Cyclotron instability of a plasma

In this paper we study the cyclotron instability of a plasma in a magnetic field when the ion distribution function is anisotropic in velocity space. For perturbations in the form of plane waves with various wave vectors k, we determine the values of plasma parameters at which instability appears (that is, the region of instability). Minimum values are found.for the parameter τ = T ⊥i / T ||i characterizing the anisotropy of ion temperatures – that is, the values at which the plasma begins to be unstable. It is shown that the largest region of instability corresponds to. the long waves propagated almost perpendicularly to the external magnetic field. It is established that two conditions must be fulfilled for cyclotron instability to develop in a plasma with cold electrons: T ⊥i / T ||i > 2, ω 0e > ω i /2 (where ω 0e is the plasma frequency of the electrons and ω i the cyclotron frequency of the ions). Heating the electrons improves the stability of the plasma—specifically, by raising the critical value of the parameter T ⊥i / T ||i from which instability appears. The growth rates of unstable solutions are calculated, and from the formulas for these it is evident that cyclotron instability has a resonance character. The waves that oscillate most strongly are those for which ω 0e k z /ω i ( k z 2 + k ⊥ 2 ) ½ ≈ ( n being a whole number).