Small-signal theory of the high-power magnetron with intense electron flow

In the work presented here, the authors have modified a linear stability analysis of the planar magnetron with intense electron flow to describe the case of a cylindrical magnetron. The eigendifferential equation for extraordinary mode oscillations is solved numerically over a range of parameters characterizing the electron flow and the magnetron geometry. The effect of the anode resonators is imposed through the boundary condition at the outer radius of the electron flow. Both the magnetron instability (doppler-shifted electron cyclotron resonance) and the diocotron instability are observed. Implications for the start-up of existing experimental high-power magnetrons will be presented