Validity criteria for local thermodynamic equilibrium in plasma spectroscopy

Abstract

We have solved the collisional-radiative equations for atomic hydrogen and hydrogenlike ions (of nuclear charges 2 and 26) in a plasma and derived their excited-state populations for a wide range of plasma temperatures and densities. The populations of the higher-lying levels are well described by the Saha-Boltzmann equation. We refer to such plasmas as being in partial local thermodynamic equilibrium (LTE), and it is the purpose of this paper to present expressions by which it is possible to predict the lowest principal quantum number that meets the criterion of being within 10% of its Saha-Boltzmann value. We treat the ionizing plasmas, the recombining plasmas, and the plasmas in ionization balance as three separate cases. These criteria are then extended to the ground state to cover plasmas in complete LTE. Finally we discuss briefly the effect of opacity on these results and the extent to which they may be used for non-hydrogen-like systems. Throughout the paper care is taken to present physical pictures to explain the numerical results and comparisons are made with LTE criteria derived using more qualitative arguments by other authors.