Nonlinear mirror waves in non-Maxwellian space plasmas

A theory of finite-amplitude mirror type waves in non-Maxwellian space plasmas is developed. The collisionless kinetic theory in a guiding center approximation, modified for accounting of the finite ion Larmor radius effects, is used as the starting point. The model equation governing the nonlinear dynamics of mirror waves near instability threshold is derived. In the linear approximation it describes the classical mirror instability that is valid for a wide class of the velocity distribution functions. In the nonlinear regime the mirror waves form solitary structures that have the shape of magnetic holes. The formation of such structures and their nonlinear dynamics has been analyzed both analytically and numerically. It is suggested that the main nonlinear mechanism responsible for mirror instability saturation is associated with modification (flattening) of the shape of the background ion distribution function in the region of small parallel particle velocities. The width of this region is of the order of the particle trapping zone in the mirror hole. Near the mirror instability threshold the saturation arises before its width reaches the ion thermal velocity. The nonlinear mode coupling effects in this approximation are smaller and unable to take control over evolution of the space profile of saturated mirror waves or lead to their magnetic collapse. This results in the appearance of quasi-stable solitary mirror structures having the form of deep magnetic depressions. A phenomenological description of this process is formulated. The relevance of the theoretical results to recent satellite observations is stressed.