Transient electric field and space charge behavior for unipolar ion conduction in liquid dielectrics

Abstract

Many liquid dielectrics, when stressed by high electric fields, support bulk space charge distributions. To model such conduction processes, recent work <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> has used a unipolar ion mobility conduction model similar to that used for solid state semiconductors, where the velocities of charge carriers injected from an emitting electrode are proportional to the electric field and in turn the electric field is related to the charge densities through Gauss's law. Diffusion can be approximately neglected when applied voltages are much greater than the contact potentials. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> This model has been applied to liquid dielectrics in the dc steady state <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> and for small signal perturbations about this steady state. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> Other work performed a heuristic analysis for the transient field and charge behavior with the application of a step current. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> Most of the published analysis has been limited to space charge limited conditions, whereby the electric field at the charge emitting electrode is assumed to be zero.