Ambipolar-to-Free Diffusion: The Temporal Behavior of the Electrons and Ions

Abstract

Simultaneous measurements of the time dependence of the electron number density and the ion wall current in a helium afterglow are reported. The transition from ambipolar-to-free diffusion is investigated as a function of gas pressure and discharge-tube size. The onset of the transition regime occurs when $\frac{\ensuremath{\Lambda}}{〈{\ensuremath{\lambda}}_{D}〉}=86$, where $〈{\ensuremath{\lambda}}_{D}〉$ is the Debye length corresponding to the average electron or ion density, and $\ensuremath{\Lambda}$ is the characteristic diffusion length of the vessel. The time dependence of the transition regime was found to depend only on $\frac{\ensuremath{\Lambda}}{〈{\ensuremath{\lambda}}_{D}〉}$ if times are scaled as $\frac{t{D}_{+}}{{\ensuremath{\Lambda}}^{2}}$. This latter result is in agreement with high-pressure theories which assume mean free paths short with respect to experimental dimensions. The ion current changed by a factor of (1.2 \ifmmode\pm\else\textpm\fi{} 0.5) \ifmmode\times\else\texttimes\fi{} ${10}^{5}$ during the transition. The ions diffuse free by space-charge effects when $\frac{\ensuremath{\Lambda}}{〈{\ensuremath{\lambda}}_{D}^{i}〉}<~0.25$, where $〈{\ensuremath{\lambda}}_{D}^{i}〉$ is the Debye length corresponding to the average ion density.