Probing hysteresis and bifurcation dynamics in reactive radio frequency plasmas

Hysteresis between capacitive (E) mode and inductive (H) modes is a fundamental characteristic of radio frequency (RF) plasmas that are driven by a saddle-node bifurcation. While considerable research has focused on the static characteristics of this bistability in noble gases, the temporal dynamics underlying these transitions, especially in reactive electronegative plasmas, remain largely unexplored. This limits the ability to predict how fast and under what conditions nonlinear transitions occur in RF systems. This study introduces a framework that couples predictive modeling with ultrafast experimental diagnostics to reveal how electronegative chemistry governs bifurcation dynamics and bistability. A global power balance model is developed that links shifts in the electron energy distribution with state-dependent electron losses to determine the location and shape of the hysteresis loop. The model predicts that dissociative attachment in O2 provides negative feedback opposing stepwise ionization, narrowing the hysteresis window and increasing the power threshold for mode transitions compared to pure argon. These predictions are validated using single-shot terahertz time-domain spectroscopy to measure plasma refractive index changes during mode switching and through the bistable region in RF plasmas, complemented by broadband high-speed imaging. The combined results confirm model predictions and reveal an asymmetry in transition timescales: while O2 addition slows the forward E→H transition, it accelerates the reverse H→E collapse by roughly 66%. This work quantifies how electron loss processes, particularly attachment and transport, play an active, state-dependent role in shaping hysteresis and mode dynamics in reactive RF plasmas.