Reply To: Peak Oil from Truth Out

[krikkitz]

Thank you for your additional thoughts on this fascinating topic.

Please allow me to be pedantic for a moment in regarding impossibility of suppressing turbulence, and also allow me to continue as if plasmas are Chaotic for the sake of the debate. Definitions matter because they limit how we may see our way through to solutions. For a well known example, noise in a communications transmission is electrical “turbulence” of the Chaotic type, and there exists no way to suppress this noise. And yet, our communications ability is not only not affected by such noise, but understanding of it in terms of Chaotic processes has allowed us to greatly increase our efficiency of communication across even the noisiest of lines. We essentially are able to do that by ignoring the turbulence and focusing on what lies in between. Just as there are islands of stability in Chaotic systems, there are islands of turbulence. That is exactly the nature of Chaos, turbulence in such systems is bounded at all scales. If we focus only on the noise as an insurmountable problem, we’ll never see the stabilities that also arise across all scales. And thus I dream of Chaos. 🙂

“The mathematical theory of limit cycles is the same theory of chaotic systems (see e.g. Kutznezov’s textbook).”

So there is a Chaotic math characterization of ITER’s emergent problems at least. That is a start. In saying “islands of stability,” I meant to imply those states where the plasma is smoothly producing increasing density in the DPF, rather than the vacuoles of helium that have appeared in the tokamak. As you know, the DPF does not have this helium evacuation problem due to the way in which alpha particles are ejected along the ion beam as the plasmoid collapses, so there is not a direct need to apply the math in the same way. Still, it is encouraging to know work is being done along these lines. Chaos principles work across all scales, and Chaotic processes produce both turbulence and smooth flows within the same system. If plasmas display Chaotic properties, then the system as a whole is indeed Chaotic by definition. So if such vacuoles do appear in the DPF plasma filaments, perhaps they are at such small scales that their effects have not been noticeable in the operation of the DPF so far.

“But such contraction implies no chaos at all. For example, in the Seventies Taylor was able to explain Bohm’s diffusion coefficient in a turbulent (non-chaotic) two-dimensional plasma only.”

By saying “contract to just a few,” I did not mean to imply that there are only two conditions that operate on plasmas in a strong magnetic field. As you obviously know given your response, there are at least three interlocking conditions of sensitivity that are required for a Chaotic system to arise. In plasmas, if they are indeed Chaotic and not simply difficult, those three conditions are likely density, magnetic field, and temperature (i.e., relative energy of the system).

It is fairly obvious that as the density increases the chance for ionic collisions also increases, affecting the localized temperature. But I do not know enough about the subject to say for sure or in depth how this effect of increasing collisions may be coupled to the evolution of the plasma’s magnetic field. At the risk of using a possible straw man argument: Does this operate only in in a one-way manner (increased field gives rise to increased density gives rise to increased collisions)? Or does this operate in the opposite direction (increased collisions gives rise to lower electron energy gives rise to lower magnetic field strength, gives rise to lower density)? If my admittedly basic understanding is correct, then, I suspect that this increase of collisions might give rise to oscillations in the field itself. The question then becomes “At what scale do these oscillations present a problem?” i.e., when do the effects of turbulence arise and interfere with the process?

The difficulty is always at the boundary in Chaotic systems, and so even though in an idealized system, the quantum field effect would characterize the ultimate “island of stability,” getting to that state may be problematic if the system is indeed Chaotic. On the other hand, the good news is that if the system is Chaotic, then this is not the only boundary encountered in plasma in the DPF, and earlier stages of evolution of the filaments of plasma may hold the key to understanding the behavior of the system as a whole as it approaches that all-important transition precisely because Chaotic systems display the same behavior at all scales.

Regarding relaxed states. All of physical reality seeks for it’s lowest energy state. It sometimes has a rather bumpy path to get there, though… 🙂 The principles of least action operate in Chaotic as well as other systems, and thus the appearance of such relaxed states do not negate the possibility of Chaotic action. It’s a matter of scale and coupling of conditions across scales…

Regarding your last paragraph, YES!!! 🙂 I would just add that if the plasma is governed by Chaotic scaling laws, then we need only characterize those laws to understand the operation of the system as a whole. A pipe dream? Could be. Or a mathematician’s dream. I don’t smoke a pipe and I’m no mathematician. I only “see” flows. It’s a gift and a curse. I should have been born with a mathematical mind instead of a spacial one. Math, after all, has a common language, but one I cannot fathom. So I rely heavily on you and others who have that gift of language, M. Da Vita. You can go where I cannot.