Tokamak magnetic field lines described by simple maps

Issue		Eur. Phys. J. Special Topics Volume 165, December 2008 Nonlinear Dynamics and Chaos: Selected Problems


Page(s)		195 - 210
DOI		10.1140/epjst/e2008-00863-y
Published online		11 December 2008

Eur. Phys. J. Special Topics 165, 195-210 (2008)
DOI: 10.1140/epjst/e2008-00863-y

Dedicated to Professor Celso Grebogi on the occasion of his 60th birthday

J.S.E. Portela¹, I.L. Caldas¹ and R.L. Viana²

¹ Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970 São Paulo, SP, Brazil
² Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19081, 81531-990 Curitiba, Paraná, Brazil

viana@fisica.ufpr.br

Abstract
The magnetic field line structure in a tokamak can be obtained by direct numerical integration of the field line equations. However, this is a lengthy procedure and the analysis of the solution may be very time-consuming. Otherwise we can use simple two-dimensional, area-preserving maps, obtained either by approximations of the magnetic field line equations, or from dynamical considerations. These maps can be quickly iterated, furnishing solutions that mirror the ones obtained from direct numerical integration, and which are useful when long-term studies of field line behavior are necessary (e.g. in diffusion calculations). In this work we focus on a set of simple tokamak maps for which these advantages are specially pronounced.

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