# Magnetohydrodynamics Explained

### Magnetohydrodynamics Explained

Magnetohydrodynamics (MHD) is the marriage between fluid dynamics and electromagnetism. It is used to describe plasma movements found in astrophysics, geophysics, nuclear fission/fusion reactions and liquid metal manufacturing industries.

Plasmas can become subject to long periods of strain, accumulating energy that will eventually be released as soon as the conditions for optimal MHD change, allowing magnetic reconnection.

## Hydrodynamics

Fluid dynamics is the branch of physics which studies liquids and gases moving, such as rivers. Fluid dynamics is what determines forces on boats when moving through them.

Magnetohydrodynamics combines fluid mechanics and Maxwell's equations of electromagnetism to describe the macroscopic behavior of electrically conducting plasma fluids. Its governing equations consist of Navier-Stokes equations for fluid dynamics and Maxwell's equations for electromagnetism.

Solving these equations numerically yields a set of self-consistent quantities which correlate the plasma mass density r, velocity V, thermodynamic pressure P and magnetic field B.

An essential aspect of ideal MHD is the frozen-in flux theorem. This theorem states that bulk fluid and an embedded magnetic field are bound together so that any two points moving in opposite directions move at equal speeds while lying along identical magnetic field lines, regardless of any fluid flow distortions within the system.

## Electromagnetism

The electromagnetic force connects negatively charged electrons to positively charged atomic nuclei, creating stable atoms which combine into molecules (including complex organic ones that make up living things) or provide everyday forces such as friction.

Magnetohydrodynamics is one of the four fundamental forces that comprise our Universe: gravity, strong nuclear force and weak nuclear force are also part of this equation. Electromagnetism does not maintain equilibrium on Earth; that task belongs to gravity alone.

As current flows through a conductor, magnetic fields are produced surrounding it. These field lines of flux do not cross over into each other but instead focus on its center for maximum magnetic attraction or repulsion strength based on how far apart each charge is located from one another. This law of conservation governs these behavior laws: similar charges repel each other while unlike ones attract, with each increasing or decreasing inversely proportionate to distance.

## Theoretical Methods

Magnetohydrodynamics is a core concept in plasma physics. It combines Navier-Stokes equations for fluid dynamics with Maxwell's laws of electromagnetism to describe plasma behavior, with many applications including astrophysics, geophysics, fission/fusion power plants, metallurgy/direct energy conversion systems as well as other fields.

Ideal MHD assumes that the magnetic field is frozen-in flux, known as "frozen-in flux". This property enables points to stay on a single magnetic field line even when being transported away by fluid flows.

When conditions of ideal MHD aren't met, such as when plasma has nonzero electron diffusivity, resistive MHD may be used as an extended theory. It entails adding an extra term in Ampere's law that models collisional resistance within a system and provides crucial support for phenomena like Hall effect, z-pinch and magnetic reconnection; computer simulations often employ this form of MHD theory too.

## Experimental Methods

Magnetohydrodynamics, more commonly referred to as magnetofluid dynamics or magnetohydromagnetism, combines Maxwell's equations with hydrodynamics to describe the behavior of electrically conducting fluids such as plasmas and liquid metals at macroscopic scale. It works on the principle that magnetic fields induce currents into moving conductive fluids that cause forces on it and alter its magnetic field itself, leading to changes in force distribution across its surface as a whole and hence changing its magnetic field itself.

Ideal MHD is an appropriate approximation for most astrophysical systems and can be used to study waves and oscillations. However, instabilities that break this ideal model include magnetic reconnection where magnetic fields re-connect rapidly after diverging as well as magnetic shear where fluid velocity changes according to direction.

Extended MHD describes the behavior of magnetized plasmas with finite electron diffusivity, and can be used to model phenomena such as Hall physics and electron pressure gradients. Its formulation more closely corresponds with Maxwell's equations than resistive MHD while being less dependent on assumptions such as negligible density perturbations within plasmas.