Geometric instability of the quasi-periodic plasma perturbations model

The search to understand and reduce plasma instabilities in magnetically confined fusion devices has driven the development of increasingly complex nonlinear dynamical models. This paper utilizes the Kosambi-Cartan-Chern (KCC) theory to transform the quasi-periodic plasma perturbations (QPP) model into a second-order differential equation (SODE), and characterise its geometric structure with five KCC invariants. Despite their stability as determined by Lyapunov's first method, the two non-trivial equilibria of the model are Jacobi unstable. The geometric instability shows that the system's trajectories are structurally sensitive, providing a previously unknown complement to the classical understanding of plasma stability. By offering a geometric explanation for the emergence of Jacobi instability, this work bridges a critical gap in plasma stability theory. Hence, the KCC theory is an essential tool for future stability analysis in plasma physics.