Scenario of a transition of oscillatory striations to chaos in a steady-state discharge in rare gases and their mixtures used in lasers

An experimental study was made of the behaviour of ionisation instabilities resulting in stratification of the positive column of discharges in argon, neon, helium, and their mixtures. The study was carried out in the vicinity of the boundaries between regions representing regular and chaotic oscillations in the discharge current–pressure plane. Variation of the current revealed sequences of period-doubling bifurcations which became more frequent as the critical point of a transition to totally chaotic behaviour of self-excited striations was reached. A 'stability window' in a chaotic region (at a current higher than the critical value), a sequence of bifurcations in this window leading to chaos again, and a series of reverse bifurcations as the current was reduced (corresponding to the left-hand limit of the transition from regular to chaotic striations) were all observed for the first time. At average pressures of 0.067–6.7 kPa the transition to chaos corresponded to the Feigenbaum scenario. The fundamental constants of this scenario, δ = 4.6 ± 0.1 and α = 2.6 ± 0.6, were determined. The presence of a stability window and the reappearance of chaos indicated that the transition to chaos involved an intermittency of the first kind (Pomeau–Manneville scenario). A bifurcation sequence was observed most clearly in discharges that took place in pure argon and neon or in the presence of small (4%–5%) amounts of helium. At higher helium concentrations the boundary regions of the transition to chaos became much narrower and they were difficult to observe in pure helium.