The report analyzes the radiation produced by randomly inhomogeneous medium excited by fast particles - transition radiation.

Magnetic field effects on both motion of fast particles and dispersion of background plasma are considered and multiple scattering of fast particles in the medium examined. Various resonant effects arising when the conditions for Cherenkov (or cyclotron) emission of a particular eigenmode are fulfilled are discussed.

The transition radiation intensity and absorption (amplification) coefficients are calculated for ensembles of fast particles with realistic distributions over momentum and angles.

The value of the developed theory of transition radiation is illustrated by applying it to astrophysical objects.

Transition radiation is shown to contribute significantly to the radio emission of the Sun, planets (including the Earth), interplanetary and interstellar media.

Possible further applications of transition radiation (particularly, stimulated one) are discussed.

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