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

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 $\frac{\Lambda }{〈{\lambda }_D〉}=86\mathrm{}$, where $〈{\lambda }_D〉$ is the Debye length corresponding to the average electron or ion density, and $\Lambda$ is the characteristic diffusion length of the vessel. The time dependence of the transition regime was found to depend only on $\frac{\Lambda }{〈{\lambda }_D〉}$ if times are scaled as $\frac{t{D}_{+}}{{\Lambda }^2}$. 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 ± 0.5) × ${10}^5$ during the transition. The ions diffuse free by space-charge effects when $\frac{\Lambda }{〈{\lambda }_D^i〉}<~0.25$, where $〈{\lambda }_D^i〉$ is the Debye length corresponding to the average ion density.