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Nonlinear effects of the trapping of resonant particles by the combinedaction of the electric field and the magnetic mirror force is studied using agyrokinetic description that includes the finite Larmor radius effects. Ageneral nonlinear solution is found that is supported by the nonlinearityarising from the resonant particles, trapped by the combined action of theparallel electric field and the magnetic mirror force. Applying these resultsto the space plasma conditions, we demonstrate that in the magnetosheathplasma, coherent nonlinear magnetic depression may be created associated withthe nonlinear mirror mode and supported by the population of trapped ionsforming a hump in the distribution function. These objects may appear eitherisolated or as the train of weakly correlated structures (the cnoidal wave). Inthe Solar wind and in the Earths magnetopause, characterized with anisotropicelectron and ion temperatures that are of the same order of magnitude, we findcoherent magnetic holes of the same form that are attributed to the twobranches of the nonlinear magnetosonic mode, the electron mirror and the fieldswelling mode, including also the kinetic Alfven mode, and supported by thepopulation of trapped electrons. The localized magnetic holes may have the formof a moving oblique slab or of an ellipsoid parallel to the magnetic field andstrongly elongated along it, that propagates along the magnetic field and maybe convected in the perpendicular direction by a plasma flow. While the ionmirror structures are purely compressional magnetic, featuring negligiblemagnetic torsion and electric field, the magnetosonic and kinetic Alfvenstructures possess a finite electrostatic potential, magnetic compression, andmagnetic torsion, but the ratio of the perpendicular and parallel magneticfields remains small.

Gyrokinetic theory of magnetic structures in high-beta plasmas of the Earths magnetopause and of the slow solar wind