THE DISPERSION RELATIONS AND INSTABILITY THRESHOLDS OF OBLIQUE PLASMA MODES IN THE PRESENCE OF AN ION BEAM

Abstract

An ion beam can destabilize Alfv\\'en/ion-cyclotron waves and\nmagnetosonic/whistler waves if the beam speed is sufficiently large. Numerical\nsolutions of the hot-plasma dispersion relation have previously shown that the\nminimum beam speed required to excite such instabilities is significantly\nsmaller for oblique modes with $\\vec k \\times \\vec B_0\\neq 0$ than for\nparallel-propagating modes with $\\vec k \\times \\vec B_0 = 0$, where $\\vec k$ is\nthe wavevector and $\\vec B_0$ is the background magnetic field. In this paper,\nwe explain this difference within the framework of quasilinear theory, focusing\non low-$\\beta$ plasmas. We begin by deriving, in the cold-plasma approximation,\nthe dispersion relation and polarization properties of both oblique and\nparallel-propagating waves in the presence of an ion beam. We then show how the\ninstability thresholds of the different wave branches can be deduced from the\nwave--particle resonance condition, the conservation of particle energy in the\nwave frame, the sign (positive or negative) of the wave energy, and the wave\npolarization. We also provide a graphical description of the different\nconditions under which Landau resonance and cyclotron resonance destabilize\nAlfv\\'en/ion-cyclotron waves in the presence of an ion beam. We draw upon our\nresults to discuss the types of instabilities that may limit the differential\nflow of alpha particles in the solar wind.\n