Double layer propagation in experiments with electron beam injection

Electron beam injection into a plasma is investigated using the analytical inverted Bernstein-Green-Kruskal method. Particle number and momentum conservation laws are applied to evaluate the propagation velocity and potential drop on the leading edge of the beam. Electric potential is supposed to be monotonic, thus the leading front has a double-layer-like structure. For the case of cold particles, analytical expressions for the double layer velocity and potential drop are obtained. It is pointed out that double layer velocity differs from the initial electron speed: even for weak beams a noticeable deceleration takes place. Strong beams are found incapable of penetrating into plasma - their propagation velocity is very small. Ambient electrons undergo a considerable acceleration forming a return current which neutralizes the injector. Possible instability of the distribution functions is discussed.