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.