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Abstract

In hot laboratory plasmas, Internal Transport Barriers (ITB) have recently been observed, localised in the radial profile "around" rational values of the winding number w(r) = 1/q(r). These are obviously related to the perturbed magnetic structure, described by a 1 + 1/2 Hamiltonian in presence of a perturbation.

We have studied the appearance of chaos of toroidal magnetic lines by a discrete area-preserving map named "tokamap". By increasing the perturbation we have observed in a wide chaotic sea the destruction of the last confining Kolmogorov-Arnold-Moser (KAM) surfaces, broken and transformed into permeable Cantor sets (Cantori). The flux across a Cantorus has been computed by using refined mathematical techniques due to MacKay et al. We have proved that the ITB observed in the tokamap is actually composed of two permeable Cantori with "noble" values of w (in the definition of Percival).

More generally, between the dominant chains of rational islands q = m/m-1, the most resistant barriers between q = m+2/m+1 and m+1/m have been checked to be localised on the "most irrational" numbers in these Ffarey intervals, i.e. on the Noble numbers N(1,m) = 1 + [1/(m+1/G] (where G is the Golden number) defined by their continuous fraction expansion N(i,m) = (i,m,(1)8].

In conclusion, the study of the tokamap mapping allowed us to predict on mathematical basis that ITB can occur in tokamak plasmas not only "around" rational magnetic surfaces but more precisely on noble q-values of irrational surfaces, and to localise them by the Fibonacci series of their convergents .

Additional information

Authors: MISGUICH J H, Association Euratom-CEA, CEA Cadarache, Saint-Paul-lez-Durance (FR);REUSS J-D, Association Euratom-CEA, CEA Cadarache, Saint-Paul-lez-Durance (FR);CONSTANTINESCU D, Association Euratom-NASTI, University of Craiova (RO);STEINBRECHER G, Association Euratom-NASTI, University of Craiova (RO);VLAD M, Association Euratom-NASTI, National Institute of Laser, Plasma and Radiation Physics, Bucharest (RO);SPINEANU F, Association Euratom-NASTI, National Institute of Laser, Plasma and Radiation Physics, Bucharest (RO);WEYSSOW B, Association Euratom-État Belge sur la Fusion, Université Libre de Bruxelles (BE);BALESCU R, Association Euratom-État Belge sur la Fusion, Université Libre de Bruxelles (BE)
Bibliographic Reference: Report EUR-CEA-FC-1725 (March 2002) pp.7. Free of charge Also published as a letter in Plasma Physics and Controlled Fusion 44 (July 2002) L29-L35, available online at: http://www.iop.org/EJ/S/UNREG/.E4N8RlQLGnC2vC9cLstnQ/toc/0741-3335/44/
Availability: Paper version available from: Association EURATOM-CEA, Département de Recherches sur la Fusion Contrôlée, CEA Cadarache, F-13108 St Paul Lez Durance (FR) Tel: (+33) 4 42 25 70 01; Fax: (+33) 4 42 25 64 21 E-mail: dirdrfc@drfc.cad.cea.fr
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