Microwave Investigation of the Transition from Ambipolar to Free Diffusion in Afterglow Plasmas

The time decay of electron density in pulsed helium afterglow discharges is studied experimentally employing both conventional and modified microwave-cavity techniques. The two methods permit density measurements from $n_e\simeq {10}^{11}$ ${\mathrm{cm}}^{-3\mathrm{}}$ to as low as $n_e\simeq 2\times {10}^4$ ${\mathrm{cm}}^{-3\mathrm{}}$ in helium at pressures of 0.4 and 4.0 Torr. For Debye lengths less than ∼1% of the characteristic diffusion length $\Lambda$, the electron loss rate is through ambipolar diffusion controlled by the atomic ion ${\mathrm{He}}^{+}$ at 0.4 Torr and by the molecular ion $\mathrm{He}_2^{}{}_{}{}^{+}$ at 4.0 Torr. At lower electron densities, the electrons diffuse more rapidly than ambipolar diffusion, and in the limit of Debye lengths much greater than the characteristic diffusion length, the electrons diffuse freely to the walls. The experimentally observed effective diffusion coefficient $D_s$ in the transition region is compared with a mathematical expression proposed by Phelps relating $D_s$ to $n_e$. Satisfactory agreement is obtained at 4.0 Torr where the electron mean free path $\lambda \ll \Lambda$. By using this expression to calculate theoretically expected decays of electron density, a computer optimization procedure produced an even better fit to experimental data by slightly altering a numerical parameter in the formula. At 0.4 Torr, where $\lambda \approx \Lambda$ and the theoretical treatment is not expected to be valid, diffusion in the transition region is observed to occur at a rate substantially less than that predicted theoretically.