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Basic properties of radiation of the atomic chains excited by a channeling particle are considered. Using a very simple two-dimensional model of a crystal lattice we have shown that the main part of this radiation is generated on the frequency of oscillations of a channeling particle between the crystal planes, shifted by the Doppler effect. Angular distribution of the radiation of the chain of oscillating atoms is sharply peaked in the direction of the velocity of channeling particle because of coherence of the fields, produced by individual atoms.

The dynamics of a charged relativistic particle in electromagnetic field of a rotating magnetized celestial body with the magnetic axis inclined to the axis of rotation is studied. The covariant Lagrangian function in the rotating reference frame is found. Effective potential energy is defined on the base of the first integral of motion. The structure of the equipotential surfaces for a relativistic charged particle is studied and depicted for different values of the dipole moment. It is shown that there are trapping regions for the particles of definite energies.

The Inverse problem for an electromagnetic field produced by a dipole is solved. It is assumed that the field of an arbitrary changing dipole is known. Obtained formulae allow calculation of the position and dynamics of the dipole which produces the measured field. The derived results can be used in investigations on radiative process in solids caused by changing of the charge distribution. For example, generation of the electromagnetic field caused by oscillations of atoms or electron gas at the trace of a particle channeling in a crystal, or fields arising at solids cracking or dislocation formation -in any case when one is interested in the details of the dipole field source.