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A Toroidal Möbius Standing‑Wave Attractor Framework (Recursive Dual‑Domain Coupling as a Model for Plasma Confinement Stability)

Authors: Nowack, Andrea Barbie;

A Toroidal Möbius Standing‑Wave Attractor Framework (Recursive Dual‑Domain Coupling as a Model for Plasma Confinement Stability)

Abstract

Summary: This research introduces a novel conceptual framework for plasma confinement stability, derived from the Triadic Recursive Operator (TRO). The paper proposes that sustained fusion confinement may be achieved through intrinsic topological phase-coherence, rather than relying exclusively on energy-intensive external active feedback control. Key Technical Propositions: Dual-Domain Coupling: The framework formalizes the interaction between configuration space (field geometry) and momentum space (particle velocity distributions) as a contractive recursive system. Topological Noise Cancellation: The model predicts that engineering magnetic field geometry to induce a Möbius-like half-phase inversion in the coupling cycle can force the destructive interference of drift-wave perturbations. Threading Dynamics: Visual and mathematical analysis of the convergence sequence demonstrates that the system naturally navigates toward stable, irrational winding-number neighborhoods (KAM-stable zones), minimizing residence time in unstable rational resonance bands. Actionable Roadmap: The paper outlines a three-phase computational validation strategy, specifically targeting the use of existing tools (BOUT++, GENE, STELLOPT) to test the feasibility of Möbius-phase field configurations in stellarator designs. Significance: This framework offers a unified geometric language for stability that bridges plasma physics, nonlinear attractor mathematics, and dynamical systems theory. It provides a falsifiable hypothesis for achieving intrinsic stabilization in toroidal fusion devices, potentially offering a pathway to reduce active feedback overhead and improve effective fusion gain ($Q$). Data and Code Availability: All TRO recursion code, convergence sequence datasets, and the source manuscript are included in this repository. The author invites collaboration with computational physics groups for numerical validation and experimental design.

Keywords

Field-Line Topology, STELLOPT optimization, Phase‑space topology, Magnetic shear, Flux surface topology, Numerical stability analysis, Intrinsic stabilization mechanisms, Recursive Attractor, GENE / GS2 / CGYRO, Passive Turbulence Suppression, TRO, Feedback Control Optimization, Topological noise cancellation, Magnetohydrodynamic (MHD) Stability, Nonlinear oscillatory systems, Turbulent transport modeling, Gyrokinetic simulation, ⟁, Plasma Confinement, Drift-Wave Turbulence, Zonal flows, Recursive dynamical systems, Stellarator Optimization, Möbius Phase Inversion, VMEC equilibrium, Turbulence suppression, Fourier duality, Winding Number, Recursive coupling framework, Reduced MHD modeling, Topological stabilization, Topological Stabilization, BOUT++, Momentum–configuration space coupling, Dual‑domain coupling, Triadic Recursive Operator, Möbius‑like phase inversion, Nonlinear Dynamics, Fusion Energy, KAM Theory, Irrational winding numbers, Toroidal attractors, KAM tori, Intrinsic Stability, Fixed‑point attractors

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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