# The Model

The plasma ball is formed when a lightning stroke induces a circular eddy current in a pocket of plasma adjacent to the lightning channel. As the eddy current absorbs energy from the stroke, it would necessarily exert a back-EMF on the channel, causing a voltage drop across the region. This "bottleneck" in the channel could cause a tremendous amount of energy to become concentrated in the region and transferred to the ball. Just as a large flow of water may result from the breakage of a dam in a river, an enormous current pulse could result when the lightning stroke forces its way past the eddy. A comparable current, approaching one million amperes or more, would be induced in the eddy. The radius of the ball would be comparable to the diameter of the lightning stroke, as one might expect if the currents are comparable. The plasma ball could persist after the lightning stroke has disappeared, if the large magnetic field compresses and stabilizes the plasma. The dense, hot plasma would also be highly opaque, preventing rapid energy loss.

It is often asserted (see Singer) that the virial theorem forbids the existence of a high-energy equilibrium ball of plasma. The assumption of equilibrium is required in the derivation of the virial theorem. Ball lightning (in this model), however, is not an equilibrium system. If one waits until equilibrium is reached, ball lightning ceases to exist. According to Landau and Lifshitz, the emission of radiation indicates that a system is not in equilibrium. Furthermore, an equilibrium system is characterized by periodic coordinates - the magnetic field and current in ball lightning certainly are not periodic. Ball lightning is an isolated system, but isolation is not equivalent to equilibrium. Even if a ball could be sustained by feeding energy into it, this system (like a waterfall) would be in a steady-state, but not in equilibrium, because the total entropy would continually increase. Hence, the virial theorem is inapplicable and nothing prevents the temporary existence of high-energy ball lightning - a conclusion which certainly agrees with observation. Similarly, the virial theorem does not forbid the existence of lightning, because lightning is also not an equilibrium system. The energy and duration of lightning are limited only by the available current. The same is true of ball lightning, which is essentially a circular form of lightning.

Shafranov used a hydrodynamic analogy to show that an external magnetic field is necessary to stabilize an equilibrium ball of plasma containing a ring current. The model presented herein, however, is not a simple ring current, so Shafranov's theorem does not apply.

Previous investigators have assumed that both poloidal and toroidal currents would be necessary for stability using an analogy with a tokamak. The tokamak, however, has a central hole and coils whereas ball lightning does not. Therefore, a more realistic model is needed.

Next: Analysis