Implementation of Hamada principle in calculations of nested 3-D equilibria

Abstract

Plasma confinement is based on the use of nested toroidal magnetic surfaces. In axisymmetric configurations the nestedness is provided by the existence of a flux function describing the magnetic surfaces explicitly. In the case of a three-dimensional magnetic field, the nested surfaces represent an exception. More typically, magnetic islands are formed on the resonant surfaces. The islands could degrade the plasma performance. The rigorous condition for the existence of nested surfaces without islands was formulated by Hamada (Nucl. Fusion, vol. 2, 1962, pp. 23–37) but was not implemented directly into numerical codes used, for example, for designing the stellarator configurations. This paper introduces a method of implementation of the Hamada principle in numerical algorithms. The proposed approach allows for simple linearized equilibrium equations (LEE) and potentially very efficient three-dimensional calculations of nested equilibria.

Three-dimensional magnetohydrodynamic equilibria with continuous magnetic fields

“…There is another possibility: rather than flattening the pressure to avoid the logarithmic infinities in the parallel current, one may restrict attention to so-called ‘healed’ configurations, for which the resonant harmonic of the Jacobian, , vanishes at each resonant surface (Weitzner 2014; Zakharov 2015; Weitzner 2016). Such a condition could only be satisfied for a restricted class of 3-D plasma boundaries.…”