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 [PoP \textbf{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 $\theta \in [0,\pi /2]$ 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 ${\gamma }_0$, and the field strength as measured by a parameter denoted $\sigma$. For $\theta =0$, four different kinds of mode are likely to lead the linear phase. The hierarchy simplifies for larger $\theta$'s, partly because the Weibel instability can no longer be cancelled in this regime. For $\theta >0.78$ (44${}^{\circ }$) and in the relativistic regime, the Weibel instability always govern the interaction. In the non-relativistic regime, the hierarchy becomes $\theta$-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.

To appear in Physics of Plasmas

References in corpus (3)

• Exact relativistic kinetic theory of an electron beam-plasma system: hierarchy of the competing modes in the system parameter space
• Collisionless Weibel shocks: full formation mechanism and timing
• Shock formation in electron-ion plasmas: mechanism and timing

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• Density filamentation nonlinearly driven by the Weibel instability in relativistic beam plasmas
• Quantum electrodynamic effects on counter-streaming instabilities in the whole \textbf{k} space