Faraday cage profiles giving self-similar charge drift and conduction on and in insulator samples

The well-known Faraday cage method for measuring drift and conduction of charges on and inside insulators works by enclosing the charged specimen in an insulated metal cage, and measures the current induced on the cage as the charge leaks away from the specimen into its grounded supports. However, for Faraday cages shaped by custom or by workshop convenience, it has proven very difficult to analyse the measured current decay curves to get the desired information about the drift and conduction mechanisms. The present work employs a different strategy: to find Faraday cage shapes that lead to self-similar charge decay and simple, analytical formulas for the current decay in terms of charge mobility and conduction. For plane foil specimens these shapes are hyperboloidal, with a 90 degree corner as the simple and very practical limit. In the axially symmetrical cylindrical case the sample is a straight cylinder, the cage profile follows a formula given by the invention, and end effects are avoided