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A New Integrated Approach for Fast Intrinsic Dielectric Breakdow

Rui FM Lobo* and Lucas M Alves

A non-equilibrium phenomenological description for a complete dielectric breakdown sequence in perfect solid electric insulators, from the dynamics of instability to the growth of branching patterns, is implemented. It represents an original treatment which allows overcoming the current lack of such a complete physical description, involving thermodynamics, and in particular equations on maximum dissipation energy for dielectric breakdown are developed. From the assumption that there is a time delay in the energy rates and propagation speeds between the system input and output, a principle of maximum energy dissipation is postulated and corresponding dynamic evolution equations were obtained. It is shown that the delay in those speeds gives rise to the appearance of iterated equations which in turn leads to the logistic maps describing the dynamic evolution of the system. The results can describe the instability process along with dissipation patterns formation. The vast theoretical and experimental analogies between mechanical fracture and dielectric rupture, lead us to foresee the potential applicability of this model in the prediction of dielectric rupture patterns. This work opens then the possibility to predict the consequent branching patterns by using a maximum energy dissipation principle, contributing in a significant way for energy efficiency engineering.