Electrons moving in circular orbits and colliding with gas atoms interact with a circular electromagnetic mode. Applying the linearized Boltzmann equation, the known nonresonant‐stimulated bremsstrahlung and the near‐resonance Landau effect are obtained. We predict that resonant electrons moving with angular velocity equal to the azimuthal phase velocity of the electromagnetic wave can exchange energy with the wave if the momentum transfer cross section for an electron‐atom collision is velocity dependent. Amplification is obtained if the momentum transfer cross section has a positive slope.