Charges in non homogeneous dielectrics

If a weakly conducting non homogeneous medium is stressed by an applied field, a charge density ρ builds up in areas where the conductivity σ and/or the permittivity ε are not uniform. The non-uniformity may be constitutional, but may also appear in uniform media, for instance if the temperature is not uniform. This is the case in particular of HVDC cables in which the core is heated by Joule effect while the sheath remains roughly at ambient. For non polar materials with an activation energy of 1 eV in a mean field of 100 kV/cm and a temperature gradient of 50 K/cm, usual in HVDC cables, this generates a charge density which should be measurable by the advanced techniques now available. The build-up of this space-charge obeys an integro-differential equation involving the mean radius at which the field equals the Laplace field. The analytic solution given by Lau [1970] for a conductivity depending on temperature alone is extended to the case where it also increases with the field, and is used to derive the current transient generated in the external circuit by the accumulating charge. Manifestations of the space-charges in question and their potential applications, are mentioned