In this work the intensity of radiation by fast ions in cold plasma is determined. This problem arose in connection with observations made on the OGRA device of resonance peaks of the electric field strength, i.e. at the ion cyclotron frequency and its overtones. Although the above-mentioned observations were made outside the wave zone, it is natural to expect that the experimentally revealed dependence of the number of observed peaks on the density of cold plasma must also be reflected in the intensity of radiation. Calculations showed that, with an increase of the ion velocity and of the plasma density, the maximum of the intensity of radiation actually shifts towards the high frequencies.This shift is analogous to the shift of the maximum of the radiation intensity for synchrotron radiation by an electron which has a velocity approaching the velocity of light. In the case of ions in plasma the role of the velocity of light is played by the phase velocity of the electro-magnetic waves in the plasma. This velocity approaches the Alfvén velocity in the region which is important in the calculations. Therefore, the high overtones already become effective at a comparatively small ion velocity, 0 ∼ cA ≪ c.