Thermodynamic properties of gaseous plasmas in zero-temperature limit

TL;DR

This paper explores the zero-temperature limit of gaseous plasma thermodynamics, revealing a universal stepped structure in equations of state and thermodynamic parameters, linked to ionization energies and providing a foundation for quasi-chemical models.

Contribution

It introduces a detailed analysis of the limiting behavior of plasma thermodynamics at zero temperature, highlighting the universal 'ionization stairs' structure and its implications for plasma modeling.

Findings

Identification of 'ionization stairs' in thermodynamic functions

Discovery of delta-like structures in thermodynamic parameters

Connection to shell oscillations in plasma EOS

Abstract

Limiting structure of thermodynamic functions of gaseous plasmas is under consideration in the limit of low temperature and density. The remarkable tendency, that was claimed previously [High Temp. 19, 799 (1981)], is carried to extreme. In the limit discussed, when temperature and density tend to zero at constant value of electron chemical potential, both equations of state (thermal and caloric) obtain almost identical stepped structure ("ionization stairs") when their special forms being exposed i.e. PV/RT for thermal EOS and (U - 3/2PV) for caloric EOS. At the same time all thermodynamic differential parameters (heat capacity, compressibility, etc.) obtain their remarkable delta-like structures ("thermodynamic spectrum"). This limiting structure appears within a fixed (negative) range of electron chemical potential ("intrinsic energy scale") that is bounded below by value of major ionization potential and above by the value connected with sublimation energy of substance. Binding energies of all possible complexes (atomic, molecular and ionic) in its ground state are the only quantities that manifest itself in meaningful details of this limiting picture as location and value of every step. The limiting stepped structure of gaseous zero-Kelvin isotherm is generic prototype of well-known "shell oscillations" in EOS of gaseous plasmas at low, but finite temperatures and non-idealities. At the same time this limiting form of plasma thermodynamics could be used as a natural basis for rigorous deduction of well-known quasi-chemical approach ("chemical picture") in frames of asymptotic expansion (on temperature, but not density) around this reference system.