Non-neutral plasmas, like electrically neutral plasmas, exhibit a broad range of collective properties, such as plasma waves and instabilities, and the ability to support long-lived, large-amplitude coherent structures. This paper reviews the equilibrium and stability properties of intense non-neutral electron flow in crossed electric and magnetic fields. Following a description of equilibrium properties for magnetically insulated electron flow in planar geometry, extraordinary-mode stability properties are investigated for relativistic non-neutral electron flow between planar conductors. Particular emphasis is placed on the magnetron and diocotron instabilities, and detailed stability behavior is shown to exhibit a sensitive dependence on the self field intensity (as measured by the dimensionless parameter $s_e=\frac{{\gamma }_e^0{\omega }_{\mathrm{pe}}^2}{{\omega }_{\mathrm{ce}}^2}$) as well as on the shape of the equilibrium profiles. The influence of cylindrical effects (such as the centrifugal and Coriolis accelerations of an electron fluid element) on stability behavior is then investigated for rotating electron flow in cylindrical geometry. Finally, the properties of large-amplitude coherent structures in non-neutral plasmas with circulating electron flow are investigated. Topics covered in this area include particle-in-cell computer simulations of dense ($s_e\sim 1$) electron flow in relativistic magnetrons which show large-amplitude spoke formation in the circulating electron density, and application of a cold-fluid guiding-center model to investigate large-amplitude vortex structures in low-density ($s_e\ll 1$) non-neutral plasma. The accessibility and stability of such stationary structures (in the rotating frame) remain important topics for future investigation.

DOI:https://doi.org/10.1103/RevModPhys.63.341