Electron distribution function formation in regions of diffuse aurora

The precipitation of high-energy magnetospheric electrons (E \~ 600 eV\textendash10 KeV) in the diffuse aurora contributes significant energy flux into the Earth\textquoterights ionosphere. To fully understand the formation of this flux at the upper ionospheric boundary, \~700\textendash800 km, it is important to consider the coupled ionosphere-magnetosphere system. In the diffuse aurora, precipitating electrons initially injected from the plasma sheet via wave-particle interaction processes degrade in the atmosphere toward lower energies and produce secondary electrons via impact ionization of the neutral atmosphere. These precipitating electrons can be additionally reflected upward from the two conjugate ionospheres, leading to a series of multiple reflections through the magnetosphere. These reflections greatly influence the initially precipitating flux at the upper ionospheric boundary (700\textendash800 km) and the resultant population of secondary electrons and electrons cascading toward lower energies. In this paper, we present the solution of the Boltzman-Landau kinetic equation that uniformly describes the entire electron distribution function in the diffuse aurora, including the affiliated production of secondary electrons (E < 600 eV) and its energy interplay in the magnetosphere and two conjugated ionospheres. This solution takes into account, for the first time, the formation of the electron distribution function in the diffuse auroral region, beginning with the primary injection of plasma sheet electrons via both electrostatic electron cyclotron harmonic waves and whistler mode chorus waves to the loss cone, and including their subsequent multiple atmospheric reflections in the two magnetically conjugated ionospheres. It is demonstrated that magnetosphere-ionosphere coupling is key in forming the electron distribution function in the diffuse auroral region.