The ballast resistor; An electro-thermal instability in a conducting wire I; The nature of the stationary states

Abstract

The stationary temperature distributions along a conducting wire, surrounded by a gas, through which a constant electric current is passed, is analysed within the framework of a Hamiltonian formalism. The nature of the inhomogeneous solutions, which occur when the homogeneous solutions become unstable, is discussed in detail taking into account the boundary conditions at the endpoints of the wire.