Sheath structure in front of an electron emitting electrode immersed in a two-electron temperature plasma: a fluid model and numerical solutions of the Poisson equation

Abstract

A one-dimensional fluid model of sheath formation in front of a large, planar, floating, electron emitting electrode (collector) immersed in a two-electron temperature plasma is presented. For certain values of the parameters the Bohm criterion is triple valued. Three methods to select the correct Bohm velocity are compared. The simplest is to find the parameters, where the floating potentials that correspond to the high and to the low Bohm velocity are equal. But sometimes-when the electron emission is small-such parameters cannot be found. The second method is the 'maximum positive ion flux criterion', proposed recently by Fernández Palop et al (2002 J. Appl. Phys. 91 2587), for electronegative plasmas. In this work it is modified for a two-electron temperature plasma with emitted electrons and applied successfully. This method is sometimes-when the electron emission from the collector is increased-not applicable because the positive ion flux as a function of potential has only 1 maximum. The third method is a numerical solution of the Poisson equation. The transition from the low to the high Bohm velocity occurs at the parameters where the numerically found space charge density profile indicates the formation of a double layer in the sheath. These parameters are always identical to the parameters found with the maximum positive ion flux method, when the latter can be applied. The 'shooting method' for the correct determination of electric field at the collector is presented. This method reveals the existence of regular and irregular numerical solutions of the Poisson equation. The irregular solutions of the Poisson equation fulfill only one of the two sheath edge conditions and they correspond to the solutions of the fluid model, that are not physically acceptable. The parameters, where the numerical solutions of the Poisson equation become irregular, are identical to those found with the 'positive square of electric field' test, which is also presented.

Emissive Langmuir probes in the strong emission regime for the determination of the plasma properties

“…Such potential structures would return a fraction of the large emitted thermionic electron current for </ > < 0 with a different energy spectrum. These complex plasma potential profiles around electron-emitting probes were considered in [6], [7], and [15].…”

“…This large flow of emitted thermionic electrons from a hot probe, i.e., 1 <C jthr(</>, T p )/j eo (4>, T e ) for </ > < 0, interacts with the surrounding plasma and may produce different physical effects. First, as discussed in [6], [7], and [15], the classical plasma sheath around the probe could be modified and might develop a plasma potential minimum acting as a virtual cathode. Hence, a fraction of the initially repelled electrons might return to the emissive probe with a different energy spectrum.…”

Propagator integral method for plasma physics kinetic equations with practical applications

“…This interaction appears in experiments carried out involving plasmas [83,143] and also, in vessels flying in space [86]. Many works have provided fluid models, as the those by T. Gyergyek et al [116,144] or kinetic descriptions, as the works by M. D.Campanell et al [89,145] or J. P.Sheehan et al [98,143], as well as many other authors [23,85,[146][147][148][149][150]. Moreover, different approaches to describe the emission of electrons as the works by J. L. Domenech-Garret et al [88,113] and references therein, can be found in the literature, but the description of the complete processes involved in the plasma-wall interaction are still an open topic of discussion because of the variety and peculiarities of each plasma device.…”

“…In some situations, plasmas or neutral gases may evolve from abrupt initial or boundary conditions or may generate thin structures, as layers or sheaths [18,[115][116][117], that make difficult the numerical resolution and may lead to non-physical evolutions or inaccurate solutions. For instance, collimated charges beam or localised emissive walls, as well as the electric applied field may result in an abrupt plasma evolution.…”

“…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.…”