Radio-Frequency, Optical and Other Properties

Abstract

We discussed the rf and optical properties of a free-electron metal in section 2.5, in terms of the conductivity σ_ω (eqn (2.27)) and the skin depth δ. At room temperature and above, the properties of real metals are described by essentially the same equations, suitably generalized: in (2.27), for example, σ₀ will then be given by (9.13), and τ must be replaced by some suitable average if τ _k varies with k. But in pure metals at low temperatures and high frequencies, the mean free path of the electrons may become large compared with δ, and the treatment of section 2.5 then breaks down. In this section, we look at the behaviour of metals under these ‘anomalous skin effect’ conditions. First, though, we must see how to calculate the current density J produced by a field E when the field is non-uniform.