# The role of second-order radial density gradient for helicon power absorption

## TL;DR

This paper investigates how the second-order radial density gradient influences power absorption in helicon plasmas, revealing that the zero-crossing point of this gradient critically affects resonance and power distribution.

## Contribution

It introduces the significance of the second-order radial density derivative in helicon power absorption, combining analytical and numerical analysis to uncover its effects.

## Key findings

- Power absorption peaks where the second-order derivative is zero.
- Positive second-order derivative enhances power absorption.
- Shift of zero-crossing affects power distribution and mode dominance.

## Abstract

To reveal the mysterious and still controversial mechanism of high ionization efficiency during helicon discharges, this work focuses particularly on the role of second-order derivative in radial density profile, both analytical and numerically. It is found that: (i) the radially localized potential well that plays a critical role in resonance power absorption from antenna to plasma is localized where the second-order derivative vanishes, (ii) the power absorption increases for positive second-order derivative, decreases for negative second-order derivative, and maximizes where second-order derivative becomes zero, (iii) the power absorption decreases near plasma core and increases near plasma edge when the radial location of vanishing second-order derivative moves outwards, which is also a process of Trivelpiece-Gould mode overwhelming helicon mode. These findings can be very interesting for helicon plasma applications that require certain power distribution or heat flux configuration, e. g. material processing, which can be controlled by adjusting the profile and zero-crossing location of second-order radial density gradient.