Stability of the positive column in a longitudinal magnetic field
Abstract
This paper presents a contribution to the theoretical and numerical treatment of the stability of a positive column in a diffusion dominated low pressure discharge with longitudinal homogeneous magnetic field. Proceeding from the basic equations of three fluid theory, the dispersion equations for the propagation of cylindrical electrostatic waves with azimuthal mode m 1 are derived. In order to discuss explicit examples, analytical expressions for growth rate and frequency as functions of wave number k have been derived in a first approximation. Regimes of stable and unstable behavior of the positive column are plotted in the kB plane. With the aid of such stability diagrams, the influence of the finite length of the positive column on its stability can be investigated. In the mathematical solution of the boundary value problem, the amplitude functions of density and potential are developed for the complete orthogonal system of first order Bessel functions of the first kind.
 Publication:

Plasma Physics
 Pub Date:
 October 1975
 DOI:
 10.1088/00321028/17/10/008
 Bibcode:
 1975PlPh...17..799M
 Keywords:

 Cylindrical Waves;
 Electrostatic Waves;
 Longitudinal Stability;
 Magnetic Field Configurations;
 Magnetohydrodynamic Stability;
 Plasma Cylinders;
 Wave Propagation;
 Bessel Functions;
 Boundary Value Problems;
 Damping;
 Diffusion Theory;
 Electric Field Strength;
 Gas Discharge Tubes;
 Maxwell Equation;
 Molecular Ions;
 Phase Velocity;
 Wave Dispersion;
 Plasma Physics