Modelling of magnetic field structure of the Ergodic Divertor of Tore Supra and comparison to the Dynamic Ergodic Divertor of TEXTOR

Abstract

An analytical model previously developed to study the structure of the magnetic field for the TEXTOR-DED [S.S. Abdullaev et al. Phys. Plasmas, 6, 153 (1999)] is applied to the similar study of the Ergodic Divertor of Tore Supra tokamak [Ph. Ghendrih, Plasma Phys. Control. Fusion, 38, 1653(1996]. The coil configuration of ED Tore Supra consists of six modules equidistantly located along the toroidal direction on the low-field-side of the torus with given toroidal and poloidal extensions. The Hamiltonian formulation of field line equations in straight-field-line coordinates (Boozer coordinates) and the computationally efficient mapping method for integration of the Hamiltonian field line equations are used to study the magnetic field structure in the ED. Asymptotical formulas for the perturbation magnetic field created by the ED coils are obtained and the spectrum of magnetic perturbations is analyzed and compared with the one of the TEXTOR-DED. The structure of ergodic and laminar zones are studied by plotting Poincaré sections, so-called laminar plots (contour plots of wall to wall connection lengths) and magnetic footprints. The radial profiles of field line diffusion coefficients are calculated for different perturbation currents and it is found that for the Tore Supra case in the ergodic zone the numerical field line diffusion coefficients perfectly follow the quasilinear formula for smaller perturbation currents although the situation is different for the maximum perturbation current.

Generic magnetic field model in poloidal divertor tokamaks in the presence of resonant magnetic perturbations

“…In this regime the diffusion coefficients of field lines can be described by the quasilinear formula. As was shown in [26,40] they closely describe ones obtained by the direct numerical calculations. For our analytical model of the magnetic field one can obtain analytical formulae for the quasilinear diffusion coefficients.…”

A three-dimensional reduced MHD model consistent with full MHD

“…However, in a finite element code, it may not be possible to represent a discontinuous function in the basis used by that code, and so one may have to approximate ψ v with a continuous function, and so ψ v will no longer be constant along field lines. However, since the field line diffusion coefficient is small in typical devices 23 , the field line drift will be small compared to machine size, and the error will not be significant. Alternatively, one can forgo computing ψ v and just find the components of its gradient by solving the system of linear ODEs derived by Xanthopoulos and Jenko 24 .…”