Inductive instability in conductors with a moving front of electric conductivity jump

It is shown that motion of the boundary separating regions with different electric conductivities can cause a decrease of the inductance of the conductor. Since the effective damping resistance of the conductor is a sum of the Ohmic resistance and the time derivative of the inductance, the damping resistance can become negative at a certain velocity of the boundary motion. This work studies the effect of the spontaneous excitation of the electric current in heterogeneous conductors due to the rapid decrease of their inductance. Excitation of the instability in various geometries is analyzed using a quasistationary theory, and the velocity of the boundary motion which is required for the excitation of the instability is determined. In the case of an expanding homogeneous cylindrical conductor, an exact analytical solution of Maxwell equations describing spontaneous excitation of the electric current is derived. The exact expression for the threshold velocity coincides with the predictions of the quasistationary theory.