Volume Recombination, Constriction, and Volt-Ampere Characteristics of the Positive Column

Abstract

Positive characteristics have been found for diffuse, striationfree, 1-20 ma dc, positive columns in 150-mm Xe, Kr, or Ar, with 0.1% ${\mathrm{N}}_2$ in 10-cm tubes. With Xe+${\mathrm{N}}_2$, a continuous spectrum is emitted; with other rare gases selections of ${\mathrm{N}}_2$ bands. The positiveness of the characteristic results from (1) the disappearance of ions principally by dissociative recombination and (2) ionization which is in effect single stage. For similar current densities the gradient varies little with tube diameter. Probe measurements indicate that the electron and ion density has a relatively flat distribution over a large central part of the tube as compared with the Bessel distribution; the latter resulting from ion loss to the walls by ambipolar diffusion. This broadening out of the discharge increases with the current. For steady convection-free discharges where volume recombination and diffusion are both contributing to ion loss, the degree of constriction should be governed by a "constriction number" $C$ given by $C=\frac{D_a}{\alpha R^2{n}_e}$, where $D_a$ is the ambipolar diffusion constant, $\alpha$ is the recombination coefficient (supposed constant everywhere), $R$ is the tube radius, and $n_e$ the ion concentration.