Modern CW or pulsed superconducting accelerators of megawatt beams require efficient RF sources controllable in phase and power. Typically, the costs of the RF sources and their operation are a significant part of the total cost for large-scale projects. The efficiency of the traditional RF sources (klystrons, IOTs, solid-state amplifiers) is lower in comparison to magnetrons and the cost of RF power per Watt is significantly higher. Therefore the magnetron-based controlled in phase and power RF sources could significantly reduce the capital and operation costs of ADS and SNS like projects or, e.g., the Electron-Ion Collider projects unlike the traditional RF sources. Currently, a number of works suggests the use of magnetrons controlled by a resonant injected (injection-locking) RF signal instead of traditional RF sources. We developed a new approach to controlling magnetrons for superconducting accelerators with megawatts beams In the presented work we describe an innovative technique producing the “stimulated” RF generation of magnetrons powered below the self-excitation threshold voltage. This was predicted and substantiated by a recently developed kinetic (electrodynamic) model of magnetron operation. The technique allowing operation in CW and pulse modes has been experimentally verified and studied. It allows stable, controllable in phase and power operation of magnetrons providing efficiency higher than other types of RF power sources. The technique does not require high voltage pulse modulators for a pulsed RF generation. It also looks to be a promising opportunity to improve magnetron reliability and extend life time. Measured characteristics of the developed technique, its experimental verification and verification of the kinetic model briefly presented in the text are discussed in our work.