Measurement of Transport Properties of Ions in Gases; Results forK+Ions inN2

Abstract

A solution is developed to the transport equation describing the drift, diffusion, and reaction of an ion swarm moving under the influence of a uniform electric field $E$ in a gas of uniform number density $N$. An easily applied analytical expression is obtained for a particular type of source input of the ions under the assumption that the only reaction occurring is one which results in the depletion of the ion species under consideration. Data obtained with a drift-tube mass spectrometer on ${\mathrm{K}}^{+}$ ions in ${\mathrm{N}}_2$ at low $\frac{E}{N}$, where the parameters in the solution can be determined from other considerations, are presented to show that the solution does closely describe the drifting ion swarm. The solution is then applied to ${\mathrm{K}}^{+}$ data obtained at higher $\frac{E}{N}$ to determine the mobility, the longitudinal diffusion coefficient and the transverse diffusion coefficient for ${\mathrm{K}}^{+}$ in ${\mathrm{N}}_2$, up to an $\frac{E}{N}$ of 350 × ${10}^{-17\mathrm{}}$ V ${\mathrm{cm}}^2$. The zero-field reduced mobility of ${\mathrm{K}}^{+}$ in ${\mathrm{N}}_2$ is determined to be 2.55 ${\mathrm{cm}}^2$/V sec, in excellent agreement with the nonmass analyzed data of other experiments and with the Langevin polarization limit prediction of 2.60 ${\mathrm{cm}}^2$/V sec. Both diffusion coefficients are found to be in agreement with the value predicted from the Einstein relation at low $\frac{E}{N}$, and to increase as $\frac{E}{N}$ is increased.