Statistical thermodynamics of temperature anisotropy driven Weibel instabilities

A statistical theory of one- and two-dimensional temperature anisotropy driven Weibel instabilities is proposed. The theory is based on a two-temperature canonical distribution and the mean field approximation. It applies to a nonlinear, periodic, charge-neutralized, and collisionless system. Using a partition function formalism, equations of state are derived which predict upper bounds on the magnetic field energy produced by a quasi-static evolution of these instabilities. Theoretical predictions are in good agreement with results from numerical simulations.