The Dispersion Relations and Instability Thresholds of Oblique Plasma Modes in the Presence of an Ion Beam

Abstract

An ion beam can destabilize Alfvén/ion-cyclotron waves and magnetosonic/whistler waves if the beam speed is sufficiently large. Numerical solutions of the hot-plasma dispersion relation have previously shown that the minimum beam speed required to excite such instabilities is significantly smaller for oblique modes with $\vec{k}\times {\vec{B}}_0\ne 0$ than for parallel-propagating modes with $\vec{k}\times {\vec{B}}_0=0$, where $\vec{k}$ is the wavevector and ${\vec{B}}_0$ is the background magnetic field. In this paper, we explain this difference within the framework of quasilinear theory, focusing on low-$\beta$ plasmas. We begin by deriving, in the cold-plasma approximation, the dispersion relation and polarization properties of both oblique and parallel-propagating waves in the presence of an ion beam. We then show how the instability thresholds of the different wave branches can be deduced from the wave--particle resonance condition, the conservation of particle energy in the wave frame, the sign (positive or negative) of the wave energy, and the wave polarization. We also provide a graphical description of the different conditions under which Landau resonance and cyclotron resonance destabilize Alfvén/ion-cyclotron waves in the presence of an ion beam. We draw upon our results to discuss the types of instabilities that may limit the differential flow of alpha particles in the solar wind.

12 pages, 10 figures

References in corpus (3)

• Kinetic cascade beyond magnetohydrodynamics of solar wind turbulence in two-dimensional hybrid simulations
• Weakly Turbulent MHD Waves in Compressible Low-Beta Plasmas
• Parametric decay of oblique Alfvén waves in two-dimensional hybrid simulations

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• Microinstabilities in the Transition Region of Weak Quasi-Perpendicular Intracluster Shocks
• Magnetohydrodynamic Slow Mode with Drifting He${}^{++}$: Implications for Coronal Seismology and the Solar Wind
• Effects of electron drift on the collisionless damping of kinetic Alfvén waves in the solar wind
• The Wave Energy Density and Growth Rate for the Resonant Instability in Relativistic Plasmas
• Unveiling the Velocity-Space Signature of Ion Cyclotron Damping Using Liouville Mapping