Plasma Drift-Diffusion Modeling of Shock Pressure Waves Generated by Streamer Discharge

Streamer discharge in transformer oil initiates shock pressure waves recognized as critical contributors to mechanical failures in oil-immersed transformers. To elucidate the direct link between streamer dynamics and primary shock wave evolution, this work develops a streamer theory using a plasma drift-diffusion model under needle-plane electrode geometry. A novel numerical approach models impulse pressure wave dynamics via volumetric pressure source density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q_{\mathrm{v}}$</tex>. Simulations reveal that shock waves exhibit group-wave behavior, resulting from interference and superposition of subwaves generated by distributed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q_{\mathrm{v}}$</tex> sources along the streamer channel. At initial stages <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(t&lt;300\ \text{ns}), Q_{\mathrm{v}}$</tex> at the streamer tip peaks at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$10^{24}\ \mathrm{s}^{-2}$</tex>. The streamer's directional growth shapes a conical wavefront instead of the conventionally assumed cylindrical symmetry. Wave propagation is further modulated by reflection from electrode interfaces due to acoustic impedance mismatch. Beyond <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t&gt;400\ \text{ns}$</tex>, the wavefront transitions to quasi-spherical propagation through multiple reflections. By elucidating the hydrodynamic genesis and spatiotemporal development of streamer-induced shock waves in oil, the proposed model provides critical guidance for waveform feature extraction in diagnostic applications.