Abstract

We present a novel approach to analysing Langmuir probe current voltage (I–V) characteristics by abstracting the continuous plasma physics into a discrete nonlinear dynamical system. Using high fidelity cubic spline interpolation and mapping the resulting function onto the logistic recurrence relation with a fixed voltage increment ∆V = 1.0 V, we extract a bifurcation parameter μ ≈ 3.481. This value places the ∆V -driven system firmly within the period-4 regime of the logistic map. The approach is supported by a physical motivation based on finite sheath response times and is validated through rigorous statistical analysis, including goodness-of-fit metrics, bootstrap uncertainty estimation, and sensitivity studies. Robustness is confirmed by comparing multiple interpolation methods. The framework is shown to be applicable across different plasma conditions and source types. The extracted bifurcation parameter provides a new, parameter-free, and physically grounded metric of sheath non-linearity that is invisible to classical equilibrium theories and offers a constructive interpretation of anomalies frequently observed in swept-probe data acquired under realistic experimental conditions.

Key words: Plasma physics Langmuir probe Bifurcation Non-linear dynamics