Energy constraints in ambipolar diffusion

The evolution of a weakly ionized collisional gas produces an energy decay proportional to a moment of the Lorentz force. Although the existence of asymptotic limit states is not guaranteed, if they exist they must be force-free ones. It is proved that in a number of simple geometries and boundary conditions, this limit state is necessarily trivial. Another point concerns the possibility of large transfers between the kinetic and magnetic energies in this process. It is found that the magnetic energy variation is bounded by a constant times the maximum of the velocity, and that both variation rates are bounded by a function of the square root of the total energy variation. Since this is very small for most advanced times, in the limit t→∞t→∞ there is no transfer between the different types of energy: They all tend to become stationary.