Drift of Ions and Electrons in a Magnetic Field

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Abstract
Townsend's equations for the drift motion of ions under the combined action of magnetic field, concentration gradient and electric field are shown to be inconsistent with the Boltzmann equation. Other relations according to which a gradient contributes a perpendicular component to the drift are shown to be satisfactory in this respect. It is proved that such contributions exist and the fallacy in the demonstration that they do not exist is exposed. These equations lead to the simple result that the drift speed is the same as would occur if the components of concentration gradient and electric field perpendicular to it, as well as the magnetic field itself, did not exist. All of the equations are only semiquantitatively correct and are subject to refinement by a more adequate statistical treatment.

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