Viability of the Harmonic Balance Method for Low-Temperature Plasma Modeling

Harmonic Balance (HB) is a popular alternative to Time-Marching (TM) for solving periodic solutions to nonlinear dynamical systems. While HB has been successfully applied to a range of dynamical systems, such as nonlinear circuits, structural dynamics, fluid flow, and semiconductor electron-hole dynamics, its application to Low Temperature Plasma (LTP) discharges has not been explored until now. In this work, we present the first successful application of HB to model a 1D RF LTP discharge and benchmark the results against those obtained via TM. We investigated three cases with varying discharge gap sizes, RF electrode frequencies, and ambient pressures. HB solutions for different numbers of harmonics are compared to two TM solutions (with different time-step sizes) for each case. The results show that HB reduces CPU times by factors of 16.6 to 31.9 and 7.9 to 19.3 times, respectively. This study demonstrates that HB is a promising method for significantly speeding up highly nonlinear LTP simulations relevant to industrial plasma processing reactors.