Theoretical Aspects of Kinetic and Inertial Scale Dispersive Alfvén Waves in Earth's Magnetosphere

We present a review of some theoretical aspects of inertial and kinetic scale Alfvén waves in Earth's magnetosphere. The basic elements of two-fluid magnetohydrodynamic theory applied to standing and propagating shear Alfvén waves are discussed, and simple estimates of the phase mixing time, latitudinal phase shift, saturation width and timescale are derived. We consider local and nonlocal aspects of the linear dispersion characteristics of dispersive scale Alfvén waves, and then discuss important nonlinear processes that arise in the presence of shear wave ponderomotive forces. We review the formation of nonlinear density structures, factors affecting their spatial scale, and the temporal dynamics of Alfvén waves excited within them. The process of nonlinear phase mixing is discussed, along with the associated time and spatial scales that lead to fast steepening of Alfvén waves inside density fluctuations associated with nonlinearly excited ion acoustic waves. We show how nonlinear structuring of low-frequency waves can lead to a spatial scale comparable to the electron or ion acoustic gyroradius, and consider the consequences of this in terms of explaining electric field-aligned potential drops that might be responsible for aspects of auroral particle acceleration. We then discuss nonlocal kinetic effects related to electrons that mirror along geomagnetic field lines with bounce times that are shorter than the period of lowfrequency standing waves. The frequency dependence of kinetic scale processes is briefly discussed, and finally, some results of a model describing self-consistent kinetic scale wave-particle interactions in high-frequency waves are presented.