The small‐signal theory of a harmonic gyrotron is presented for the case of axis‐encircling electron orbits. The beam current required for oscillation is found to be highly dependent on the electron energy. Gyrotron cavities operating on this principle at very high harmonic numbers (n&bartil;10) and high frequency in weak magnetic fields are well matched to low‐current, moderate‐energy, rf‐accelerated electron beams (&bartil;50 mA, &bartil;250 keV), resulting in compact submillimeter wave systems.