What is the explanation for magnetic pinching in plasmas and conductive fluids?

[Crusoe]

Can someone give me an intuitive explanation why plasmas or conductive fluids tend to follow magnetic flux lines?

E.g. http://en.wikipedia.org/wiki/Magnetohydrodynamics" entry on this says:

In ideal MHD, Lenz's law dictates that the fluid is in a sense tied to the magnetic field lines. To explain, in ideal MHD a small rope-like volume of fluid surrounding a field line will continue to lie along a magnetic field line, even as it is twisted and distorted by fluid flows in the system. The connection between magnetic field lines and fluid in ideal MHD fixes the topology of the magnetic field in the fluid—for example, if a set of magnetic field lines are tied into a knot, then they will remain so as long as the fluid/plasma has negligible resistivity.

If I take a stab at a qualitative explanation, is it because magnetic flux lines are equipotential lines, therefore if the conductor deviates from the flux lines, induced currents are produced which oppose the motion in accordance with Lenz's law?

Also, I know the explanation for Lenz's law is conservation of energy, but it just seems odd that induced currents so happen to be set up to precisely keep energy conserved.

What causes magnetic pinching, e.g. in lightning bolts or even lightning rods (below) then? I would have thought an axial current along a conductive fluid would cause charged particles within it to follow a circular orbit. Where do they get the centripetal force to both follow such an orbit, and in fact exceed that for a stable orbit, and end up reducing their orbital radii?

http://upload.wikimedia.org/wikipedia/en/7/77/Crushed_rod_pollock_barraclough.jpg​

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[Vailanor]

In the case of a lightning bolt or a lightning rod, the magnetic field is generated by an electric current flowing through the conductor. This electric current creates a magnetic field around it, which then exerts a force on any other charged particles in the vicinity. The force exerted on the particles causes them to move in a circular motion following the lines of the magnetic field. This circular motion results in the particles being pinched together, reducing the radius of their orbits and creating the "pinched" effect seen in lightning bolts and lightning rods.

 

[astrokreng]

The explanation for magnetic pinching in plasmas and conductive fluids lies in the fundamental principles of magnetohydrodynamics (MHD). MHD is a branch of fluid mechanics that studies the behavior of electrically conducting fluids in the presence of magnetic fields. In MHD, the fluid is treated as a continuous medium, rather than individual particles, and the behavior of the fluid is governed by the equations of fluid motion and Maxwell's equations for electromagnetism.

In MHD, the magnetic field lines act as guide rails for the fluid, causing it to follow the same path as the magnetic field lines. This is due to the fact that the fluid is electrically conducting, and therefore, any motion of the fluid will induce currents that interact with the magnetic field and produce forces on the fluid. These forces act to align the fluid with the magnetic field lines, resulting in the observed "pinching" effect.

To understand this further, let's consider the example of a lightning bolt. Lightning is a discharge of electricity that occurs between a cloud and the ground, or between two different clouds. The air in the path of the lightning bolt is ionized, meaning that it becomes a plasma, which is a highly conductive fluid. As the lightning bolt travels through the air, it creates a strong magnetic field around it due to the flow of current. This magnetic field then interacts with the surrounding plasma, causing it to follow the path of the magnetic field lines. This is what causes the "pinching" effect that we observe in lightning bolts.

Similarly, in lightning rods, the conductive rod acts as a guide rail for the lightning bolt, allowing it to travel safely to the ground. As the lightning bolt travels along the rod, it induces currents in the rod, which in turn create a magnetic field that acts to keep the lightning bolt on the rod. This is why lightning rods are designed to have sharp points - to facilitate the flow of current and the resulting magnetic field.

In summary, the explanation for magnetic pinching in plasmas and conductive fluids lies in the interaction between the fluid and the magnetic field. The fluid is "tied" to the magnetic field lines due to its conductivity, and any motion of the fluid will result in induced currents that act to align the fluid with the magnetic field lines. This fundamental principle of MHD can be observed in various natural phenomena, such as lightning bolts, and is also utilized in various technologies, such as plasma confinement in