Modeling Time-Evolving Electrical Conductivity in Air Ionization Plasma under DC Voltage: A Finite-Difference Time-Domain Approach for Needle-Plate Setup Based on Laboratory Experiments

Abstract

In this paper, we develop a finite-difference time-domain (FDTD) model in which the time-evolving electrical conductivity of the air ionization plasma in DC voltage needed-plate setup is represented. Maxwell’s equations are solved using the FDTD method, and the associated currents and discharge fields are computed over time and in three-dimensional space. The proposed model for the electrical conductivity is dependent on time, the applied DC voltage, and the gap length. The necessary data for developing the proposed model is obtained experimentally using a standard discharge needle, with its spherical tip measuring approximately 40 μm in diameter. Once high voltage is applied, a steady state is achieved. The electrical conductivity σ(t) and its associated parameters are then calculated using nonlinear equations proposed to reproduce the experimentally obtained plasma behavior in the full-wave FDTD model. Voltage ranges from 4 kV to 9 kV, and gap distances are between 4 mm and 8 mm.