Asymptotic Theory of a Photoionization Chamber

A photoionization chamber consists of two parallel plates between which a test gas is photoionized. The charged particles thus produced then diffuse to the plates where they recombine. This process is analyzed in detail when the fraction of ionization is very low and the mean free path for charged-neutral encounters is very small compared to the chamber width. Particular attention is paid to the physically important limit of sufficiently large charged particle densities to make the Debye length small compared with any macroscopic dimension. In this limit the plasma is quasi-neutral in the body of the chamber. Near the walls, however, quasi-neutrality breaks down and a new scaling of the variables is necessary to account for the changed orders of magnitude of the properties in the sheaths. The sheath equations are reduced to one previously solved by the author (in connection with a spherical electrostatic probe problem). The sheath solution and quasi-neutral plasma solution are asymptotically matched in their region of common validity. Thus, charged particle and electric field distributions are found and typical curves are given. From the tabulated data, current-voltage characteristics of the photoionization chamber may be constructed. Three sample characteristics are given with a little discussion of their interpretation.