Maxwell intuition — E & B fields driving motion

9:12>> Great movie. >> Yeah. It's a great movie. Um those were the original, right? >> Yes. Yes. Yes. Yes. >> Um and this interaction between the electric fields and the fluids is what is described by magneto hydrodnamics. Okay. Magneto because there's magnetism involved. the fact that charged particles are moving around they create a magnetic field and hydrodnamics because it's a fluid of charged particles right so you're combining the Maxwell's equations with the Navier Stokes equations in some sense to create this really complicated physics >> there's there's so many mult there are multiple layers of dynamics dynamic

9:53things happening at the same time >> and to be able to have an understanding. You need to be able to model all those dynamic layers and how they change over time. >> Yeah. And each little thing is affecting the other thing, right? So, you can't really make a lot of a lot of the times in physics, we like to be like, h in this regime, this we don't have to worry about this. In this regime, we don't have to worry about this. Well, in plasma, you got to worry about everything. Right. >> Right. And so it's incredibly difficult to make sense of what is going on which is why the problem of fusion containment in these reactors is so hard. >> Okay. And the governing equation for the magnetic field in a plasma is this which

10:35is a pretty a pretty daunting equation. Okay. On the left hand side you have dbdt which is the time change how how the magnetic field changes with time. >> And then you've got two terms. You've got del cross v crossb which is that's that's what we would call the adve vection term. Okay, it's basically velocity velocity perpendicular with magnetic field is going to give you some kind of force and then the the how that force curls around is going to tell you how the magnetic field so there's like all these vectors that are going in right and then so but but at the end of the