Parametric instability in the expanding solar wind

Recent measurments of Parker Solar Probe show that alfvenic fluctuations in the solar wind often appear in the form of swithcback with constant total magnetic field. Our aim is to understand if and how such fluctuations can contribute to the heating or acceleration of the solar wind, via the Parametric Instability. The intability of one dimensional Alfvénic fluctuations has been extensively studied in both homogenoeus plasma and in the expanding solar wind, less so for the two-dimensional case which is closer to expected three-dimensional nature of switchbacks. In this work we study under which condition an Alfvén wave with a two dimensional spectrum (as introduced in Primavera et al ApJ 2019) can decay in the expanding solar wind and we will present preliminary results.