Regimes of validity for transport models in low-temperature plasmas based on pd and f/p scaling

The validity of commonly used transport models in plasma fluid simulations is assessed through a systematic comparison of drift–diffusion (DD), momentum equation for ions only (ion momentum), and momentum equation for both ions and electrons (full momentum, FM) formulations. One-dimensional, power-controlled simulations of an argon capacitively coupled plasma are performed over a wide range of operating conditions, including pressure, driving frequency, electrode gap, and input power. The study focuses on quantifying the role of electron and ion inertia using the classical scaling parameters pd and f/p. Results show that inertial effects strongly depend on operating conditions. Ion inertia is negligible for f/p<0.2 GHz/Torr and pd>0.2 Torr cm, whereas electron inertia remains significant at low pressures, indicating the need for its inclusion in sub-atmospheric, high-frequency microplasmas. At high f/p, ion inertia becomes increasingly important, while electron inertia contributes up to ∼20% at f/p=50 GHz/Torr. It is also found that electron inertia exhibits a non-monotonic dependence on f/p, remaining significant at low f/p, decreasing over an intermediate range, and increasing again at higher values. In contrast, ion inertia increases gradually with f/p but remains below 20% for pd>0.5 Torr cm. These results establish clear regimes of validity for reduced transport models: DD models are adequate for high-pressure or low-frequency conditions, whereas FM models are required to accurately capture plasma behavior at low pressures and high frequencies.