Quasi-linear Zakharov simulations of Langmuir turbulence at rocket altitudes in the auroral ionosphere

A quasi-linear Zakharov simulation model has been constructed to study intense Langmuir waves and precipitating field-aligned electrons observed in the auroral ionosphere at altitudes below 1000 km. This self-consistent model couples the magnetized Zakharov equations to a modified quasi-linear diffusion equation, which includes an advective term describing electrons streaming into the simulation region. Two-dimensional beam-driven simulations demonstrate that for the parameters of the auroral ionosphere below altitudes of 1000 km, Langmuir wave-wave and wave-particle interactions occur on similar timescales. The resulting reduced electron distribution has multiple shoulders and is a result of a balance between quasi-linear beam-flattening, wave-wave instabilities and beam replenishment due to streaming electrons.