Radial distribution of the plasma potential in a cylindrical plasma column with a longitudinal magnetic field

The possibility of controlling the electrostatic field distribution in plasma has yielded wide prospects for modern technologies. As a magnetic field primarily allows for creating electric fields in plasma, it serves as an additional obstacle for the current flow through a medium. In the present paper, an axially symmetric system is considered in which the magnetic field is directed along the axis and concentric electrodes are located at the ends. The electrodes are negatively biased. A model which solves the problem of the radial distribution of the plasma potential inside the cylindrical plasma column supported by the end electrodes is proposed. The most commonly encountered configurations of the electrical connection for the end electrodes are considered, and the particular solutions to the problem of the radial distribution are presented. The contribution of ions and electrons to the transverse conductivity is evaluated in detail. The influence of a thermionic element on the radial profile of the plasma potential is considered. To verify the proposed model, an experimental study of the reflex discharge is carried out with both cold electrodes and a thermionic element on the axis. A comparison of the computational model results with experimental data is given. The presented model makes it possible to solve the problem concerning the plasma potential distribution in the case of an arbitrary number of end electrodes, and also to take into account the inhomogeneity of the distribution of plasma density, neutral gas pressure and electron temperature along the radius.

Linear Pinch Equilibrium of Non-Neutral Plasma Revisited: Phenomenological Consequences of a Numerical Accuracy Problem

Weibel in 1959 under considerations of a collisionless non-neutral cylindrical plasma column studied a linear pinch confinement equilibrium. As reported here, due to non-linearity of the ordinary differential equations obtained for the electrostatic and magnetostatic fields is possible to demonstrate that the confining features previously obtained are extremely dependent on the initial conditions, and the arrangement of two parameters (β - the ratio between ion and electron mass; M/KT - ratio between relativistic rest energy associated with the pair electron-ion and thermal energy kT ) related to the plasma column characteristics. We investigated in this paper the plasma column behavior (confining or non-confining) under modifications of that set of parameters. We detected a set of parameters values that imposes a confining configuration with an electronic skin effect on the plasma column, not yet reported or discussed in the literature.<br /><br />

The Evolution of Growth Rate and Eigenfunction in a Cylindrical Plasma Column

The evolution of growth rate and eigenfunction of kink instability in a cylindrical plasma column with different plasma pressure is studied by a semi-analytical method. The method can transform magnetohydrodynamics (MHD) equations into a second-order ordinary differential equation. Growth rate can be obtained by solving the second-order ordinary differential equation. 2-D radial eigenfunction can be calculated with a fixed growth rate. The significant change of growth rate and eigenfunction indicates inhomogeneous plasma pressure P0 is destructive for kink instability. The advantage of our method is that it can divide problem into two parts and then solve them separately.