## Thursday, May 23, 2013

### Plasmas are hard

A passerby saw a man frantically looking for his lost keys under a lamp post and asked him if he could help. After a fruitless few minutes he asked for the man to point out where he lost them and was told that he actually lost them in the bushes - but he was looking for the keys under the lamp because the light there was brighter.

That's not really fair to researchers--they have to start in the light and work their way outward. But it does feel frustrating sometimes. It works like this:

Even the simplest models of physical systems are often intractably hard to solve. One of the standard tools in the physicist's box is to consider the system at some kind of equilibrium or simple early state and then do a formal expansion of the true (but unknown) solution as the initial state plus some linear variation plus a second order variation plus etc--and then argue that the variation is small and solve the linear equation. (If you can't argue that, then you try to find some remapping of the problem that will make it small, and if you can't do that -- so much for this tool.) The procedure doesn't seem quite fair, but it works very well a lot of the time.

When you're dealing with mostly homogenous things (empty space with a few balls in it, water, etc) with a few simple boundary conditions, you can often exactly solve the equations describing the system. Even when the boundary conditions get too hairy, you can usually manage excellent approximations with simple computer programs, and have a general notion of what the solution will look like before you start.

The equations describing simple plasmas start to get very hairy, because energy moves through the system both as kinetic energy (motion of the particles) and electromagnetic field energy--and each influences the other. It isn't easy to linearize these in real-life kinds of problems. (Classroom exercises have all sorts of simplifying assumptions to keep the problems simple enough for students to solve.)

That means that not only is there not a "formal" exact solution, but that computer solutions are going to be very sensitive to the initial conditions and round-off, and be apt to give misleading answers. (Chaos, anyone?) Worst of all, you typically don't have a good general notion of what the solution should look like.

All this is preface to explain why it has taken so long to get explanations of things we've known about for years, such as why solar flares change so fast or how they manage to accelerate electrons to such high energies.

Have you ever tried to open a breaker on a high-current line? If not, have you noticed that they tend to have very long handles? It is almost as though the current wants to keep flowing, and is willing to jump long arcs to do it. That effect is related to "flux pinning". If you have a magnetic field inside a conducting medium (like a plasma), if the field starts to change that will (by Maxwell's equations) create an electric field, which then moves the charged particles in the plasma, and the resulting current creates a magnetic field that tends to sustain the existing magnetic field. So if there's a magnetic field (e.g. the Sun's) in the middle of a chunk of plasma (e.g. something ejected in a solar flare), it should stay with it as the chunk of plasma moves. That's "pinning".

Except that sometimes it very spectacularly doesn't stay pinned, but jumps over and reconnects with other magnetic fields and releases large amounts of energy.

This team modeled a way that could work when there is a certain kind of turbulence. Without turbulence of some kind, the fields stay pinned.

I have to think about this paper a while, and would have to do quite a bit of literature review (and refresh my memory--I haven't studied plasmas since a class back in '81) to make sure what they're doing covers the bases. But it is encouraging to see progress.

This is the sort of problem that could not have been solved without computers. It is too complex for pencil and paper.

But of course small scale effects, though they are critical and sometimes dramatic, aren't the whole story. Another group studied how "shear waves" smooth out the small variations to leave behind large collective effects.

Unfortunately it is hard to stick probes in the Sun to measure these shear waves. For that matter, it isn't easy to put probes in a rotating globe of molten sodium either, but they're trying, and maybe the results can shed some light on the Sun. So to speak.

There are lots of collective electromagnetic/plasma phenomena that we don't quite understand yet. Describe, yes. But why do they take the form they do?