Similarity rules for inductive radio frequency plasmas with thermohydrodynamic coupling effects

We demonstrate similarity rules for inductively coupled plasmas with thermohydrodynamic coupling effects using two-dimensional fluid simulations and theoretical analyses of the gas flow and heat transfer equations. The results confirm the validity of conventional similarity laws, e.g., the similarity relation for electron density, which can be violated by the nonlinear gas heating effects from exothermic and endothermic reactions. The nonlinear gas heating can obviously perturb the invariance of spatial distributions of the gas flow velocity, resulting in the electron density decreasing nonproportionally with different scaling factors. Adding an external heat source can mitigate the violation of the gas temperature scaling law, thus maintaining the validity of similarity relations to some extent. In addition, two kinds of scaling relations for excited-state argon atoms are identified with and without the consideration of nonlinear collisions.