Radiation and near field in resistance-inductor circuit transients

Abstract

A full wave solution to the classical problem of a transient response in an RL circuit is analyzed. We show that when radiation effects are rigorously taken into account, the response differs from a familiar exponential decay. The circuit behaves more like an RLC circuit and can exhibit an underdamped response. As a result of a two way energy transfer between the circuit and the near field in the underdamped regime, despite the radiation losses, current decay may be slower than predicted by the standard RL circuit model. During a transient, when retardation effects become important, inductance can no longer be defined as a coefficient of proportionality between the magnetic flux through the circuit and the current in the circuit. If rate of current decay is nearly constant, one can define a time-dependent generalized inductance which turns into conventional inductance after time D/c, where D is the diameter of the current loop. Connection of this generalized inductance with the radiation damping problem is discussed. The theory developed in this paper has been used to analyze ultra wide band radiation observed during a fast laser triggered superconducting to normal transition of a superconducting switch.