Reply To: Peak Oil from Truth Out

[Di Vita]

Interestingly, your remark (relevance of islands of stability to nuclear fusion) has been put forward many years ago by a friend of mine , a nuclear engineer who worked with me on nuclear fusion in Italy. Then, I am going to repeat here my old answer.

Chaos – i.e. strong dependence on initial conditions- affects even relatively simple systems, like the triple pendulum, which are described by few degrees of freedom (like the Euler angles in mechanics, or the voltage in a Van Der Pol oscillator, etc.). Islands of stability actually occur in chaotic systems, like those investigated by Feigenbaum and others.

The trouble with plasmas is that they are usually turbulent, not just chaotic. Turbulence implies the coexistence of many modes, each one with its own wawelength and phase. These wavelengths and phases are degrees of freedom. Thus, we may say that turbulence involves many degrees of freedom, while chaos may invove few of them.

In plasmas as well as in ordinary fluids, turbulence may be the outcome of instabilitites affecting an initial, non-turbulent (i.e. laminar) configuration.

This is why turbulence cannot be neglected in Dense Plasma Focus: the latter exploits a succession of spontaneously occurring instabilities, rather than suppressing them.

Moreover, this is also the very reason of the attractiveness of Dense Plasma Focus: turbulence suppression e.g. in tokamaks requires huge, stabilising magnetic fields, and the magnets are themselves a non-trivial engineering issue. Such expensive devices are useless in the Dense Plasma Focus approach to fusion, which, if confirmed, will turn out to be by far the cheapest way to ‘make fusion’.

In a nutshell:
a) the Dense Plasma Focus is relatively cheap because it allows turbulence to occur;
b) as you have correctly stated, chaos allows islands of stability to exist;
but unfortunately
c) turbulence does not require chaos.

Ironically, islands of stability exist in tokamaks. The magnetic field lines give birth to something like knots in the wood, which appear in a Poincarè map of the magnetic field as islands in a chaotic sea. (This is due to the fact that the field lines obey a system of weakly-non-Hamiltonian equations, where Kolmogorov-Arnold-Moser theorem applies). From a practical point of view, however, such islands are a nightmare, as they allow electrons to surf all around them. As a consequence, they raise transport coefficients and lower the confinement time.

In analogy to what happens in fluid dynamics, scaling laws provide useful insight in turbulent plasmas. My work aimed at pointing out those scaling laws which are relevant to the evolution of the plasma in a Dense Plasma Focus. I have tried to compare Lerner’s predictions to what is obtained from currently accepted scaling laws (Remarkably, Lerner’s original papers never refer to the plasma as to a chaotic system).

In my opinion, such laws contradict Lerner’s predictions and prevent break-even, unless some conditions are satisfied (see the paper for further discussion). To be honest, however, I should add that published scaling laws do not apply exactly to LPPX plasmas, so that some uncertainty still remains.

This is not to say that Lerner’s research is not to be funded. In contrast, I think it deserves careful attention (and suitable funding), as even a failure can teach useful lessons. And in Lerner’s case, such lessons could be much, much cheaper than in case of failure of ITER or NIF.

P.S. Thank you for Feigenbaum’s e-mail address