Sheaths, particle fluxes, floating potentials and electromotive force in a cylindrical discharge plasma containing an internal coaxial wall

Abstract

A two-fluid theory of a positive column in a cylindrical geometry having an internal coaxial wall is given. The space charge density throughout the whole plasma and inertia and diffusion controlled conditions are taken into account. An eigenvalue problem with a free boundary is solved. The radial distributions of the number densities and of the drift velocities of the ions and electrons and the profile of the electric potential are calculated. The boundary of the regions of particle collection for the inner and outer walls is exactly determined. The results show that the particle fluxes and the number densities of ions and electrons and, in particular, the floating potential at the inner wall are different from the values at the outer wall. The differences increase with an increasing ratio of the radii of the outer and inner walls. Under these conditions a so called impressed voltage or electromotive force occurs within the plasma which compensates the electric voltage between the inner and the outer wall since no radial electric current flows.

Response to ‘‘Comment on ‘Bohm criterion for the collisional sheath’ ’’ [Phys. Plasmas 3, 1459 (1996)]

“…Thus, a few different statements have been used to define the sheath edge. [4][5][6][7] The sheath criterion giving the conditions for the existence of a sheath is related to the sheath edge.…”

Multifluid equations of a plasma with various species of positive ions and the Bohm criterion

“…Representing inequalities (6) and the Bohm criterion (12) in terms of hydrodynamics quantities at the sheath edge, one finds conditions that must be obeyed by a hydrodynamics solution for the above matching to be possible:…”

Sheath formation in the presence of non‐extensive electron distribution

“…This assumption leads to a good approximation for low-pressure discharges. [20,33,34] In plasma, electrons are thermally mobile and inertially light particles. Usually, their distribution is found to be Boltzmann distribution, as given by Equation (3).…”