idealMHD

Ideal magnetohydrodynamics (ideal MHD) is a fluid model for conducting plasmas that assumes infinite electrical conductivity, neglecting resistive dissipation. In this limit the magnetic field is frozen into the moving fluid, so magnetic flux through any material loop is preserved (flux freezing).

The model combines fluid dynamics with electromagnetic effects under the assumption of negligible displacement current. The governing relations include the continuity equation for mass, the momentum equation with magnetic pressure and tension, the induction equation for the magnetic field, and the constraint that the magnetic field remains divergence-free. An energy equation tracks the total energy, including kinetic, internal, and magnetic contributions. Ohm’s law reduces to E + v×B = 0, so current is sustained by the fluid motion rather than by resistive diffusion, and the current density is J = (1/μ0) ∇×B in standard notation.

Key consequences and phenomena of ideal MHD include the Alfvén speed vA = B/√(μ0ρ), which sets characteristic wave speeds, and the existence of Alfvén waves as well as fast and slow magnetosonic waves. The magnetic field exerts pressure and tension forces that couple to the flow, and magnetic field lines are advected with the fluid, influencing structures such as shocks, jets, and accretion flows.

Limitations and context: ideal MHD neglects resistivity, viscosity, Hall effects, and magnetic reconnection, all of which can be crucial for energy dissipation and topology change. Real plasmas often require extended MHD or kinetic treatments. Applications span solar and astrophysical plasmas, the solar wind, accretion disks, astrophysical jets, and magnetically confined fusion experiments.