Double layers with a virtual cathode and instabilities of a beam-plasma system

Experimental data obtained previously are used to analyze the relationship between the conditions for the formation of electrical double layers of two types in magnetized beam-plasma systems. Layers of the first type form near the surface of the hot cathode (the source of the beam), while those of the second type form in the plasma volume. The relationship is a simple one: If the current density of the beam electrons, n1v1, does not exceed the random current density of plasma electrons, n2v2/4, then only the first type of layer forms in the system. Under the conditions n1 v1>n2v2/4, both types of layers form; the second layer is associated with a virtual cathode of the electron beam in the plasma volume. The latter case occurs only in a system in which there is a longitudinal gradient of the plasma density, directed toward the beam source. A classification is proposed for the beam instabilities responsible for the formation of a double layer with a virtual cathode. In part, this classification is based on some recent data. It is used, in particular, to identify the instability responsible for the formation of a double layer in some earlier experiments