Short dense electron bunches are attractive from the viewpoint to use them for the implementation of powerful and compact radiation source based on the spontaneous mechanism of radiation. The regime of spontaneous radiation is realized, when the bunch phase size is smaller than 2π. Modern photo-injectors insure formation of mildly relativistic dense electron bunches with duration less than 1 ps. Such bunches are “ready” to radiate waves at terahertz frequencies in the spontaneous regime. However, the repulsion of particles caused by a strong Coulomb field inside the dense electron bunch strictly limits the duration of the radiation process due to the increase in the bunch length. We propose two mechanism of cyclotron radiation to solve this problem. The first one is the regime of group synchronism of particles with the radiated wave; in this case compensation of Coulomb repulsion in the phase space takes place. The second proposed solution is to use compression of bunch by radiated electromagnetic fields.