The ion acoustic instability of the cylindrical inhomogeneous helicon discharge plasma with rotating electrons

TL;DR

This paper develops a kinetic theory for microinstabilities in cylindrical inhomogeneous helicon plasmas, revealing how azimuthal electron rotation and plasma inhomogeneity influence ion acoustic instability.

Contribution

It introduces a new theoretical framework accounting for radial inhomogeneity and electron rotation effects on plasma microinstabilities in helicon discharges.

Findings

Derived a linear integral equation for electrostatic potential in inhomogeneous plasma.

Found an analytical solution for high-frequency ion acoustic instability.

Identified the role of electron rotation and plasma inhomogeneity in instability development.

Abstract

The kinetic theory of the microinstabilities of a cylindrical plasma, produced by the cylindrical azimuthally symmetric (azimuthal mode number $m_{0}=0$) helicon wave, is developed. This theory is based on the derived linear integral equation for the Fourier-Bessel transform of the electrostatic potential, which accounts for the plasma response on the macroscale radial inhomogeneity of the helicon wave, which is commensurable with radial scale of the plasma density inhomogeneity, and on the microscale, which is commensurable with the thermal Larmor radius of electrons. The developed theory reveals new macroscale effect of the azimuthal steady rotation of electrons with a radially inhomogeneous angular velocity, caused by the radial inhomogeneity of the helicon wave. The solution of the integral equation for the electrostatic potential, derived in the short-wavelength limit, is derived in the form of the the functional equation for the electrostatic potential, coupled with infinite number of its satellites at a frequency separation equal to the frequency of the helicon wave. It is the basic equation for the investigations of the dispersion properties of the parametric and current driven instabilities of the cylindrical plasma in the radially inhomogeneous helicon wave. The analytical solution of the derived dispersion equation is found for the high frequency kinetic ion acoustic instability of the cylindrical helicon plasma, driven by the coupled effect of the electron diamagnetic drift and of the steady azimuthal rotation of electrons relative to the ions with a radially inhomogeneous angular velocity.