Numerical study on EOS of lightning return stroke channels and its application in lightning discharge simulations

In previous work [Phys. Plasmas 21, 032901 (2014), Q. Chen et al.], a two dimensional Eulerian finite difference code was developed for solving the non-ideal magnetohydrodynamics (MHD) equations including the effects of self-consistent magnetic field, thermal conduction, resistivity, gravity, and radiation transfer, which when combined with specified pulse current models and plasma equations of state (EOS), can be used as a unified lightning return stroke solver. In this work a detailed EOS model of lightning return stroke channels is introduced, which can be equipped in the lightning return stroke solver conveniently. The partition functions, including excited states, for nitrogen and oxygen separately are calculated. The Coulomb interaction between charged particles are introduced based on the Debye-Huckel theory. The nonlinear Saha equations are solved by a specified iteration method. The comparison between the numerical results and the SESAME database shows a good consistency. With the new EOS model a class of numerical tests are implemented, which show its effective and robust.