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We propose a novel source of high-power 1–3-THz radiation based on frequency multiplication in a planar gyrotron, with transverse energy extraction. In such a scheme, it is possible to increase significantly the transverse size both of the cavity and of the electron beam, and, correspondingly, the output power at the fundamental harmonic. At the same time, equidistant mode spectrum of a cavity of planar gyrotrons is favorable for generation at high-order cyclotron harmonics in the frequency multiplication regime, providing a much higher efficiency of nonlinear conversion when compared with conventional cylindrical gyrotron schemes. In simulations of a 1-THz planar gyrotron, within the multimode time-domain model, we demonstrate a possibility of kilowatt-level radiation at the second cyclotron harmonic and power of several watts at the third one. The obtained results are partially confirmed based on direct 3-D particle-in-cell (PIC) simulations. [ABSTRACT FROM AUTHOR]