# The Properties of Plasma Sheath Containing the Primary Electrons with a Cairns Distribution

## TL;DR

This paper investigates how a non-thermal electron distribution affects plasma sheath properties, showing differences from traditional thermal models.

## Contribution

The study introduces a generalized Bohm criterion and new parameters for plasma sheath properties under a Cairns electron distribution.

## Key findings

- The plasma sheath properties depend significantly on the α-parameter in the Cairns distribution.
- The floating potential at the wall and critical secondary electron emission coefficient are newly derived.
- Results differ from those assuming a Maxwellian distribution for primary electrons.

## Abstract

We study the properties of a plasma sheath containing cold positive ions, secondary electrons, and primary electrons with a Cairns distribution (a non-thermal velocity distribution). We derive the generalized Bohm criterion and Bohm speed, the new floating potential at the wall, and the new critical secondary electron emission coefficient. We show that these properties of the plasma sheath depend significantly on the α-parameter in the non-thermal α-distribution, and so they are generally different from those of the plasma sheath if the primary electrons were assumed to be a Maxwellian distribution.