We discuss the behavior of steady cylindrical plasma in the longitudinal magnetic field by using the two-fluid model of plasma. The calculation is restricted the case that both the ionization and the recombination of electrons and ions by collision are constant throughout the cylinder of plasma and that the collision terms of the momentum equations in both radial-and azimuthal-directions are negligible small. We also assume that the kinetic energy of electrons in radial direction is zero.
Then, the “ambipolar electric potential” distribution is deduced as a function of radius, and this potential becomes infinite at a certain radius. We consider this radius means the surface of the plasma cylinder. The important conclusions are as follows;
(1). Under the condition that Te and Ti are spatialy constant (where Te : the electron temperature and Ti : the ion temperature) the radial velocity of ions at the surface of plasma does not depend on the longitudinal magnetic field B, as is given by Eq. (32) in §3.2, although it is inversely proportional to B2 in the binary collision theory. When the magnetic field exceeds over a critical value, the direction of the radial component of electric field is reversed so that the ions are accelerated towards the tube-axis.
(2). Under the condition that Te and Ti change adiabaticaly, the radial velocity of ions at the surface of plasma is inversely proportional to B1/3, see §4.
(3). Applying the calculation to the low pressure positive column of small electric current, we can get a Te-Pa. Rw diagram (where Pa : the pressure of neutral atom and Rw : the radius of tube) with a parameter of B/Pa, see Figs.2 and 3. From the diagrams we can understand that there is no value of electron temperature corresponding to the value of pa Rw in a certain range depending on the value of B/Pa, and that in certain range of pa Rw two electron temperatures can be found for the identical value of B/Pa. We are going to investigate these phenomena by experiment.