As mentioned in Section 1.1, for a really cold plasma (Tα → 0) the condition (1.1) is no longer valid and all the theory developed in Chapter 1 breaks down. Thus when speaking about cold plasma we will assume that its temperature is so low that the contributions of thermal and relativistic corrections to ∈ij (the terms ∈ijt and ∈ijr in (1.78)) to the process of wave propagation are small when compared with the contribution of ∈ij0, but at the same time this temperature is high enough for condition (1.1) to remain valid. This definition of a cold plasma obviously depends on the type of waves under consideration. The cold plasma approximation allows us to write the dispersion equation for various waves in a particularly simple form and it has been widely used for the analysis of waves (in particular, whistler-mode) in the magnetosphere. Some results of plasma wave theory based on this approximation will be recalled below.

Neglecting the contribution of the terms ∈ijt and ∈ijr in (1.78) we can assume ∈ij = ∈ij0 in the expressions for A, B and C defined by (1.43)–(1.45) and rewrite them as:

where index 0 indicates that the corresponding coefficients refer to a cold plasma approximation; S, R, L and P are the same as in (1.79).