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The fast solar wind shows a wide spectrum of transverse magnetic and velocityfield perturbations. These perturbations are strongly correlated in the senseof Alfv\'en waves propagating mostly outward, from the Sun to theinterplanetary medium. They are likely to be fundamental to the accelerationand the heating of the solar wind. However, the precise origin of the broadbandspectrum is to date unknown. Typical periods of chromospheric Alfv\'en wavesare limited to a few minutes, and any longer period perturbations should bestrongly reflected at the transition region. In this work, we show that minutelong Alfv\'enic fluctuations are unstable to the parametric instability.Parametric instability enables an inverse energy cascade by exciting severalhours long periods Alfv\'enic fluctuations together with strong densityfluctuations (typically between 1 and $20 R_{\odot}$). These results mayimprove our understanding of the origin of the solar wind turbulent spectrumand will be tested by the Parker Solar Probe.

Parametric decay and the origin of the low frequency Alfv\'enic spectrum of the solar wind