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Title: A semi-analytical solver for the Grad-Shafranov equation

In toroidally confined plasmas, the Grad-Shafranov equation, in general, a non-linear partial differential equation, describes the hydromagnetic equilibrium of the system. This equation becomes linear when the kinetic pressure is proportional to the poloidal magnetic flux and the squared poloidal current is a quadratic function of it. In this work, the eigenvalue of the associated homogeneous equation is related with the safety factor on the magnetic axis, the plasma beta, and the Shafranov shift; then, the adjustable parameters of the particular solution are bounded through physical constrains. The poloidal magnetic flux becomes a linear superposition of independent solutions and its parameters are adjusted with a non-linear fitting algorithm. This method is used to find hydromagnetic equilibria with normal and reversed magnetic shear and defined values of the elongation, triangularity, aspect-ratio, and X-point(s). The resultant toroidal and poloidal beta, the safety factor at the 95% flux surface, and the plasma current are in agreement with usual experimental values for high beta discharges and the model can be used locally to describe reversed magnetic shear equilibria.
Authors:
;  [1]
  1. Departamento de Física Aplicada, Universidade de São Paulo, 05508-090, São Paulo (Brazil)
Publication Date:
OSTI Identifier:
22299748
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 11; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ASPECT RATIO; EIGENVALUES; ELECTRIC CURRENTS; GRAD-SHAFRANOV EQUATION; HIGH-BETA PLASMA; MAGNETIC FLUX; MAGNETIC SURFACES; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; REVERSED SHEAR; SAFETY