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An ion beam can destabilize Alfv\'en/ion-cyclotron waves andmagnetosonic/whistler waves if the beam speed is sufficiently large. Numericalsolutions of the hot-plasma dispersion relation have previously shown that theminimum beam speed required to excite such instabilities is significantlysmaller for oblique modes with $\vec k \times \vec B_0\neq 0$ than forparallel-propagating modes with $\vec k \times \vec B_0 = 0$, where $\vec k$ isthe wavevector and $\vec B_0$ is the background magnetic field. In this paper,we explain this difference within the framework of quasilinear theory, focusingon low-$\beta$ plasmas. We begin by deriving, in the cold-plasma approximation,the dispersion relation and polarization properties of both oblique andparallel-propagating waves in the presence of an ion beam. We then show how theinstability thresholds of the different wave branches can be deduced from thewave--particle resonance condition, the conservation of particle energy in thewave frame, the sign (positive or negative) of the wave energy, and the wavepolarization. We also provide a graphical description of the differentconditions under which Landau resonance and cyclotron resonance destabilizeAlfv\'en/ion-cyclotron waves in the presence of an ion beam. We draw upon ourresults to discuss the types of instabilities that may limit the differentialflow of alpha particles in the solar wind.

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