: Astronomie: Grad-Shafranov equation

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Grad-Shafranov equation

The Grad–Shafranov equation (H. Grad and H. Rubin (1958); Vitalii Dmitrievich Shafranov (1966)) is the equilibrium equation in ideal magnetohydrodynamics (MHD) for a two dimensional plasma, for example the axisymmetric toroidal plasma in a tokamak. This equation takes the same form as the Hicks equation from fluid dynamics. This equation is a two-dimensional, nonlinear, elliptic partial differential equation obtained from the reduction of the ideal MHD equations to two dimensions, often for the case of toroidal axisymmetry (the case relevant in a tokamak). (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Grad%E2%80%93Shafranov_equation)

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