The concept of large-radius multistage coaxial cyclotrons having separated orbits is described, to generate proton beams of 120-2000 MeV energy at tens of GW pulsed and hundreds of MW in continuous beam power operation. Accelerated beam losses must be less than 0.1 W/m for the intercepted average beam power linear density. The concept is inherently configured to actively compensate the longitudinal and transverse space charge expansion in beam bunches. These are based on (1) actively varying the bunch acceleration equilibrium phase while maintaining isochronism, independently for each cyclotron turns; (2) independently changing the acceleration voltage for each turn together with orbit corrections that preserve isochronism; (3) independently changing the transverse betatron oscillation tune shift, to assure non-resonant operation. Also, (4) sextupole lenses are included to compensate for chromaticity effects. Moreover, the concept is based on optimum uses of practical successful results so far achieved in beam acceleration and storage techniques. This accelerator can be used to deliver a pulsed intense source of neutrons without the use of storage rings, and to drive the different transmutation technologies. As an example of such a cyclotron system, we describe our approach of accelerating single-bunch proton beams at up to 1 GeV energy, with pulsed beam power of 80 GW and bunch duration of 2 ns. The exemplar cyclotron accelerator system is configured to be located in the shielded structure of the 6-GeV Yerevan Electron Synchrotron. The cost of such a cyclotron system is estimated to be approximately 40,000,000 US dollars, if implemented in Armenia at substantially reduced labor costs.