Collisionless damping of parametrically unstable Alfvén waves

Abstract

Linear Vlasov theory and one‐dimensional hybrid simulations are used to study the parametric instabilities of a circularly polarized parallel propagating Alfvén wave in a homogeneous, magnetized, and collisionless plasma. We discuss the linear and the weakly nonlinear development of the instabilities of the Alfvén waves, including kinetic effects, and investigate the structure, the growth, and the damping of the driven ion acoustic‐like waves. The dispersion relation reproduces the fluid characteristics of the instabilities in the case that protons are cold but contains an infinite number of roots in the general case. We show that at low proton plasma βp (βp ≈ 0.1), kinetic effects break the degeneracy of the mode‐coupling solutions of the fluid theory, and we unambiguously identify the growing and the damped modes. We find that contrary to traditional thought, kinetic effects are important even for very low‐βp in the late stages of the linear evolution, leading to a dephasing effect between the plasma pressure and the density fluctuations. The relevance of the results to the experimental identification of the instabilities, to the generation of local turbulence, and to the reduction of cross helicity in the solar wind are pointed out.