When operated at sufficiently high pressures, inductively coupled plasmas (ICPs) can produce intense gas heating which is useful for a range of applications including materials processing, gas conversion, and analytical chemistry. However, the use of physical measurement probes can be challenging inside ICPs because of the high-temperature plasma-gas environment and diagnostic access may often be limited or perturb the system. Non-invasive diagnostics, such as optical emission spectroscopy (OES), are therefore attractive alternatives but often require an associated mathematical model for complete analysis and interpretation. In this work, we present a collisional-radiative model (CRM) of a radio-frequency (RF) ICP operating with argon gas and terminated with a supersonic nozzle. The two-temperature model considers 20 different charged and neutral particle species, and accounts for important collisional (such as excitation and de-excitation), radiative (including radiation trapping), and diffusive processes. The CRM is coupled to a global plasma discharge model that enables the temperatures and species population densities to be self-consistently determined as a function of ICP operating conditions (such as mass flow rate, RF power, and nozzle size). The coupled model is compared with both a simplified analytical theory and experimental measurements obtained with several non-invasive diagnostics (including OES and electrical circuit probes) showing good agreement. The system is found to be non-equilibrium even near atmospheric pressure conditions, although the model electron temperature is close to the measured argon excitation temperature indicating at least partial local thermodynamic equilibrium between electrons and excited neutral states.
Ammar et al. (2025) studied this question.