Recent progress in nonlinear kinetic Alfvén waves

Abstract. This paper presents a review of recent progress in nonlinear kinetic Alfvén wave (KAW hereafter). We start with the two-fluid theory of KAWs and show how the difference between the motions of electrons and ions in small-scale fields of KAWs modifies the Alfvén wave properties. Then, we focus on nonlinear solitary structures of KAWs. A general criterion of the existence for solitary KAW (SKAW hereafter) and its exact analytical solution in a low-β plasma (β<m_e/m_i are presented, where the electron drift velocity along the background magnetic field is larger than the thermal speed within a SKAW, and hence can excite, for instance, ion acoustic turbulence as showed by in situ observations of satellites in space plasmas. In consequence, the turbulence results in kinetic dissipation of the SKAW and dynamical evolution in its structure. We further discuss the structure of the dissipated SKAW (DSKAW hereafter) that evolves from the SKAW due to the dissipation. The result shows that the DSKAW has a local shock-like structure in its density profile and a net electric potential drop over the shock-like structure. In particular, the electric potential drop of the DSKAW can be expected to accelerate electrons efficiently to the order of the local Alfvén speed. The application of the DSKAW acceleration mechanism to the auroral electron acceleration is also discussed. Finally, a few perspectives of KAW studies in future are presented.