 Ideal magnetohydrodynamics

Ideal magnetohydrodynamics describes a conducting fluid whose electromagnetic evolution neglects electrical resistivity. Its defining electric-field relation isso the electric field vanishes in the local nonrelativistic fluid rest frame. Together with Faraday's law this gives the ideal magnetohydrodynamic induction equationThe Lorentz force density couples the field back to fluid momentum. ^[ref]

For sufficiently smooth fields, the induction equation implies magnetic flux freezing: flux through a material surface moving with the fluid is conserved. Stretching the fluid can therefore amplify the magnetic field while preserving its connectivity. Magnetic tension supports Alfvén waves, providing a direct dynamical consequence of the coupling.

A large magnetic Reynolds number $\mathrm{Rm}=UL/\eta$ motivates neglecting diffusion on the chosen scales. Thin current sheets can still make nonideal terms important locally. The ideal induction condition alone does not set fluid viscosity; mechanical dissipation and magnetic diffusion are different approximations.