Hysteresis Characteristics and Topological Analysis of Jet Mode Transition in Plasma Igniter

During the wide-range operating conditions of a scramjet engine, the dynamic variation of the combustion chamber pressure significantly affects the jet characteristics of the plasma igniter, thereby inducing nonlinear transitions between jet modes. This phenomenon poses a critical challenge for the precise regulation of the jet characteristics of igniter. To investigate the hysteresis behavior exhibited during jet mode transitions in a plasma igniter, a cusp catastrophe model based on Thom’s classification theorem is developed in this study, with voltage and ambient pressure as control variables. The model elucidates the route dependence of jet mode transitions and reveals the mechanism underlying the hysteresis characteristics. The results demonstrate that under ascending versus descending voltage regulation paths, distinct differences exist in the mode transition thresholds, and the hysteresis loop narrows with decreasing ambient pressure. Based on the constructed topological model, the relationship between jet mode transition and the control variables is clarified: a sudden transition in jet mode occurs only when the operating path crosses the singularity set. The model further verifies irreversible transition behaviors such as abrupt jumps and delayed switching. The fundamental cause of this route dependence is the asymmetry in electron excitation temperature and energy state: the transition from takeover mode to restrike mode requires overcoming a complete ionization barrier, whereas the reverse transition only needs to fall back to a maintenance threshold sustained by thermal inertia, resulting in asymmetric transition thresholds. Decreasing ambient pressure reduces this energy barrier disparity, thereby narrowing the hysteresis region and weakening the memory effect of its historical state of system. This study enhances the understanding of the nonlinear dynamical behavior and state memory effects of plasma igniters and provides a theoretical basis for dynamic igniter control.