Electromagnetic Fields Due to an Electron Avalanche

In electric power and electronic systems, localized breakdown of air in the form of corona, partial discharge (PD), and electrostatic discharge (ESD) occurs frequently. These processes are known to be sources of electromagnetic fields. Corona on overhead line conductors produces electromagnetic noise over a wide frequency range leading to electromagnetic interference. The magnetic field due to PD can be employed to detect and possibly locate PD inside the apparatus. The fields due to ESD assume importance in designing suitable protection systems. Therefore, there is a need to relate the electromagnetic field produced by the discharge phenomenon to the physical ionization process, which constitutes them. The basic mechanism behind naturally initiated electrical discharges is the electron avalanche and an expression for its total electric field has been derived and validated in the literature. The next step in this direction is to obtain the magnetic field produced by it. An expression for the complete magnetic field, i.e., both near- and far-field components, is derived starting from Lienard-Wiechert potentials. The derived expression is validated with the numerical solution of Maxwell's equation. A simplified procedure to extend avalanche results for practical discharges is demonstrated. Close agreement is obtained between the estimated results and measured results reported in the literature.