Magnetic field line mappings for a tokamak with ergodic limiters

Abstract

Abstract-An ergodic magnetic limiter is a device whose main effect in a tokamak is to create a cold boundary layer of chaotic magnetic field lines. In order to study its effect we have used two approaches. The first is a description of magnetic island formation through an analytical method to describe its dimensions, results being in accordance with numerical Poincare maps for magnetic field lines. The second is a model which simulates the ergodic limiter action as a sequence of impulsive perturbations, enabling the derivation of analytical formulae for the Poincare maps.

Field-line stochasticity in a Tokamak with an Ergodic Magnetic Limiter

“…we will describe the localized character of this perturbation by supposing a periodic sequence of delta function pulses, which modulates the magnetic field components in equation (2), in the form: (z!2;rrR,,). A more realistic model would assume a square pulse waveform of length g, but a Fourier analysis shows similar results if g<< 2nRo, and the mode number n (to be defined later) is not too large (Caldas et al, 1996).…”

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

“…. , N r − 1 [28]. Proceeding in this fashion, the following area-preserving mapping can be associated with the EML Hamiltonian (equation (11)) [24]:…”

“…The effect of the EML on the equilibrium configuration can be approximated by a sequence of delta function pulses at each piercing of a field line in the surface of section. In cylindrical approximation [3,28,35], such a mapping (r n+1 , θ n+1 ) T = F 2 (r * n , θ * n ) T has been described by [37]:…”

Critical Exponents and Scaling Properties for the Chaotic Dynamics of a Particle in a Time-Dependent Potential Barrier

“…Indeed, mixed phase space is a property of nondegenerate Hamiltonian systems [Zaslavsky, 1998] and can be observed in many different systems including those described by twodimensional, nonlinear and area-preserving mappings. Applications include the study of magnetic field lines in toroidal plasma devices [Caldas et al, 1996;Abdullaev & Zaslavsky, 1996;Punjabi et al, 1997], waveguide [Iomin & Bliokh, 2003;Smirnov et al, 2001;Leonel, 2007], Fermi acceleration [Ladeira & da Silva, 2006;Livorati et al, 2008], transport properties [Venegeroles, 2007[Venegeroles, , 2008[Venegeroles, , 2009 and many others.…”