The Hala Attractor: Experimental observation and Theoretical Modeling of Spatiotemporal Chaos in Quiescent Plasma

This paper presents a comprehensive investigation into the deterministic chaotic behavior of a quiescent physical plasma system, bridging empirical observation with a new theoretical framework. We first revisit an experimental analysis of Langmuir probe current-voltage (I-V) traces, where a quadratic fit of the electron saturation region revealed a discrete recurrence relation. The resulting bifurcation diagram unequivocally demonstrates a period-doubling cascade leading to a chaotic regime, providing strong empirical evidence for nonlinear dynamics inherent in the plasma-probe interaction. To model this observed behavior, we introduce the Hala attractor, a low-dimensional dynamical system inspired by the Lorenz equations but modified with a self-regulating feedback mechanism. We demonstrate the Hala attractor’s ability to model two key phenomena: a spatial transition from chaos at the magnetically confined plasma boundaries to a stable state in the quiescent bulk, and a temporal transition to chaos induced by the active perturbation of a diagnostic probe. The model’s simulation results, including a bifurcation from a stable fixed point to a chaotic attractor and the emergence of hysteresis in simulated I-V curves, quantitatively validate the Langmuir probe's experimental findings. By unifying these empirical and theoretical approaches, we establish that chaos in this system is not a fixed, intrinsic property but a dynamic, tunable state dependent on both spatial location and the influence of external measurement. This work provides a powerful, unified framework for interpreting experimental data and reinforces the value of applying chaos theory to understand complex plasma phenomena.