A family of analytic equilibrium solutions for the Grad–Shafranov equation

2007/11/01 by L. Guazzotto, J. P. Freidberg · 1 voice
Physics and Astronomy · Materials Science · #Magnetic confinement fusion research #Laser-Plasma Interactions and Diagnostics #Fusion materials and technologies

paper · doi:10.1063/1.2803759

openalex publication_date 2007/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

A family of exact solutions to the Grad–Shafranov equation, similar to those described by Atanasiu et al. [C. V. Atanasiu, S. Günter, K. Lackner, and I. G. Miron, Phys. Plasmas 11, 3510 (2004)], is presented. The solution allows for finite plasma aspect ratio, elongation and triangularity, while only requiring the evaluation of a small number of well-known hypergeometric functions. Plasma current, pressure, and pressure gradients are set to zero at the plasma edge. Realistic equilibria for standard and spherical tokamaks are presented.

Discussions

• I am currently trying to find a numerical solution to the Grad-Shafranov equation. I am currently using a sort of "toy problem", in which I set the flux surface to be square shaped and zero. I am usin [stackexchange, 1 points]

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