Electron Drift and Diffusion Measurements inH2andD2with Crossed Electric and Strong Magnetic Fields

Abstract

In a strong magnetic field, the cyclotron frequency of the electron is much larger than the elastic-collision frequency with neutral molecules (${{\omega }_b}^2{\tau }^2\gg 1$). Expressions derived from the Boltzmann equation for the energy distribution, drift velocities, and diffusion coefficients in crossed electric ($E$) and magnetic ($B$) fields are simplified in the limit of a strong magnetic field, with the average electron energy a function of $\frac{E}{B}$. Experiments were done in a coaxial cylindrical geometry with $E$ perpendicular to $B$. Measurements of the ratio of the perpendicular (E×B) to transverse (E) drift velocities in the range $12<\mathrm{}{\omega }_b\tau <48\mathrm{}$, and of diffusion parallel to B in the range $3<\mathrm{}{\omega }_b\tau <8\mathrm{}$, showed that the average energy is a function only of $\frac{E}{B}$, the perpendicular drift velocity. Curves were obtained for hydrogen, deuterium, and helium which give the transverse drift velocity in terms of the parameters $\frac{E}{B}$ (cm/sec) and $\frac{B}{p}$ (kG/mm Hg at 20°C). Comparison of drift velocity and diffusion measurements with theoretical expressions yielded a momentum-transfer cross section for ${\mathrm{H}}_2$ which is 10 to 20% larger, in the range of 0.3 to 4 eV, than that obtained by other authors. Average electron energies of 0.3 to 4.5 eV were determined for hydrogen and deuterium as a function of $\frac{E}{B}$ which ranged from ${10}^6$ to ${10}^7$ cm/sec; proper comparison with average energies measured as a function of $\frac{E}{p}$ with $B=0\mathrm{}$ shows good agreement. The inelastic, molecular-excitation energy losses in ${\mathrm{H}}_2$ are about twice those in ${\mathrm{D}}_2$.