Finite Larmor Radius Diocotron Instability

The diocotron instability of an electron layer in which the electron Larmor radius is of the order of the layer thickness is studied. Remarkably, exact analytical solutions are obtainable in a nontrivial special case. These results allow an examination of the effects of finite Larmor radius for arbitrary ratios of Larmor radius to wavelength and of Larmor radius to layer thickness. In addition, an energy principle which yields a necessary and sufficient condition for instability for general distribution functions is derived.