The effect of a virtual cathode on the electromagnetic stability of high-power ion diodes

Previous stability analyses have shown magnetically insulated ion diode equilibria to be unstable. However, important equilibrium features such as a virtual-cathode and a charge–neutral region were not included. A stability analysis including these features is presented, which indicates that the stability behavior is strongly affected by the equilibrium model. In particular, the diocotron instability displaces the ion resonance instability found in the previous analyses. The calculated growth rates for the diocotron mode are consistent with a fast growing mode that has been observed in recently reported three-dimensional numerical simulations. These simulations exhibit a transition from the diocotron to an ion resonance mode and a subsequent increase in ion divergence due to the much lower frequency of the ion mode. The stability analysis presented in this paper demonstrates how the evolution of the electron sheath reduces the diocotron growth rate resulting in unstable ion modes, thus explaining the transition to ion modes observed in the simulations.