Theory of the electron sheath and presheath

TLDR

Electron sheaths form near Langmuir probes, traditionally assumed to collect a random electron flux without a presheath, implying the sheath is governed solely by velocity‑space truncation of the electron distribution. This study develops a dedicated theory demonstrating that electron sheaths are more complex than previously thought. A one‑dimensional model, motivated by PIC‑simulated electron velocity distributions, shows that in low‑temperature plasmas the electron pressure gradient accelerates presheath electrons to speeds exceeding the thermal velocity at the sheath edge. The resulting pressure‑driven flows produce electron presheaths that extend farther than ion presheaths, alter ion density via a surrounding flow, excite ion‑acoustic waves causing sheath‑edge fluctuations, and the model agrees well with time‑averaged PIC simulations.

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 Particle-In-Cell (PIC) simulations, a 1D model for the electron sheath and presheath is developed. In the model, under low temperature plasma conditions ($T_e\gg T_i$), 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.