Theory of a strong double layer in a Franck-Hertz tube

Summary form only given, as follows. The formation of a stead-state electric double layer (DL) in the plasma volume inside the intergrid space of a Franck-Hertz tube has been modeled theoretically. The experimental data were accounted for by a collisionless approach involving cold beams of electrons and positive ions, and low-energy particles trapped by the potential structure. This gives rise to a narrow, strong DL provided the electron current density is large enough. It is found that the ratio, R, of the number densities of the high- and low-potential plasmas surrounding the DL must rise continuously as the electron beam energy E is increased, in order for the DL to survive, as it does, in the range swept by the accelerating potential. The manner of the rise of R(E) obtained from a self-consistent Vlasov-Poisson system provides a reasonably good description of the actual rise of this number, which is a function of atomic phenomena. Collisional effects have been incorporated. It has been shown that the DL withstands these effects and even provides a mechanism for the transition between a presheath and an aftersheath in a steady-state situation in accordance with the experimental evidence.<>