A 670GHz gyrotron with record power and efficiency Appl. Phys. Lett. 101, 153503 (2012) Harmonic mode competition in a terahertz gyrotron backward-wave oscillator Phys. Plasmas 19, 103103 (2012) Effect of ripple taper on band-gap overlap in a coaxial Bragg structure operating at terahertz frequency Phys. Plasmas 19, 092105 (2012) Low-order-mode harmonic multiplying gyrotron traveling-wave amplifier in W band Phys. Plasmas 19, 093103 (2012) The Ka-band 10-kW continuous wave gyrotron with wide-band fast frequency sweep Rev. Sci. Instrum. 83, 074706 (2012) Additional information on Phys. PlasmasThe theory is developed describing how the optimization of gyrotron parameters should be done taking into account two effects deteriorating the gyrotron efficiency: the spread in electron velocities and the spread in the guiding center radii. The paper starts from qualitative analysis of the problem. This simplified theory is used for making some estimates for a specific gyrotron design. The same design is then studied by using more accurate numerical methods. Results of the latter treatment agree with former qualitative predictions. V C 2012 American Institute of Physics.