Interaction of electrons with the walls confining a plasma

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Man-made plasmas are in contact with solids. In fact, it is the plasma-solid interaction, which is the core of many technological plasma applications. Not in all plasma devices, however, is the plasma-solid interaction beneficial. For instance, to keep fusion plasmas, Hall thrusters, and miniaturized dielectric barrier discharges stable, the interaction with the solid, and hence the plasma fluxes onto the walls, should be minimized. Since the fluxes depend on the electric response of the plasma-wall interface, resulting from charge-transferring atomic collisions and the interaction of electrons from the plasma with the wall, controlling the latter is of technological interest. The interaction typically occurs at energies below 50~eV, an energy range which has not been widely addressed. Little is thus quantitatively known about the coefficients characterizing it. In this project, we develop a theoretical tool for studying the interaction of low-energy electrons with solids, as it applies to plasma devices, and use it to start building up - for homogeneous and coated walls - a data base for electron emission yields and their complements, the electron sticking coefficients. To counter the lack of crystallographic information about the walls, we base the calculations on a Jellium-type model, augmented by the most generic crystal effects, coherent Bragg scattering on planes coplanar to the interface and incoherent elastic scattering on ion cores. Describing moreover the scattering and physical processes included in a manner that depends only on a few easily accessible parameters, we get a surface and scattering model applicable to different classes of materials. It is used, within an invariant embedding principle for the backscattering function, summing up the backscattering trajectories arising from the interaction of the primary electron with the excitations and imperfections of the solid, to calculate the yield for secondary electron emission as well as the electron sticking coefficient. The embedding equations for backscattering from homogeneous and coated walls are derived and solved numerically with strategies developed for interface transport in nuclear physics. Using them, we tap the full potential of the embedding approach for quantifying the interaction of low-energy electrons with solids, a prerequisite for future efforts to optimize plasma devices by judiciously choosing the wall materials.