Volumetric stability of two-step ionization dominated discharges

The stability of self-sustained discharges is investigated both analytically and numerically. The dominant ionization mechanism in the discharge is assumed to be two-step ionization while both electron loss mechanisms attachment and recombination are considered. It is shown that the stiff voltage source is marginally stable when the electron loss rate is due solely to electron-molecular ion recombination. In the presence of attachment the stiff voltage source is unstable and the growth rate of the instability is approximately the attachment rate. A stiff current is shown to be more stable and the discharge is stable irrespective of the loss rate. The theory is verified numerically for at atmospheric Co₂ laser discharge.