In this paper, a compact self-coherent high power microwave source based on dual beams is presented. It consists of a two-cavity triaxial klystron amplifier (TKA) (noted as the outer sub-source below) and a multiwave Cerenkov generators (noted as the inner sub-source) inserted in the TKA's inner conductor. These two sub-sources share a common cathode and the magnetic field. The injected signals to the outer sub-source are leakage microwaves from the inner sub-source through the anode-cathode gap (A-K gap). Particle-in-cell simulation shows that when the diode voltage is 687 kV and the axial magnetic field is 0.8 T, two microwaves with power of 1.02 GW and 2.65 GW and the same frequency of 9.72 GHz are generated in the inner and the outer sub-source, respectively; the corresponding power efficiencies are 24% and 31%. Two sub-sources reach the phase locking at 23 ns with a phase difference fluctuation within 63 . The fast and stable phase locking in the voltage ranging from 665 kV to 709 kV further suggests that the proposed source is promising for coherent power combination and to export a higher power of combined microwaves. V C 2015 AIP Publishing LLC. [http://dx.