A unified picture of the parallel whistler mode instability

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Abstract
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⊥ 1. 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.