Double-layer formation in the extended Franck-Hertz experiment.

A model is developed which explains the collective plasma phenomena associated with the extended Franck-Hertz experiment described in an earlier paper by Nicoletopoulos [Eur. J. Phys. 23, 533 (2002)]. The particular focus is on the formation of the free steady-state monotonic double layer. The approach used is a Bernstein-Greene-Kruskal theory in which one postulates the space potential and a suitable multicomponent electron distribution and uses Poisson's equation to solve for a physically meaningful ion distribution. A key feature is that the input space potential is chosen with a spatial scale much larger than the electron Debye length, with a restricting condition derivable from the prescribed form of volume production of positive ions. The model provides good quantitative agreement with the experimental results for mercury vapor, and can provide sufficient and necessary conditions for double layer formation in other atomic gases in similar experimental arrangements.