Stability of a Magnetized Positive Column in the Single Cylinder and Between Coaxial Cylinders.
Under the assumption of quasi neutrality of electric charge and neglecting the sheath at walls, the behavior of plasma in a magnetized positive column is governed by the conservation equations for mass and momentum of electrons, ions and neutrals. Self-consistent infinitesimal perturbations of plasma density and electric potential, which satisfy the governing equations to the same degree of approximation, are used to derive the dispersion equations. In the first problem, the stability of a magnetized positive column in the single cylinder is considered. The effect of the ratio of the mobilities of electrons to ions and non-dimensional axial electric field on the stability for all unstable mode is studied. The minimum non-dimensional electric field at which a magnetized positive column becomes unstable for different ratios of the mobilities of electrons and ions is determined. Steady state analysis is also carried out to find plasma density and radial electric potential distributions, as well as electron temperature and axial electric field. In the first part of the second problem, steady state analysis is developed for the magnetized positive column between coaxial cylinders. The radial distributions of plasma density and electric potential are given as function of the ratio of inner and outer radii of two cylinders. For any given value of this ratio and gap size, an equivalent radius of cylindrical plasma is given that has the same temperature and axial electric field for the same physical conditions as the coaxial plasma. The equivalent radius may be used to determine the temperature and axial electric field of the coaxial plasma when the temperature and axial electric field of a cylindrical plasma of the same gas under same physical conditions, are known. In the second part stability of plasma in different gaps is studied, when the ratio of inner and outer radii of cylinders has the various values. The critical magnetic field is evaluated for a given non-dimensional axial electric field and the ratio of mobilities of electrons to ions for all unstable modes. The minimum axial electric field at which the magnetized positive column between coaxial cylinders for different gaps, becomes unstable (at a certain ratio of electron and ion mobilities) is also determined.
- Pub Date:
- Physics: Fluid and Plasma