  Evolution of an overpopulated gas of magnons to a Bose-Einstein condensate
and excitation of a magnon supercurrent, propelled by a phase gradient in the
condensate wave function, can be observed at room-temperature by means of the
Brillouin light scattering spectroscopy in an yttrium iron garnet material. We
study these phenomena in a wide range of external magnetic fields in order to
understand their properties when externally pumped magnons are transferred
towards the condensed state via two distinct channels: A multistage
Kolmogorov-Zakharov cascade of the weak-wave turbulence or a one-step
kinetic-instability process. Our main result is that opening the kinetic
instability channel leads to the formation of a much denser magnon condensate
and to a stronger magnon supercurrent compared to the cascade mechanism alone.
