Bi-Directional Energy Cascades and the Origin of Kinetic Alfv\'enic and Whistler Turbulence in the Solar Wind

The observed sub-proton scale turbulence spectrum in the solar wind raises the question of how that turbulence originates. Observations of keV energetic electrons during solar quite-time suggest them as possible source of free energy to drive the turbulence. Using particle-in-cell simulations, we explore how free energy in energetic electrons, released by an electron two-stream instability drives Weibel-like electromagnetic waves that excite wave-wave interactions. Consequently, both kinetic Alfv\'enic and whistler waves are excited that evolve through inverse and forward magnetic energy cascades.