Reply To: Peak Oil from Truth Out

[Di Vita]

FIRST PART OF MY ANSWER TO KRIKKITZ

“Thank you […] I dream of Chaos.”

Even where there is no magnetic field, you may suppress turbulence provided that you act on the turbulent energy balance. In turn, this is possible (R. Narasima and K. R. Srinivasan, Advances Appl. Mech. 19, 221, 1979) either by lowering Reynolds number (e.g. the flow speed at given kinematic viscosity) or by raising Richardson number (i.e., inducing a stabilising buoyancy force, through suitable external heating, pipe curvature etc.). There is no ‘window’, as no resonance survives the simultaneous interaction among a quasi-infinite number of modes. Indeed, reduction of the number of modes is possible, but only if some catastrophic instability explodes spontaneously, thus ruling the behaviour of the whole system. This seems e.g. to be the case of combustion instabilities – see e.g. V. Nair. R. J. Sujith, J. Fluid Mech. 747, 635 (2014). In all cases, turbulence just decays within a typical linear size, so you may observe turbulence suppression only if the system is larger than this size. In plasmas, the strategies above are equivalent either to lower magnetic Reynolds number (i.e., cooling the plasma, thus spoiling fusion) or to suppress Rayleigh-Taylor instability. The latter suppression requires external magnetic fields (remember Ioffe’s experiments in USSR) which are not available in DPF. In all cases, should turbulence suppression be possible in DPF plasmas, the latter should be larger than the typical decay length, a requirement thin filaments and tiny hot spots are unlikely to satisfy in DPF .

“So there is a Chaotic math […] so far.”

Now, please let me be pedantic 🙂 . Chaos means ‘high sensitivity to initial conditions’. It may affect solutions of ‘dynamical systems’. The latter are systems of ordinary differential equations (ODEs). Plasmas and fluids are described by partial differential equations (PDEs). In contrast with ODEs, PDEs describe systems with infinite degrees of freedom. Aproximate simplification of PDEs to ODEs is possible in particular problems only. Turbulence may affect solution of systems of PDEs.

“By saying […] system”

The magnetic field is a vector quantity, i.e. it is made of three components. Thus, you are actually listing five quantities (density, temperature and the three components of the magnetic field). More than enough for Chaos, indeed. Much worse, however, is the fact that all these quantities are fields, i.e. the depend also on space (and not just on time, as in ODEs). As such they are described by PDEs. Turbulence strikes back 🙂

“It is […] density)?”

Your line of reasoning is precisely what plasma physicists do: you are looking for a scaling law. What happens if I raise so-and-so while keeping tic-tac-toe constant? This is a common approach when dealing with turbulence. Trouble is, scaling laws may be written down provided that physics is understood. Unfortunately, different physics act at different scales in plasmas. For example, magnetic flux is approximately constant at frequencies below the ion cyclotron frequency only: this is the fact which allowed Alfven to earn his own Nobel prize. In the DPF all scales are relevant during the discharge, sooner or later. This is why nobody -with the possible exception of LPPX people- has yet understood how precisely to do fusion with plasmas.

“If my admittedly basic understanding [..] the process?”

You have stumbled upon one of the sad histories of nuclear fusion. Once upon a time, an Italian professor at MIT, Bruno Coppi, put forward the proposal of a tokamak (IGNITOR) with extremely large plasma density. According to Coppi, at such large density plasma oscillations are less troublesome as far as turbulence-affected heat transport is concerned, thus improving energy confinement and allowing fusion. Unfortunately, the fusion community has never accepted Coppi’s proposal, and IGNITOR remains a dream (or a nightmare, depending on your point of view). The song remains the same: nobody knows if there is just one scaling law (or, alternatively, one set of scaling laws) which rules the behaviour of the plasma. (Another Italian, Enrico Fermi, had been luckier. After all, solid uranium is not turbulent).

By the way, this is why our governments keep on funding ITER. Allegedly, the larger the plasma, the longer the time required for energy diffusion across it, the better the chance of success. In this Godzilla-like approach, size counts more than ignorance. If this looks like expensive gambling with taxpayers’ money, it is because it is just expensive gambling with taxpayers’ money.

“The difficulty is always at the boundary in Chaotic systems, and so even though in an idealized system, the quantum field effect [..] Chaotic.

If you want to make use of the word ‘quantum’, then you have to check that the typical action of the system (i.e. the product of typical time scale and typical energy scale) is not much larger than Planck’s constant. This seems to be unlikely in DPF plasmas. Even the quantum effects invoked by Lerner act on subatomic scales only. In fluid dynamics, it is the kinematic viscosity which rules the size of the smallest whirls, not Planck’s constant.

“On the other hand, the good news is that if the system is Chaotic, then […] system”

That’s all well and good, but earlier stages of evolution of the filaments are among the less understood questions in DPF physics. For example, a decade-old question in DPF physics is the role of the insulator at the beginning of the discharge.

“as a whole as it approaches that all-important transition precisely because Chaotic systems display the same behavior at all scales.”

Indeed, self-similarity is a property of strange attractors in Chaos theory and of some turbulent energy (Kolmogorov) spectra in fluid dynamics. Unfortunately, however, it is no general property of turbulence.