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Reflection of diffusing metastable gas molecules at the boundary

Generally, in Townsend discharges, the behaviours of metastable molecules are treated by solving the diffusion equation. The boundary condition for the diffusion equation has previously been assumed to be that the density at the boundary is zero. Such an assumption is found to be unsatisfactory in determining effective lifetimes from the experimental data. The authors solve the diffusion equation using boundary conditions of the third kind. By adopting the two-stream approximation, the reflection coefficient of the metastables is introduced naturally into the theory. An expression which depends implicitly on the reflection coefficient is derived for the effective lifetime of the metastables as a function of pressure. By fitting the calculated curves to the experimental data, the authors succeed in determining the various physical parameters, including the newly introduced reflection coefficient.