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A symplectic mapping for the ergodic magnetic limiter and its dynamical analysis. (English) Zbl 0954.76099

Summary: We present a model for a two-dimensional symplectic mapping describing magnetic field line trajectories in a tokamak perturbed by ergodic magnetic limiter coils. Numerical examples of these trajectories, computed for plasma described by large aspect-ratio equilibria, simulate the main characteristics of trajectories in the toroidal geometry. We also demonstrate the importance of symplecticity of the new mapping regarding certain features of nonlinear dynamical analysis, for which a large number of iterations is necessary. Thus, we apply some standard algorithms, such as the Lyapunov exponents and the rotational transforms, in order to characterize regular and chaotic regions in the parameter space, to improve the study of bifurcations, routes to chaos, and diffusion in this system.

MSC:

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
76W05 Magnetohydrodynamics and electrohydrodynamics
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
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