Conductivity of Ions in Crossed Electric and Magnetic Fields

The effect of collisions of ions moving through crossed electric and magnetic fields is investigated. (a) Collisions of ions with one another are shown to be without effect, the transverse current at right angles to the fields having the same value $\mathrm{neu}$, where $u$ is the velocity of progression, as would exist in the absence of collisions. (b) Collisions of free ions with neutral particles are investigated for the case where $u$ is small compared to the speed $v$ of thermal agitation. As the mean free path is increased the current parallel to the electric field increases to a maximum and then falls asymptotically to zero, the transverse current parallel to $u$ rising from zero to the limiting value $\mathrm{neu}$ for infinite mean free path. Calculation of the Hall coefficient on the present theory, which differs from the usual theory in that it takes account of long free paths, shows that the coefficient increases with increasing magnetic field.