We use a method based on the conservation of energy, the mean-energy error criterion, to approximately locate the place of a cantorus by locating the series of its convergents. The mean-energy error curve has nearly stationary parts in the vicinity of elliptic (minimax) orbits, the so-called magnetic islands. Stable minimax orbits converge to orbits homoclinic to a cantorus. By tracing the island series, we limit the cantorus to a narrow region. A near-critical perturbation parameter is used so that, while the cantorus may be destabilized, its high-order minimax orbits remain intact. As illustrations, we consider two symplectic maps, systematically derived from the Hamilton–Jacobi equation and Jacobi’s theorem, in the context of the magnetically confined plasmas in a tokamak: a symmetric tokamap realistically reproduces the main features of a tokamak, and a symmetric ergodic magnetic limiter (EML) map is defined to describe the action of EML rings on the magnetic field lines in the tokamak.
Cantori Symplectic maps Ergodic magnetic limiter map Tokamap Tokamak
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E.C. da Silva, I.L. Caldas, R.L. Viana, The structure of chaotic magnetic field lines in a tokamak with external nonsymmetric magnetic perturbations. IEEE Trans. Plasma Sci. 29(4), 617 (2001)ADSCrossRefGoogle Scholar