Fluid Model of a Sheath Formed in Front of an Electron Emitting Electrode Immersed in a Plasma with Two Electron Temperatures

Abstract

The formation of a sheath in front of a negatively biased electrode (collector) that emits electrons is studied by a one-dimensional fluid model. Electron and ion emission coefficients are introduced in the model. It is assumed that the electrode is immersed in a plasma that contains energetic electrons. The electron velocity distribution function is assumed to be a sum of two Maxwellian distributions with two different temperatures, while the ions and the emitted electrons are assumed to be monoenergetic. The condition for zero electric field at the collector is derived. Using this equation the dependence of electron and ion critical emission coefficients on various parameters -like the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons -is calculated for a floating collector. A modification of the Bohm criterion due to the presence of hot and emitted electrons is also given. The transition between space charge limited and temperature limited electron emission for a current-carrying collector is also analyzed. The critical potential, where this transition occurs, is calculated as a function of several parameters like the Richardson emission current, the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons.

Sheath in Front of a Negatively Biased Collector that Emits Electrons and is Immersed in a Two Electron Temperature Plasma

“…This was analyzed in more detail in the previous paper [18]. Both critical emission coefficients γ ec (β 0 ) and γ ic (β 0 ) have very well observable maximum values, when regarded as functions of β 0 .…”

“…What happens if energetic electron population is present in the plasma and the wall emits electrons has not yet been investigated so thoroughly, but has recently become a subject of and increased interest [16,17] mainly because of possible fusion applications. This problem has already been addressed also by our group [18,19].…”

“…Our recent paper [18] is basically an extension of the model recently presented by Ye et al [11] - [14] in three directions. First, we assumed that additional high temperature maxwellian electron population is present in the plasma.…”

“…Whether all 3 values of the low pre-sheath potential drop are physically possible is a question that is still open for further investigation. The conditions for the splitting of the low solution predicted by our model [18] are rather stringent and will be difficult to achieve even in a computer simulation and even more so in an experiment.…”

A Fluid Model of the Sheath Formation in Front of an Electron Emitting Electrode with Space Charge Limited Emission Immersed in a Plasma that Contains a One‐Dimensional Mono‐Energetic Electron Beam

“…Attempts to study the effects of the energetic and emitted electrons to the sheath formation simultaneously [22] are more rare. Our group has also been quite active in this field in recent years [23] - [26]. In the present work sheath formation in front of a floating, electron emitting electrode is studied by way of a one-dimensional fluid model.…”