When enough electrons get ripped off the molecules of a gas, it can become so electrically conductive that long-range electric and magnetic fields dominate its behavior. Then you've got PLASMA.
Plasma rules the world of astrophysics. It spans an enormous range of densities and temperatures, from interstellar space to the Sun's core.
For some reason I never seriously studied plasma until a few weeks ago, when the Parker Solar Probe penetrated the boundary separating the solar wind from the Sun's upper atmosphere - its corona.
Trying to understand this, I started reading about the equations of 'magnetohydrodynamics'. These are a combination of the equations for electromagnetism and the equations describing fluid flow. Not all plasmas are well described by the equations of magnetohydrodynamics - they're approximate - but many are. And these equations describe a bunch of weird things that plasmas do!
First of all, in these equations the magnetic field is generally more important than the electric field - as the name implies.
Second, when the electrical conductivity of the plasma is very high, the magnetic field tends to get 'frozen in' to the plasma. In other words, you can visualize the magnetic field as a bunch of 'field lines' that move along with the flow of the plasma.
But third, these magnetic field lines have pressure: parallel field lines tend to push each other away. And they have tension: curved field lines tend to straighten out!
And as the field lines do these things, they push the plasma around.
The math of this is pretty fascinating. The equations are terribly hard to solve, but beautiful to contemplate.
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Here's my little initial foray into the wonderful world of magnetohydrodynamics:
https://johncarlosbaez.wordpress.com/2025/01/01/magnetohydrodynamics/
I show how to derive the basic equations, and I use them to explain magnetic pressure and magnetic tension. All this stuff is standard. I just never learned it in school! I was too enamored with the charms of pure mathematics and 'fundamental' physics.
If you're scared to look at my article, I'll still show you the key equations. (Do my next posts need a content warning for the math averse?)
The animated gif here is from
• Philip Mocz, Create your own constrained transport magnetohydrodynamics simulation (with Python), https://levelup.gitconnected.com/create-your-own-constrained-transport-magnetohydrodynamics-simulation-with-python-276f787f537d
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@johncarlosbaez wow magnetohydrodynamics is a topic I quite enjoy. I studied it very briefly in undergrad because it was my undergrad advisor's research specialty. Excited to get into your blog post!
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@JadeMasterMath - wow, I didn't know that. I wish I'd managed to get you doing some combination of physics and category theory, because at that time I was sad that none of my students were doing physics except Blake. (Kenny was studying Markov processes but he didn't really enjoy the differential equation side of the story.)
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@johncarlosbaez Eh at the time categories felt more exciting 👍
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@JadeMasterMath - I'm glad you enjoyed 'em. My friend Robert Kotiuga had a sign on his door saying "Functorial Electomagnetism Lab".
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