Strange Attractors (Branch of General: Zomes)

[Brent]

This is in response to MSimon's posting in the general discussion forum under Zomes. I felt that it would be better than I post my response here.

OK. I get it now.

The question is: is there some frequency of drive or wave shape that will get us the results we want? A monoenergetic beam that gives us the particle energy annealing we want in order to limit upscattering and increase the density in the reaction zone.

Is that a fair representation?

I hadn’t thought about using the Strange Attractors concept to control the Polywell. It was more of an exploration of different means to describe the dynamic behavior of the particles inside the machine. In addition, a less technical reason was that the words “Strange Attractor” and “fractal” were funny to say. So I wondered what kind of response I would get if a facetiously mentioned them.

That said, what you said brings up an interesting point. If my guess is right that electron upscattering is what prevents the plasma in the Polywell from obtaining a Strange Attractor state, then if we could somehow detect the deviation from the strange attractor state could we not get some idea of the state of the system? On the other hand, maybe I am wrong. Maybe electrons can be lost and the same sort of Strange Attractor, or other recognizable configuration, is formed regardless of the number of particles in the system (to some degree maybe).

Now concerning your question. There are several things I want to find out:

1) If there is a strange attractor, is its shape a function of the confinement. Changing the field strength may change the shape of the attractor (seems logical).

2) Verification or disproof of the ideas mentioned above

3) The more I think about this, the more confused I get. What is the answer?

Any ideas? Maybe someone who has had more than a few days exposure?
See: http://en.wikipedia.org/wiki/Attractor

[Brent]

One other thought. Strange attractors tend to form sheets in phase space that infinitely fold back on themselves, so I read.
I thought I would share.

See the lovely book by Steven H. Strogatz, Nonlinear Dynamics and Chaos.

[drmike]

Recursiveness is one of the ideas behind the math of chaos theory and fractals. There is self similarity on all levels. This is partially true in a plasma, but the microscopic scale has chaotic action which is quite different from the macroscopic scale where things can appear to be uniform and fluid.

It's definitly fun and interesting, but I think it would be hard to map chaos theory to plasma physics in a polywell.