Hierarchy of instabilities for two counter-streaming magnetized pair beams

The instabilities triggered when two counter-streaming pair beams collide are analyzed. A guiding magnetic field is accounting for, while both beams are considered identical and cold. The instability analysis is conducted over the full \textbf{k}-spectrum, allowing to derive the hierarchy map of the dominant unstable modes, in terms of the initial beams energy $γ_0$ and a magnetic field strength parameter $Ω_B$. Four different regions of the $(Ω_B,γ_0)$ phase space are identified, each one governed by a different kind of mode. The analysis also unravels the existence of a "triple point", where 3 different modes grow exactly the same rate. A number of analytical expressions can be derived, either for the modes growth-rates, or for the frontiers between the 4 regions.

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