A Geometric Constraint Framework for Kinematic Particle Confinement in Maxwell-Compatible Plasma Fields

This theoretical and numerical study develops a geometric framework for investigating bounded trajectories and spatially localized finite-time sensitivity in a prescribed flow associated with Maxwell-compatible electromagnetic fields. Its central objective is to examine how rotational motion, damping, and attraction toward a geometrically shaped target surface influence trajectory evolution, while distinguishing electromagnetic consistency from a self-consistent theory of plasma confinement. The reduced model combines a radially decaying rotational envelope with linear damping and nonlinear attraction to a corrugated target surface. Its parameters control the strength and spatial extent of rotation, the attraction rate, and the target geometry. Because the longitudinal coordinate remains constant, trajectories evolve within invariant two-dimensional planes. The mathematical analysis uses the Jacobian and its symmetric part to characterize instantaneous perturbation growth and develops conservative sufficient conditions for transverse contraction. These conditions concern infinitesimal separation within the reduced dynamics; they are not equivalent to establishing confinement of a physical plasma. The electromagnetic construction specifies a divergence-free magnetic field, a conservative static electric field, and the charge and current densities required by Maxwell’s equations. Supporting calculations examine source consistency, regularization, and conditions for finite magnetic-field energy. Numerical results include finite-time Lyapunov-exponent maps, trajectory-resolved Jacobian eigenvalue diagnostics, ensemble statistics, parameter sweeps, and comparisons between absorbing and reflecting boundary treatments. The reported computations illustrate parameter-dependent regions of stretching and contraction. Positive finite-time estimates are interpreted as evidence of transient trajectory separation, rather than sufficient proof of sustained chaos or a chaotic attractor. The appendices provide additional electromagnetic calculations, a derivation of the transverse-contraction criterion, and a proposed extension to two-fluid magnetohydrodynamics. This extension considers how a structured velocity perturbation contributes to generalized Ohm’s law and introduces a pressure-like correction to the momentum balance. Suggested keywords: plasma confinement; reduced dynamical systems; Maxwell-compatible fields; finite-time Lyapunov exponents; local stability; transverse contraction; nonlinear dynamics; two-fluid magnetohydrodynamics.