The positive column in a magnetic field at low pressures: the transition from free-fall to ambipolar conditions

The paper describes how the free-fall theory, given in a previous paper, of a positive column in a magnetic field may be extended to a more general form applicable over the whole pressure range normally used for arc discharges. The theory is asymptotic in the low-pressure range to that of the Langmuir and Tonks free-fall model, and in the high-pressure range to that of the Schottky ambipolar model. The theory is used to predict, for a number of gases, the transition region where correction to either of the above models becomes necessary, and to evaluate the variation of electron temperature with the similarity variable pressure times discharge radius for mercury. The variation of electron temperature and radial electrostatic field for a plasma column in a magnetic field are also discussed.