Editing Magnetohydrodynamics (section)

=== Magnetic confinement fusion ===
MHD describes a wide range of physical phenomena occurring in fusion plasmas in devices such as [[tokamak]]s or [[stellarator]]s.

The [[Grad–Shafranov equation|Grad-Shafranov equation]] derived from ideal MHD describes the equilibrium of axisymmetric toroidal plasma in a tokamak. In tokamak experiments, the equilibrium during each discharge is routinely calculated and reconstructed, which provides information on the shape and position of the plasma controlled by currents in external coils.

[[Plasma stability|MHD stability]] theory is known to govern the operational limits of tokamaks. For example, the ideal MHD kink modes provide hard limits on the achievable plasma beta ([[Troyon limit]]) and plasma current (set by the <math>q > 2</math> requirement of the [[Safety factor (plasma physics)|safety factor]]).

In a tokamak, instabilities also emerge from resistive MHD. For instance, [[Tearing mode|tearing modes]] are instabilities arising within the framework of non-ideal MHD.<ref>{{Cite book |last=Zohm |first=Hartmut |title=Magnetohydrodynamic Stability of Tokamaks |publisher=Wiley-VCH |year=2015 |isbn=978-3-527-41232-7}}</ref> This is an active field of research, since these instabilities are the starting point for disruptions.<ref>{{Cite thesis |last=Bauer |first=Magdalena |title=Analysis of magnetohydrodynamic instabilities in the ASDEX Upgrade tokamak by frequency dependent modelling of magnetic measurements |date=2025-03-28 |degree=Text.PhDThesis |publisher=Ludwig-Maximilians-Universität München |url=https://edoc.ub.uni-muenchen.de/35104/ |doi=10.5282/edoc.35104 |language=de}}</ref>