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This preprint presents a theoretical framework for controlled chaos in plasma confinement.The work originated from curiosity-driven exploration of field model dynamics, where simulations revealed that a proposed configuration can sustain localized chaotic regions. These regions form a distinct attractor that confines perturbations instead of amplifying them, suggesting that chaos—traditionally treated as harmful in confinement systems—may be used as a programmable control mechanism.

The framework is formulated analytically, supported by stability analysis, Jacobian structure, and numerical simulations. The results indicate new possibilities for plasma physics, nonlinear dynamics, and dynamical systems theory, opening a path for approaches that combine mathematical rigor with exploratory intuition.