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To enlarge the interaction structure to a feasible dimension and to decrease the required magnetic field to an available strength, the gyrotron devices at THz frequencies must be designed with a high-order-mode interaction, which is weaker in a beam–wave interaction and more susceptible to mode competition. Using the same interaction structure (a circular waveguide) as in the gyrotron traveling-wave amplifier (gyro-TWT), but replacing the axial magnetic field of the gyro-TWT with a tapered helical magnetic field, we found that the gyrating electrons are able to perform strong interaction with the TE11 mode in the THz region. Through an example case, we explored the behavior of the particles and wave fields as in a beam–wave interaction under a modified scheme of the gyro-TWT with a numerical simulation code. The equations required for the simulation are presented. The simulation result of the example case indicates that, through the TE11 beam–wave interaction under the presented scheme, more than one quarter of the beam energy can be converted to the wave at 612.7 GHz and to heat, dissipated on the waveguide wall, of radius 2.5 cm. [ABSTRACT FROM AUTHOR]