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