magnetohydrodynamischen

Magnetohydrodynamics (MHD) is the field that studies the dynamics of electrically conducting fluids in the presence of magnetic fields. It combines the principles of fluid dynamics with electromagnetism to describe how flows of plasmas, liquid metals, and similar media interact with magnetic fields. MHD is used to model phenomena ranging from astrophysical plasmas to industrial liquid-metal processes.

The core of MHD consists of coupling the equations of fluid motion with Maxwell’s equations. The fluid momentum is governed by a Navier–Stokes type equation that includes the Lorentz force J × B. The magnetic field evolves according to the induction equation, which arises from Faraday’s law and Ohm’s law in a moving conductor. In many formulations, the current density J is related to the electric field E and the fluid velocity v by J = σ(E + v × B), where σ is the electrical conductivity. A key constraint is the solenoidal condition ∇·B = 0. In ideal MHD, infinite conductivity yields the frozen-in condition E + v × B = 0, so magnetic field lines move with the fluid.

Important concepts include the magnetic Reynolds number, which measures the relative importance of advection of magnetic fields by the flow to magnetic diffusion, and Alfven waves, magnetic tension effects, and magnetic reconnection. MHD also supports dynamo processes that can amplify magnetic fields in conducting fluids.

Applications span astrophysical and space plasmas, fusion research (tokamaks and stellarators), magnetohydrodynamic generators, and metallurgical and cooling systems using liquid metals. While powerful, MHD is an approximation; kinetic effects can be important in some regimes, requiring more detailed plasma models.