John Carlos Baez on Nostr: Here are the equations of magnetohydrodynamics, or MHD for short! The variables here ...
Here are the equations of magnetohydrodynamics, or MHD for short!
The variables here are
• the velocity of our plasma, 𝐯
• the density field of our plasma, ρ
• the electric current, 𝐉
• the electric field, 𝐄
• the magnetic field, 𝐁
The quantities in boldface are vector fields while the density ρ is a scalar field. I'm assuming the plasma's pressure is some function 𝑓 of its density, so that's why you see 𝑓(ρ) in the equations.
But my blog article explains step by step how we get these equations, and a few basic things we can do with them. I do *not* explain how the magnetic field can get 'frozen in' to the plasma. Maybe I'll do that some other time. I'm not completely happy with the usual story about that, so I'd like to expand on it a bit.
(3/n, n = 3)
The variables here are
• the velocity of our plasma, 𝐯
• the density field of our plasma, ρ
• the electric current, 𝐉
• the electric field, 𝐄
• the magnetic field, 𝐁
The quantities in boldface are vector fields while the density ρ is a scalar field. I'm assuming the plasma's pressure is some function 𝑓 of its density, so that's why you see 𝑓(ρ) in the equations.
But my blog article explains step by step how we get these equations, and a few basic things we can do with them. I do *not* explain how the magnetic field can get 'frozen in' to the plasma. Maybe I'll do that some other time. I'm not completely happy with the usual story about that, so I'd like to expand on it a bit.
(3/n, n = 3)