Magnetohydrodynamics

Magnetohydrodynamics, often called MHD, is a scientific model used to study electrically conducting fluids. These fluids include liquid metals and plasmas, which are gases made of charged particles. Instead of tracking every single particle, MHD treats all these charged particles together as one continuous fluid. This approach allows scientists to study how magnetic fields and fluid movement interact on a large scale. It is a vital tool in fields like astrophysics, geophysics, and space physics.

To describe how these fluids move, scientists use a specific set of mathematical equations. These include the continuity equation, the equation of motion, and an equation of state. They also use laws from electromagnetism, such as Ampère's law, Faraday's law, and Ohm's law. The motion of the fluid is determined by combining the current density and the center of mass velocity. By using these equations, researchers can calculate how magnetic fields exert forces on the moving fluid. This includes the Lorentz force, which can be split into magnetic tension and magnetic pressure.

One of the most important concepts in MHD is called ideal MHD. This is the simplest form of the model and assumes that electrical resistivity is nearly zero. In this state, a principle known as the frozen-in flux theorem applies. This theorem states that the fluid and the magnetic field lines are tied together. If the fluid moves, the magnetic field lines must move with it. This means the shape, or topology, of the magnetic field stays the same as long as the fluid remains ideal.

However, real-world fluids are often not perfectly conducting, leading to resistive MHD. When resistivity is present, the magnetic field can move through the fluid via a process called diffusion. This can cause the magnetic field lines to break and join back together. This event is known as magnetic reconnection. Reconnection is a powerful process because it can release huge amounts of stored magnetic energy. This energy often turns into heat, particle acceleration, or violent bursts of radiation.

In these systems, electricity often concentrates into very thin areas called current sheets. These sheets act like ribbons that divide the fluid into different magnetic domains. In the solar corona, these sheets can be as thin as a few meters. This is tiny compared to the magnetic domains, which can span hundreds of thousands of kilometers. In Earth's magnetosphere, current sheets separate different regions of space. Even in seawater, magnetic diffusion can happen incredibly fast, in just milliseconds.

Moving through these fluids are special types of waves called magnetohydrodynamic waves. There are three main types of MHD waves derived from ideal equations. The first is the Alfvén wave, which is a transversal and incompressible wave. The second is the fast magnetosonic wave, which is a compressional wave. The third is the slow magnetosonic wave, which is also compressional. Scientists use these waves as tools for remote diagnostics, such as in coronal seismology to study the Sun.

The history of MHD began with the work of Hannes Alfvén. In 1942, he published a paper in the journal Nature regarding electromagnetic-hydrodynamic waves. He later simplified the name to magnetohydrodynamic waves. His groundbreaking discoveries eventually earned him the Nobel Prize in Physics in 1970. Since his work, the field has expanded into many specialized branches. These include Hall MHD, which accounts for Hall currents, and Electron MHD, which focuses on very small scales where electrons move much faster than ions.