Particle-in-cell study of the ion-to-electron sheath transition

TL;DR

This study uses 2D particle-in-cell simulations to analyze how the sheath near an electrode transitions from ion-dominated to electron-dominated as the bias varies relative to the plasma potential, revealing different EVDF behaviors.

Contribution

It provides detailed simulation-based insights into the sheath transition regimes and EVDF characteristics near biased electrodes, which were not fully characterized before.

Findings

Electron velocity distribution functions vary with bias, showing Maxwellian, loss-cone, and shifted profiles.

No sheath forms when bias is near plasma potential, maintaining quasineutrality.

Different sheath regimes significantly affect ion and electron dynamics near the electrode.

Abstract

The form of a sheath near a small electrode, with bias changing from below to above the plasma potential is studied using 2D particle-in-cell (PIC) simulations. Five cases are studied: (A) an electrode biased more than the electron temperature ($T_e/e$) below the plasma potential, (B) an electrode biased less than $T_e/2e$ below the plasma potential, (C) an electrode biased nearly at the plasma potential, (D) an electrode biased more than $T_i/2e$ but less than $T_e/2e$ above the plasma potential, and (E) an electrode biased much greater than $T_e/2e$ above the plasma potential. In case (A), the electron velocity distribution function (EVDF) is observed to be Maxwellian with a Boltzmann-type exponential density decay through the ion sheath and presheath. In cases (B) and (C), the EVDFs exhibit a loss-cone type truncation due to fast electrons overcoming the small potential difference between the electrode and plasma. No sheath is present in this regime, and the plasma remains quasineutral up to the electrode. The EVDF truncation leads to a presheath-like density and flow velocity gradient. In case (D) an electron sheath is present, and essentially all ions are repelled. Here the truncation driven behavior persists, but is accompanied by a shift in the maximum value of the EVDF that is not present in the negative bias cases. In case (E), the flow shift becomes greater and the loss-cone moves further into the tail of the EVDF. In this case the flow moment has significant contributions from both the flow shift of the EVDF maximum, and the loss-cone truncation.