Theory of the electron sheath and presheath

Abstract

Electron sheaths are commonly found near Langmuir probes collecting the electron saturation current. The common assumption is that the probe collects the random flux of electrons incident on the sheath, which tacitly implies that there is no electron presheath and that the flux collected is due to a velocity space truncation of the electron velocity distribution function (EVDF). This work provides a dedicated theory of electron sheaths, which suggests that they are not so simple. Motivated by EVDFs observed in ParticleIn-Cell (PIC) simulations, a 1D model for the electron sheath and presheath is developed. In the model, under low temperature plasma conditions (T e T i ), an electron pressure gradient accelerates electrons in the presheath to a flow velocity that exceeds the electron thermal speed at the sheath edge. This pressure gradient generates large flow velocities compared to what would be generated by ballistic motion in response to the electric field. It is found that in many situations, under common plasma conditions, the electron presheath extends much further into the plasma than an analogous ion presheath. PIC simulations reveal that the ion density in the electron presheath is determined by a flow around the electron sheath and that this flow is due to 2D aspects of the sheath geometry. Simulations also indicate the presence of ion acoustic waves excited by the differential flow between electrons and ions in the presheath which result in sheath edge fluctuations. The 1D model and time averaged PIC simulations are compared and it is shown that the model provides a good description of the electron sheath and presheath.

Interaction of biased electrodes and plasmas: sheaths, double layers, and fireballs

“…This is the same expression as was obtained for the ion sheath thickness in equation (13). It is over twice as large as what is obtained based on the random flux model [19]. Simulation results are consistent with equation (35), as shown in figure 19.…”

“…In this case, the electron current lost to the electrode is conventionally thought to be the random thermal flux incident on the electrode eΓ e,th A E , representing a half-Maxwellian electron velocity distribution function at the electron sheath edge. However, recent work has shown the existence of an electron presheath, which establishes a flow shift of the electron distribution function by the sheath edge that satisfies an electron sheath analog of the Bohm criterion: V e = T e /m e ≡ v e,B [18,19]. Further 2D-3V PIC simulations revealed that both a combination of flow-shift and loss cone distribution contribute to the electron flux [16].…”

“…Figures 17 and 19 confirm that the general behavior predicted by this simple analysis is observed in PIC simulations; see Refs. [16,18,19] for details.…”

“…These correspond to equations (19) and (20) from the ion presheath. A comparison of these models to PIC simulations is shown in figure 19.…”

Steady‐State Solution of a Solar Wind‐Generated Electron Cloud in a Lunar Crater

“…A laboratory example of an electrostatically confined pure electron plasma, called an electron sheath, is formed at the plasma interface of a positively charged surface (Scheiner et al, ). As described herein, two key features differentiate the presently studied electron cloud from an electron sheath: (i) The electron cloud can be much larger than the typical Debye length scale for plasma charge separation, and (ii) the electron cloud produces a negative floating potential at the surface.…”