Nonlinear steepening of inertial Alfvén waves in the ionospheric Alfvénic resonator

Inertial Alfvén waves are thought to accelerate electrons to auroral energies via their parallel electric field in many aurorae generating magnetospheres. During active geomagnetic times, it is estimated that a significant percentage of electron precipitation energy into the Earth's ionosphere can be attributed to these waves. However, self-consistent wave/particle interactions of inertial Alfvén waves with the accelerated electron population are not fully understood. We show that recent self-consistent models have a strong nonlinearity in them which results in a strengthened electric field and stronger particle acceleration. A reduced set of equations which describe this nonlinear steepening is derived and shown to agree with drift-kinetic simulations and other published studies. The physical relevance of this model to Alfvénic precipitation at Earth is considered.