The Grad–Shafranov equation is a partial differential equation that arises in the study of magnetically confined plasmas, particularly in the context of magnetohydrodynamics (MHD) and plasma physics. It describes the equilibrium state of a plasma in a magnetic field under the influence of pressure and other forces.
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The Grad-Shafranov equation governs the poloidal magnetic flux of an axisymmetric magnetohydrostatic equilibrium. Pressure and toroidal-field contributions depend on the flux function. The Grad-Shafranov equation for a force-free magnetic field is its zero-pressure-gradient reduction.