New insights in the stratification of an argon positive column plasma. I. Theory

Abstract

This study investigates the conditions leading to stratification in a quasineutral argon positive column plasma, focusing on a pressure-column radius product, pR, in the range 0.1–10 Torr cm neglecting Coulomb collisions and electron–ion recombination. We achieve this by linearizing the electron transport equations while incorporating metastable ionization. Dispersion relations indicate that positive column stratification may result from a thermoelectric transport term in the electron energy equation, particularly the density gradient term in the energy flux related to the Dufour effect, or from the non-linearity of ionization due to metastable ionization. The present study shows that for small values of the pR product (less than about 0.3–0.5 Torr cm), the plasma is maintained by direct ionization and the stratification of the positive column is entirely due to the thermoelectric term of the electron energy equation. For larger pR products, the reduced electric field decreases due to lower charged particle losses to the wall, and the plasma is maintained by stepwise and associative ionization of metastable atoms. The dispersion relations show that the growth of instabilities above 0.3–0.5 Torr cm is still linked to the thermoelectric coefficient but that the presence of metastable atoms is necessary for the development of instabilities. The non-linearity of the metastable density with the electron density is not the cause of the stratification in this range of pR product, contrary to previous claims. Experiments and particle simulations presented in Paper II [Dosbolayev et al., Phys. Plasmas 13, 085015 (2024)] are qualitatively consistent with the theory presented in this article.