A self-consistent solution for nonlinear theory of the positive column in a magnetic field

Only the electron and ion gases were taken into account in all previous theories of the positive column of intermediately-low-pressure arc discharge with or without the longitudinal magnetic field, while the motion of neutral gas was neglected. In 1982, the authors^1] presented a nonlinear theory of a positive column which indicated that the rotating velocities of neutral gas and ion gas were nearly equal, and the motion of neutral gas could not be ignored. They further discussed the problem of validity of Bohm's criterion. However, some of the parameters with which the computation was worked out in Ref. 1] were not correlated to the initial discharge parameters. In the present paper, two integral relations are supplemented, so that a complete mathematical formation of the problem is given. A convergent numerical solution is obtained by iteration and the solution of Ref. 1] turns out to be the first iteration approximation. It is shown that both functions and parameters obtained by self-consistent solution differ significantly from those obtained in the first iteration approximation. According to this paper the computation can be conducted when the initial discharge parameters are given, so this method could have certain practical applications.