Non-twist field line mappings for tokamaks with reversed magnetic shear

Abstract

The structure of magnetic field lines in a tokamak with reversed magnetic shear is investigated by means of analytically derived area-preserving non-twist Poincaré maps. The basic configuration is the magnetic field produced by an ergodic limiter, superimposed to the tokamak equilibrium field in suitable coordinates. We consider the cases of one and two resonant modes, focusing on magnetic island dimerization and the formation of a transport barrier in the chaotic layer of field lines.

Modifying locally the safety profile to improve the confinement of magnetic field lines in tokamak plasmas

“…For twist systems, KAM or Aubray-Mather theories or Greene's criterion can be applied to characterize transport barriers using the discrete system generated by the Poincaré map [8]. The non-twist systems have also been intensively studied [9][10][11][12][13][14][15][16][17] (see also [5,18]). It was proved that a robust transport barrier (formed by many invariant tori, corresponding to invariant circles in the discrete system) exists in the lowshear region.…”

Interference of robust tori on the resonance overlap

“…Besides this technique of robust tori, the resonance structures that we have presented for the reconnection process will allow an understanding a little better of how some structures are destroyed and how some stickiness can be generated inside the plasma chamber [18]. We also point out that even though there are non-twist maps which approach the plasma dynamics in Tokamaks [19,20] they do not carry any robust tori. So, the inclusion of robust tori in the non-twist maps can improve the theoretical understanding of plasma confinement and simultaneously to suggest some new experimental setup [21].…”

“…The Hamiltonian function typically used in plasma confinement approaches, in Tokamaks, has the form [18,20],…”

Effect of robust torus on the dynamical transport

“…In a previous work [1] we introduced a non-twist map with a new transport barrier called robust torus (RT), through a known Hamiltonian derivation in which the RT had been introduced in a systematic way [2,3,4]. The motivation to create this new map was the relevance of transport barrier to plasma confinement in tokamaks [5][6][7] and also because our map could be a natural extension of usual maps [8][9][10][11][12][13] applied to study theoretically transport in tokamaks. In another work [14] we adapted our map with a single robust torus and adjusted the parameters according to the experimental ones used in the tokamak TCABR.…”