Existence of a virtual cathode close to a strongly electron emissive wall in low density plasmas

Abstract

The interaction between an electron emissive wall, electrically biased in a plasma, is revisited through a simple fluid model. We search for realistic conditions of the existence of a non-monotonic plasma potential profile with a virtual cathode as it is observed in several experiments. We mainly focus our attention on thermionic emission related to the operation of emissive probes for plasma diagnostics, although most conclusions also apply to other electron emission processes. An extended Bohm criterion is derived involving the ratio between the two different electron densities at the potential minimum and at the background plasma. The model allows a phase-diagram analysis, which confirms the existence of the non-monotonic potential profiles with a virtual cathode. This analysis shows that the formation of the potential well critically depends on the emitted electron current and on the velocity at the sheath edge of cold ions flowing from the bulk plasma. As a consequence, a threshold value of the governing parameter is required, in accordance to the physical nature of the electron emission process. The latter is a threshold wall temperature in the case of thermionic electrons. Experimental evidence supports our numerical calculations of this threshold temperature. Besides this, the potential well becomes deeper with increasing electron emission, retaining a fraction of the released current which limits the extent of the bulk plasma perturbation. This noninvasive property would explain the reliable measurements of plasma potential by using the floating potential method of emissive probes operating in the so-called strong emission regime.

Three species one-dimensional kinetic model for weakly ionized plasmas

“…For instance, the analysis of the interaction between plasma and emissive or collecting walls is a problem often studied by traditional fluid descriptions 5,6 but also dealt from a kinetic point of view [7][8][9][10] by proposing pre-defined velocity distribution functions not directly obtained by solving specialized kinetic equations. Many works do not account for collisions or other effects that may become relevant for the plasma dynamics.…”

Propagator integral method for plasma physics kinetic equations with practical applications

“…Consequently, as wall temperature increases, a deeper well is found [149], meaning that electrons require a higher energy to reach positions far from the wall. Nevertheless, pressure reduces this well, indicating that electrons must jump a lower potential barrier but they have more encounters with neutrals, which also reduce J T .…”

“…Nevertheless, after an electron crosses the potential well, the E makes it to increases its velocity and to overcome the collisions with the neutral gas. This phenomena is commonly found in experimental and theoretical models [89,98,149,150] and it is usually referred to a potential well or virtual cathode. On the contrary, collisions affect all electrons entering the vacuum chamber.…”

“…In addition, a saturation scenario is expected to be reached when the electric field shape is such that no barrier appears for any emitted electron, regardless its energy, and the amount of returning electrons is minimum. The voltage difference required to reach the saturation current depends on the wall temperature [149,157], but it is reasonable to assume that a dependency on the background pressure arises, since it imposes an additional barrier for the emitted electrons. Figure 6.9 presents the emitted current far from the wall, x = 0.02 mm, for five high wall temperatures as a function of the potential wall.…”

“…This is usually modelled as a boundary value problem from both fluid [116,150] and kinetic [98,149] approaches. By heating up a metallic wall or wire, electrons are ejected from the metal.…”