An equation for the drift velocity of relativistic electrons scattered isotropically and a negative magneto-resistance effect

Abstract

Previous work on non-relativistic electrons isotropically scattered by neutral atoms is extended to the relativistic case, and an equation is derived for the electron drift velocity. In the non-relativistic case the drift-velocity equation contains a corrected momentum-transfer term arising from the fact that the collision phenomenon is characterized by the mean free path rather than by the mean collision time. In the present work it is found that the time variation of the electron mass has a very complicated effect on the relativistic equation for the drift velocity. In addition, an unexpected theoretical result is obtained: a negative magneto-resistance effect in which the magneto-resistance decreases as the magnitude of a magnetic field imposed on the plasma increases. However, this effect is not a relativistic one but is rather due to the correction in the momentum-transfer term.