Zero-Dimensional Modeling of a Nanosecond Pulsed Discharge

• Published in: IEEE access 2024, Vol.12, p.157807-157821
• Main Authors: Balmelli, Michelangelo, Farber, Raphael, Soltic, Patrik, Bleiner, Davide, Franck, Christian M., Biela, Jurgen
• Format: Article
• Language: English
• Subjects: Discharges (electric); Electrons; ignition; Integrated circuit modeling; Ionization; Load modeling; Mathematical models; Nanosecond pulsed discharge; non-equilibrium plasma; NPD; Plasma temperature; Plasmas; spark-ignition engines; Sparks; thermal spark; transient plasma; Voltage measurement
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2024.3486583

This article proposes a 0D model for Nanosecond Pulsed Discharges (NPD). The model incorporates the high-frequency transmission line, a lumped equivalent circuit for the load, a two-temperature model for heavy particles and electrons, and an ionization scheme. The load impedance is modeled as a stray capacitance in parallel with a stray inductance and a time-varying electrical resistance, which depends on the plasma radius and electron number density. The ionization mechanism used to simulate the electron number density includes the impact ionization of N2 and O2 and two- and three-body attachments on O2, all dependent on the applied electric field and gas temperature. The temperature variation is calculated using the energy conservation equation, with electrical power as the source. The model is tested against current and voltage measurements of NPDs in sub-mm gaps at pressures ranging from 2 to 8 bar. The comparison of simulation results with experimental data shows that the plasma's electrical resistance rapidly drops to low values within approximately 1-2 ns after breakdown. This drop is attributed to the formation of a fully ionized micrometer-sized thermal spark, a conclusion supported by optical emission spectroscopy measurements. This model is intended for experimental plasma researchers seeking a simple tool to understand plasma states through basic electrical measurements and for electrical engineers needing insights into varying load impedance, a crucial parameter for pulse generator design.