The theoretical framework that treats plasma as a single electrically conducting fluid threaded by magnetic fields, governing equilibrium, stability, and large-scale dynamics in fusion devices.
Magnetohydrodynamics (MHD) merges the Navier–Stokes equations of fluid dynamics with Maxwell’s equations of electromagnetism. The plasma is described by macroscopic quantities—mass density, fluid velocity, pressure, and magnetic field—rather than individual particle orbits. This simplification is valid when the phenomena of interest have length scales much larger than the ion Larmor radius and timescales much longer than the ion cyclotron period.1
In ideal MHD, the plasma conductivity is taken as infinite. Magnetic field lines are “frozen” into the fluid: they move, compress, and bend with the plasma but cannot break or reconnect. This frozen-flux condition underpins the Grad–Shafranov equation, the workhorse for computing axisymmetric tokamak equilibria—the nested flux surfaces on which pressure and current density are constant.2
Resistive MHD restores finite resistivity, allowing magnetic field lines to slip through the plasma and reconnect. Reconnection drives tearing modes that form magnetic islands, disrupting the nested flux-surface topology and degrading confinement. At large scale, resistive MHD governs disruptions—sudden losses of plasma equilibrium that pose one of the chief engineering challenges for ITER and future power plants.3
Modern fusion modeling extends the single-fluid picture. Two-fluid MHD separates ion and electron dynamics, capturing Hall effects and diamagnetic drifts important near reconnection layers. Kinetic-MHD hybrid approaches treat energetic particle populations (alpha particles, neutral-beam ions) with a kinetic equation while the bulk plasma follows MHD, enabling study of fast-ion-driven instabilities such as toroidal Alfvén eigenmodes that could eject alpha particles from a burning plasma before they thermalize.4