Large-amplitude hydromagnetic waves

We examine several aspects of the theory of large-amplitude hydromagnetic waves and their behavior in the interplanetary medium. We consider the characteristic modes of the full (i.e., nonlinearized) MHD equations and their modification by collisionless and finite-frequency effects. We give special attention to the transverse Alfvén mode, which is undamped and characterized by strictly constant pressure, density, and |B|; this seems to be the predominant propagating fluctuation at 1 AU. We show that its propagation in the small-wavelength (WKB) approximation is essentially identical to that of the small-amplitude Alfvén wave of linearized theory. We also suggest that its presence at 1 AU may provide a natural explanation of the observed power anisotropy of the fluctuations. We use a second-order analysis to study fluctuations that are not characteristic modes. We find that for a small range of propagation directions, and subject to third-order effects, a finite-amplitude wave can exist that is linearly polarized with δB perpendicular to both B0 and k; such a wave can damp nonlinearly. But the situation is different for other directions of propagation, and our analysis suggests a possible explanation for the presence of the transverse Alfvén mode at 1 AU. Our results are used to discuss several possible mechanisms by which hydromagnetic waves may heat the solar wind.