Parametric decay of radial Alfvén waves in the expanding accelerating solar wind

Abstract

We study the onset and evolution of the Alfvén wave parametric decay instability within the Accelerating Expanding Box model in the framework of a one‐fluid description of the plasma. As we are interested in understanding wave propagation and dissipation in the inner heliosphere and solar wind, the expansion of the solar wind itself may not be neglected. In this sense, the Accelerating Expanding Box provides a useful and simple model to mimic the effects that the expansion of the underlying atmosphere has on wave propagation and plasma dynamics. In the simulations, we follow the evolution of Alfvén waves along a fast solar wind stream, from the sub‐Alfvénic region up to a maximum heliocentric distance of nearly 4 AU. We consider exact solutions of the compressible MHD system given by circularly polarized Alfvén waves which propagate in the radial direction, along the mean magnetic field. Both monochromatic waves and a nonmonochromatic wave are considered. Monochromatic waves have periods ranging from a few minutes to a few hours, the latter being stabilized by the expansion. The nonmonochromatic wave has a central period of the order of a few minutes, with a broad spectrum containing frequencies near the threshold of the instability. In this case the Alfvén wave partly decays into backward daughter Alfvén waves up to the instability saturation, then giving rise to a nonlinear cascade of incompressible and compressible modes.