Two species Wigner lattice state of unconfined electron-positron plasma and application to the theory of ball lighting

Thunderstorms generates strong flows of 512 keV gamma-rays, indicating that substantial amount of positrons participate in this process. This takes people to an idea that ball lighting is the vortex of electron-positron plasma. The stability of the plasma can be achieved by balancing the attractive Coulomb forces between electron and positron by the kinetic energy and the temperature. The concept of the first order phase transition leading to formation of electron–hole drops in semiconductors is known since 70ies. However, the electron–hole liquid drop has short life time and cannot describe relatively long lived ball lighting. Here I report two–species Wigner crystal solution to the equation of state, which is only possible when positive and negative charges have exactly same mass. The model is valid for all observed ball lighting temperatures; the density of electron–positron pairs in the crystal n ∼ (0.65T/e²)³, ranges from 1.7×10¹⁵cm⁻³ at the room temperature, to 1.7×10²⁰cm⁻³ at 14000C. The annihilation of electron–positron pairs and evaporation of electrons and positrons from the crystal surface set the ball lighting life time. For the above temperature range the estimated life time for typical ball lighting is between few hundreds seconds and few seconds.