The quasi-static electromagnetic approximation for weakly conducting media

In a conducting medium dielectric charge and electric field decay with a time constant tau(R) = c/sigma. In a weakly conducting medium, as e.g. glass or melamine-phenolic laminate in use in Resistive Plate Chambers (RPC), this time is about 10(-3) s; so it is long compared to the time the charge cloud needs to move through the gap and to the time the signal needs to propagate through a dielectric to the electrode. A quasi-static theory to deal with transient phenomena in weakly conducting media has been developed in Haus and Melcher (Electromagnetic Fields and Energy, Prentice-Hall, Englewood Cliffs, NJ, 1989), Fano et al. (Electromagnetic Fields, Energy and Forces, Wiley, New York, 1963), Th. Heubrandtner (Dissertation, Technisch-Naturwissenschaftliche Fakultat, Technische Universitat Graz, 1999); it simplifies the analysis considerably since it requires only the solution of a scalar diffusion-type equations in place of the time-dependent Maxwell equations. This little known theory is applied to treat the generation of signals in simple models for chambers with such materials. (C) 2002 Elsevier Science B.V. All rights reserved.