A new Concept of Ball Lightning

We suggest that the ball lightning (BL) is a weakly ionized gas, in which the electromagnetic radiation can be accumulated through the Bose-Einstein condensation and/or the photon trapping in the plasma density well. We derive the set of equations describing the stability of BL, and show that the BL moving along charged surface becomes unstable. Eventually the instability leads to explosion of BL and release of energy of the trapped photons and/or the Bose-Einstein condensate.

💡 Research Summary

The paper puts forward a novel hypothesis that ball lightning (BL) is essentially a weakly ionized plasma sphere in which electromagnetic (EM) energy can be stored for a finite time. Two distinct mechanisms for energy accumulation are proposed. The first is a photon Bose‑Einstein condensate (BEC). The authors argue that, under conditions of sufficiently low temperature and high photon density inside the plasma, photons can acquire an effective mass and occupy a single quantum state, thereby forming a macroscopic coherent condensate that traps EM energy. They present a simple thermodynamic relation between photon number density, energy density, and chemical potential, and claim that when the chemical potential approaches zero the condensate forms. The second mechanism is photon trapping in a plasma density well. Because the electron density (n_e(r)) varies radially, the refractive index (n(r)=\sqrt{1-\omega_p^2(r)/\omega^2}) also varies, creating a potential well for photons. The authors model the density profile as a Gaussian and show that total internal reflection at the high‑density boundary can confine photons in a spherical “photon trap,” allowing the plasma sphere to act as an energy reservoir.

To describe the dynamics of such a BL, the authors write down a coupled set of five nonlinear partial differential equations: the continuity equation for mass, the momentum (Navier‑Stokes‑like) equation including the Lorentz force, an energy equation for the electron temperature, the wave equation for the EM field, and a photon‑number conservation equation for the trapped photons or condensate. They emphasize that when the BL moves along a charged surface (e.g., a region of accumulated atmospheric charge), the surface charge density (\sigma) and the internal electric field (\mathbf{E}) interact, giving rise to an electro‑plasma instability.

A linear stability analysis is performed by perturbing each variable as (\propto \exp(i\mathbf{k}\cdot\mathbf{r}+\gamma t)). The resulting dispersion relation can be written in a compact form:
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