A unified picture of the parallel whistler mode instability

A parametric investigation of parallel right-hand electromagnetic waves below the electron cyclotron frequency has been carried out; this wave is unstable for anisotropic temperatures if T <T₁. Simple analytic expressions for the maximum growth rate have been obtained for the full range of the parameters β₁, _ and A_ ≡ (T/T₁)_ -1 as they range from zero to infinity. It is shown that the parameter P ≡ β₁_A_(A_+1)² has an important role: (i) for P 1, the results of Kennel & Petschek (1966), for large resonant velocities, hold; (ii) for P 1, the results of Sudan (1963, 1965) for small resonant velocities are recovered; (iii) for P 1 and A 1, the growth rate approaches an upper limit (near the plasma frequency for hot plasmas) identical to the zero field instability of Weibel (1959). For the case P l and moderate A values (i.e. Sudan's regime), analytic expressions for the rates of growth are calculated without restriction on their magnitude.