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.
Xun Zhang (Thu,) studied this question.