Diocotron stability properties of relativistic non‐neutral electron flow in a planar magnetron are investigated within the framework of the cold‐fluid‐Maxwell equations. The eigenvalue equation for the extraordinary‐mode waves in a relativistic velocity‐sheared electron layer is obtained, and is solved in the massless, guiding‐center approximation. Approximating the electromagnetic field in the anode resonator by the lowest‐order mode, the dispersion relation for the diocotron instability is obtained. Although the tenuous beam approximation is assumed, the eigenvalue equation and corresponding dispersion relation are both fully electromagnetic, and valid for relativistic electron flow. The dispersion relation is numerically investigated for a broad range of system parameters. From numerical calculations of the dispersion relation, it is shown that the typical growth rate of the diocotron instability indicates a strong instability. The early evolution of the diocotron instability as an important precursor to the evolution of the full magnetron oscillation is discussed.
