Electrothermal instability of a polar polymer dielectric above the glass transition temperature

A stationary temperature state of a polar polymer dielectric exposed to an electric field is studied. A special feature of the dielectrics of this type is the presence of a maximum in the loss factor ε″(T) above the glass transition temperature. Using an approach based on the Kirkwood formula for ε″(T), exact solutions to a nonlinear model problem are obtained. These solutions show the multiplicity of the stationary temperature states and the surface of these states in the “load-ambient temperature” space of parameters exhibits a topological singularity of the “fold” type.