We study the interaction of the synchrotron radiation, produced by a relativistic particle in a bending magnet, with the electron cloud present in the same magnet. The cloud is described as a collisionless magnetized plasma of very low, but finite temperature. Expressions are derived for the spectral intensity of synchrotron radiation far from the particle, which in absence of a cloud reduce to the Schott spectrum of radiation in vacuum. For typical cloud parameters -a rarefied plasma, we fully

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... neglect the refraction and only take into account the damping of the extraordinary and ordinary plasma waves at frequencies near the first electron cyclotron resonance (wave lengths mm) via interaction with resonance electrons. This effect would be the strongest in the hypothetic case of electron beam and electron cloud, but is found to be weaker in the realistic case of positively charged beam particle (proton, positron). In the latter case, by taking Maxwellian velocity distribution of the electrons (r.m.s. velocity ¡ £ ¢ ¥ ¤ § ¦ ¢ © ) and fully neglecting the ordinary wave (factor ¦ ¢ ), we demonstrate that the dominant effect is coupling of -mode of the spontaneous radiation with the extraordinary plasma wave.