Coulomb interaction and ionization equilibrium in partially ionized plasmas

Abstract

A recently developed quantum-statistical theory of multicomponent plasmas is applied to a partially ionized gas in thermal equilibrium. The theory is developed on the basis of two different models of the real plasma. From the physical model standpoint the plasma is considered as a system of electrons and singly-charged ions. In the chemical model the plasma is assumed to exist as a mixture of free electrons, free singly-charged ions and neutral atoms in chemical equilibrium. Phenomenological and statistical formulae of the thermodynamic functions are derived for both of these models. Convergent expressions are given for the atomic partition function and the ionization constant. Using this “reduced” ionization constant the Debye—Hückel theory is shown to be valid at temperatures below 50 000 K. The equation of state and the degree of ionization for hydrogen plasmas are studied on the basis of numerical calculations. It is shown that the theory developed on the basis of the chemical model gives reasonable expressions for the pressure and the degree of ionization for a wide range of temperatures and densities.