Mathematical modeling of double-frequency operating capacitive coupled low-pressure plasmas

This study investigates the behaviour of a dual-frequency capacitively coupled plasma reactor through a self-consistent computational framework. The model links electrostatic potential, electron density, ion density, and electron temperature by means of four coupled conservation equations that are spatially discretised on a structured grid. The resulting large, sparse algebraic system is balanced with row-column equilibration and solved iteratively using a Newton–Krylov procedure, which promotes rapid convergence without artificial damping. Simultaneous excitation by low and high radio-frequency components allows the algorithm to capture both slow sheath breathing and fast bulk oscillations within a unified temporal loop. Numerical experiments show that the dual-frequency regime suppresses potential corrugations across the electrode surface and yields a more homogeneous current distribution relative to a single-frequency benchmark. The computed source terms also reveal a pronounced sensitivity of ionisation and recombination to local electron temperature, highlighting the need for precise thermal control in reactor design. Qualitative agreement with published Langmuir probe and optical emission measurements confirms the physical fidelity of the approach. The resulting field maps clarify the localisation of potential wells and density peaks, offering a practical metric for predicting surface erosion sites and guiding scale-up of industrial coating systems.