Effects of the resonant modes on the magnetic footprint patterns in a tokamak wall

Abstract

Magnetic footprints, or deposition patterns of chaotic magnetic field lines in a tokamak wall, are studied for a configuration with resonant modes due to an ergodic limiter. The formation of magnetic footprints using a nontwist symplectic mapping for a nonmonotonic safety factor radial profile is investigated numerically. The radial position of the resonant mode we focus on changes drastically the magnetic footprints. Deeper resonant modes produce a concentrated field line deposition pattern, whereas a resonant mode closer to the plasma edge yields a broader deposition pattern. Although these shearless equilibria can present robust transport barriers, the magnetic footprints are still present and can deteriorate the plasma confinement quality.

Escape patterns of chaotic magnetic field lines in a tokamak with reversed magnetic shear and an ergodic limiter

“…A method to obtain a numerical approximation to these invariant manifolds is to consider the first N 0 ͑say, 80͒ forward and backward images of a small disk filled with a large number of initial conditions ͑say, 5000ϫ 5000͒ and centered at the location of a saddle point embedded in the chaotic orbit. 66 For large enough limiter currents there is a chaotic region in the outer tokamak region, as can be seen in Figs. 4͑a͒ and 4͑b͒.…”

“…39,51,62,64 An approximated solution of the canonical equations related to the Hamiltonian ͑14͒ gives a local approximation of the field line mapping, 62 which allows a detailed analysis of field line transport and escape. 65 Due to the delta functions appearing in the Hamiltonian ͑17͒, the field lines receive a kick whenever they cross a toroidal section = constant.…”

“…The observed fractal structure of magnetic footprints follows from the mathematical structure underlying the area-filling chaotic region of magnetic field lines-a chaotic manifold tangle, comprising the homoclinic and heteroclinic intersections of invariant manifolds of unstable periodic orbits embedded in the chaotic region. 29,38,39 Another consequence of this manifold tangle is an involved structure of escape basins, which indicate the loci of points such that a field line passing through that point will escape through a given region at the tokamak wall. 51 In this paper we investigate the magnetic footprints and related escape basins for a tokamak with reversed magnetic shear, obtained through using a nonmonotonic plasma current profile.…”

“…Magnetic footprints have been obtained by using numerically 29,[38][39][40][41][42][43][44][45][46] and analytically [47][48][49][50] obtained maps of the perturbed magnetic fields. The observed fractal structure of magnetic footprints follows from the mathematical structure underlying the area-filling chaotic region of magnetic field lines-a chaotic manifold tangle, comprising the homoclinic and heteroclinic intersections of invariant manifolds of unstable periodic orbits embedded in the chaotic region.…”

Chemical transformations of chlorophyll and its application in the design of a new generation of environmentally safe dyes

“…On the inner plasma region, the field lines lie on magnetic surfaces, while the chaotic and unstable periodic lines are in the outer scrape-off layer. The external chaotic layer configuration is essentially 0029-5515/06/040192+07$30.00 © 2006 IAEA, Vienna Printed in the UK S192 determined by the chaotic set on the scrape-off layer [17][18][19][20][21]. As a consequence of this chaotic configuration, the field lines with long connection lengths hit the tokamak wall nonuniformly producing the so-called field line escape pattern.…”