bound is much less than the energies reported for some occurrences. For permissible energies the kinetic temperature and density of the plasma can be chosen so that it will not be degraded by internal Coulomb collisions or dissipated by cyclotron radiation for some seconds. It is however necessary to insulate the plasma from the air. A self-field that is able to do this will give up the total stored energy to ohmic heat in the air boundary in a much shorter time than is reported. It is concluded that the plasmoid model is impossible and that energy must be supplied to the ball during its existence if the order of magnitude of the reported energies and times are accepted. Therefore a new model is examined. The high dc electric fields associated with lightning storms are invoked as energy source, and an idealized nonlinear conduction problem is shown to admit ball-like solutions. This leads to a ball lightning model of a low-current glow discharge in an atmospheric dc field. A region of higher conductivity results in a local increase of the electric field and current density sufficient to produce a glow discharge, which provides the higher conductivity and is thus self-consistent. If this model is appropriate, then ball lightning has no relevance to controlled-fusion plasma research. © 1964 The American Physical Society.