Magnetic surfaces in non-symmetric plasmas

Abstract

An averaging method is developcd in order to dctermine anslytically the magnetic stwcturc of a system with symmetry broken by small pcrturbations. In particular, Puincare maps are obtained for toroidal hclical fields using the typical parameters of the Brazilian Tokamak TBR-I. The technique is fairly general as the small parameter uscd in the construction of this lheory is the original symmetry-breaking perturbation pardmcler; it is applicable in analyses of ficlds in more compact devices or with cross-sections with any shape as well. Unless the unperturbed system is doubly symmetric (circular cylinder) a single helical perturbation made (PE, n) can excite many other modes. Thc coupling between any two modes arises in a very natural way.

Coupling of modes in RFPs: an analytical approach

“…The primary modes couple themselves exciting other modes. Applying the averaging method developed by Kucinski et a1 [17], we derive an analytical expression for the magnetic surfaces around primary and secondary resonances. We assume that the plasma field is given by the superposition of the Taylor field with a perturbative field associated with the magnetic oscillations.…”

Spectra of helical modes produced by toroidal helical currents

“…Experimental investigations have demonstrated that the m = 2, n = 1 tearing mode plays a crucial role in disruptions in Tokamaks (FUSSMANN et al, 1981). Currents flowing along field lines on a rational magnetic surface of a Tokamak plasma in an equilibrium state may form magnetic island structures at each rational surface (KUCINSKI et al, 1991) causing the disruption of the plasma. The formation of chains of islands in different rational surfaces is determined by the intensity of different helical modes; the position and the shape of the rational surfaces and the direction of the field lines are determined by the equilibrium conditions (the solution of the Grad-Shafranov equation).…”

“…Basically, three approaches have been taken up till now in similar calculations: direct determination of the magnetic field using the Biot-Savart law (SY, 1981), direct determination of the vector potential (MIRIN el al., 1976) or the application of boundary conditions on the scalar potential expression (e.g. KUCINSKI and CALDAS;1987). In all the referred works the surface current is taken on a circular toroidal surface.…”