Instability Thresholds for Oblique Alfvén/Cyclotron Modes in the Presence of an Alpha Particle Beam

Fully-ionized helium particles are the most abundant particle species after the protons and electrons in the solar wind. Observations of alpha particles in the fast wind show that they typically drift with respect to the protons at a speed of order the Alfvén speed. Since the Alfvén speed in the solar wind decreases with increasing heliocentric distance, the alpha particles undergo a continuous deceleration process. It is thought that this deceleration results from the action of Alfvénic instabilities, which are excited if the alpha particle drift velocity (or "beam speed") and density are sufficiently large. Numerical solutions of the hot plasma dispersion relation have previously shown that the minimum speed required to excite such instabilities is significantly smaller for oblique modes with ěc k× ěc B_0≠q 0 than for parallel-propagating modes with ěc k× ěc B₀₌₀, where ěc k is the wavevector and ěc B₀ is the background magnetic field. In this presentation, we explain this result using analytical theory. We derive the cold-plasma dispersion relation for oblique Alfvén/ion-cyclotron and fast/whistler waves in the presence of an ion beam and discuss the instability thresholds within the framework of quasilinear theory. The dispersion, polarization, energy state, and phase speed of the waves determine the instability thresholds, which are found to be in agreement with observations and nonlinear simulations. We discuss the relevance of this work to alpha particles in the solar wind and its implications as a wave excitation mechanism.; Dispersion and polarization of oblique waves with a relative drift speed of 1.1v_{mathrm A} and an angle of 45^o between ěc k and ěc B₀. The color coding describes the polarization of the waves (+1 is right-handed and -1 is left-handed for positive frequencies). The straight (red) lines show the cyclotron-resonance conditions for alpha particles. The (blue) dashed line represents an upper limit for unstable waves.