A nonlinear analysis of the wave–particle interaction in the output cavity of a frequency‐doubling magnicon amplifier is presented. The cavity is immersed in an axial magnetic field, wherein electrons interact with a rotating TM210mode via a gyroresonant mechanism. The electron equations of motion and the wave equation for the radio‐frequency (rf) field are derived and expressed in terms of scaled variables in order to study the general scaling of the output cavity. Single‐electron, time‐dependent simulation of the interaction in the cavity is performed to assess the accessibility and stability of high‐efficiency states for an X‐band magnicon. Results from multielectron, steady‐state simulation are presented to show the effect of spreads in electron‐beam radius, energy, and transverse momentum on the efficiency.