For nonlocal thermodynamic equilibrium (LTE), the equations of state are not well defined and therefore the hydrodynamic equations are not applicable. In this case, the general transport equations (e.g., Boltzmann or Fokker–Planck) should be used. However, the coupling between atomic physics (rate equations) and the transport equations is extremely complicated. This article shows how the information given by the rate equations is translated into an effective potential. This “potential” theory is explicitly shown for two cases: lithium-like iron plasmas and aluminum plasmas. Moreover, it is suggested that the “collision terms,” and all other interactions that are not taken into account by the explicit rate equations, are described by a stochastic force given by a Langevin equation or equivalently by a Fokker-Planck equation in the ion density space.
Equations of state for ions in non-LTE plasmas
