The dynamics of current carriers in standing Alfvén waves: Parallel electric fields in the auroral acceleration region

The acceleration of current carriers in an Alfvén wave current system is considered. The model incorporates a dipole magnetic field geometry, and we present an analytical solution of the two‐fluid equations by successive approximations. The leading solution corresponds to the familiar single‐fluid toroidal oscillations. The next order describes the nonlinear dynamics of electrons responsible for carrying a few μAm −2 field aligned current into the ionosphere. The solution shows how most of the electron acceleration in the magnetosphere occurs within 1 R E of the ionosphere, and that a parallel electric field of the order of 1 mVm −1 is responsible for energising the electrons to 1 keV. The limitations of the electron fluid approximation are considered, and a qualitative solution including electron beams and a modified E ∥ is developed in accord with observations. We find that the electron acceleration can be nonlinear, ( v e ∥ ∇ ∥ ) v e ∥ > ω v e ∥ , as a result of our nonuniform equilibrium field geometry even when v e ∥ is less than the Alfvén speed. Our calculation also elucidates the processes through which E ∥ is generated and supported.