Simulation and Modeling of Prompt Electrical Tree Formation During Dielectric Breakdown in Space-Charged Dielectrics

Electrical treeing is a principal degradation mechanism in polymeric dielectric material bombarded with charged particles. Such bombardment occurs when the material is exposed to space radiation environments. Treeing occurs during the rapid evacuation of charges that are embedded in the material and often culminates in catastrophic equipment failure. This article outlines the development and validation of a novel simulation model to depict electrical tree discharge within a dielectric polymethyl methacrylate block, but this model provides predictive power for any similar dielectric material. Dielectric materials have advantageous insulating properties and are crucial for aerospace applications, but the possibility of discharge failure due to electrical treeing poses a substantial risk to in-flight equipment. It jeopardizes expensive equipment, mission objectives, and the safety of any on-board crew. This article utilizes insights from novel imaging techniques that reveal characteristics of electrical treeing, such as the speed and development of the erosion wavefront and the speed at which the detrapped charge evacuates the material. A geometric model and an RLC model are proposed to model this observed behavior, and a stochastic model for the development of the Lichtenberg figure (LF) that incorporates these insights is presented and compared with the experimental results, validating the model with an ${R}^{{2}}$ value of 0.93 and highlighting areas for future development.