Ion-acoustic instability of the cylindrical inhomogeneous helicon discharge plasma with rotating electrons

Abstract

The kinetic theory for the microinstabilities of a cylindrical plasma, produced by the cylindrical azimuthally symmetric (azimuthal mode number m0=0) helicon wave, based on the Vlasov–Poisson system of equations, is developed. The derived linear integral equation for the Fourier–Bessel transform of the electrostatic potential is the basic equation for the investigations of the parametric and the current-driven instabilities of the radially inhomogeneous cylindrical plasma in the radially inhomogeneous helicon wave. The short-wavelength solution of this equation for the electrostatic potential is derived in the form of the functional equation, which includes an infinite number of its satellites at a frequency separation equal to the helicon wave frequency. The analytical solution is derived 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.