A more mathsy post, it’s Monday.

I’m playing around with Mathematica at the moment and wanted to check out how well it handles systems of differential equations.

In the last post on particle drift I talked about drift caused by a changing B field. This like I’ll look at the drift caused by an electric field at 90 degrees to the magnetic field. Maxwell tells us the equation of motion for a particle is

Equation of motion for a particle in both E and B fields
Equation of motion for a particle in both E and B fields

Splitting into components we get

latex-image-3

And setting all the constants like charge and E and B to 1 gives

latex-image-1

That looks like something I can type into mathematica without crying and fortunately the built in function DSolve will solve this in one go

The gory details
The gory details

And there we have it. As you can see I changed the E to 0.5 otherwise you get a plot like this

When E/B = 1
When E/B = 1

Which I don’t think looks so nice.

What’s surprising is that the speed of the drift is just E/B, the particle’s charge, mass and speed have no effect whatsoever. So the whole plasma just drifts in the same direction at one speed. But get this, if you’re drifting along with the plasma at speed E/B then from your point of view there is no drift happening so the E field vanishes! It’s been transformed away.