Validity of 2-D Axisymmetric Simplification in Modeling Microwave Discharges in Waveguide-Based Plasma Sources

Modeling microwave discharges in waveguide-based plasma sources is a complex multiphysics problem involving the intricate interplay of electromagnetic, thermal, and plasma dynamics, which is extremely computational demanding. Previous studies often neglected the rectangular waveguide, focused only on the cylindrical discharge tube, and simplified it further into two-dimensions 2-D by assuming axisymmetry for the microwave and plasma distributions in the discharge tube. However, the validity of the assumption and the simplification remains controversial. To address this issue, this study compares the discharge characteristics between 3-D models and their 2-D axisymmetric simplifications to identify the conditions under which the simplified approach is appropriate and to clarify its limitations. The results indicate that the 2-D axisymmetric models can capture the main features of the 3-D discharge behavior effectively under certain conditions, offering significant computational cost savings. However, deviations become significant when the microwave electric field that sustains discharge breaks axial symmetry. This is evident in glass tubes with either a small thickness or high-permittivity walls that permit the nonaxisymmetric electromagnetic modes. Furthermore, this study introduces a method to enforce axisymmetry in the microwave field and plasma distributions in the discharge tube of a two-port waveguide-based plasma source using coherent wave excitations. The findings of this study can serve as a valuable reference in using the 2-D axisymmetric model to investigate and design other microwave plasma sources (MPSs).