Hierarchy of instabilities for two counter-streaming magnetized pair beams: Influence of field obliquity

Abstract

The hierarchy of unstable modes when two counter-streaming pair plasmas interact over a flow-aligned magnetic field has been recently investigated [Phys. Plasmas 23, 062122 (2016)]. The analysis is here extended to the case of an arbitrarily tilted magnetic field. The two plasma shells are initially cold and identical. For any angle θ ∈ [0, π/2] between the field and the initial flow, the hierarchy of unstable modes is numerically determined in terms of the initial Lorentz factor of the shells γ0, and the field strength as measured by a parameter denoted σ. For θ = 0, four different kinds of mode are likely to lead the linear phase. The hierarchy simplifies for larger θ's, partly because the Weibel instability can no longer be cancelled in this regime. For θ > 0.78 (44°) and in the relativistic regime, the Weibel instability always govern the interaction. In the non-relativistic regime, the hierarchy becomes θ-independent because the interaction turns to be field-independent. As a result, the two-stream instability becomes the dominant one, regardless of the field obliquity.