Stability of Non-Neutral Plasma Cylinder Consisting of Magnetized Cold Electrons and of Small Density Fraction of Ions Born at Rest: Non-Local Analysis

Abstract

The non-local stability problem of the plasma cylinder, filled with "cold" magnetized rigidly rotating electrons, and a small density fraction of ions, is solved. The ions are supposed to be bom at rest by ionization of background gas. The study is based on the kinetic description of ions. The equilibrium distribution function, taking into account the peculiarity of ions birth, is used. The radial electric field is caused by space charge of non-neutral plasma. The dispersion equation for plasma eigen frequencies is obtained analytically. It is valid within the total admissible range of values of electric and magnetic fields. Normahzed eigen frequencies of / Q.. are calculated for the basic azimuth mode m = 1 (o' = o-rno*, ffli^ = (-ffli,;+0;)/2 , Q.. ={m^.-AeE^ Im.rj is called the "modified" ion cyclotron (MIC) frequency), for the density fraction of ions of atomic nitrogen / = Af / n = o, 01 and are presented in graphic form versus parameter 2ffl\/ft/. The spectra of osciUations o'/O,. consist of the family of electron Trivelpiece -Gould (TG) modes and of the families of MIC modes. The frequencies of MIC modes are located in a small vicinity of harmonics of the MIC frequency Q. above and below the harmonic. The TG modes in non-neutral plasma fall in the region of MIC frequencies O,. and interact strongly with MIC modes. The slow TG modes become unstable near the crossings with nonnegative harmonics of MIC frequencies. The instabilities have a resonant character. The lowest radial TG mode has a maximum growth rate at crossing with a zero harmonic of O,. ((Imo'/O;)jjj^ = 0,074). The growth rates of MIC modes are much lower ((Imco'/ Q..)^^ < 0,002). Their instability has a threshold character. The instabilities of TG and MIC modes take place mainly at the values of parameter 2ffl\ / wl, corresponding to strong radial electric fields (ffii,/ «\eE^ / m/\), in which the ions are unmagnetized. The oscillations of small amplitude are seen on some frequency dependencies of MIC modes. They are similar to oscillations on dispersion curves of electron waves in metals and are caused by the similarity between the ion equihbrium distribution function and the degenerate Fermi -Dirac one. The results obtained give the solution to the stability problem discussed by R.H. Levy, J.D. Daugherty and O. Buneman[ Phys. Fl. 12, 2616 -2629(1969] for a special case of plasma bounding directly with metal casing and possessing the volumetric eigen modes only.