On some necessary conditions for p-11B ignition in the hot spots of a plasma focus

[Di Vita]

Dear Sirs,

my name is Andrea Di Vita. I am an Italian plasma physicist, and this is my first post on the Focus Fusion Society Forums. I would like to introduce a paper of mine

On some necessary conditions for p-11B ignition in the hot spots of a plasma focus
Eur. Phys. J. D (2013) 67: 191 DOI: 10.1140/epjd/e2013-40096-3

where I discuss LPPX in comparison with existing Plasma Focus experiments all over the world, and check the applicability of available scaling laws to LPPX.

Here is the abstract:

‘Recently, it has been predicted that hydrogen-boron (p-11B) nuclear fusion may attain ignition
in the hot spots observed in a plasma focus (PF) pinch, due to their huge values of particle density,
magnetic field and (reportedly) ion temperature. Accordingly, large magnetic fields should raise electronic
Landau levels, thus reducing collisional exchange of energy from ion to electrons and Bremsstrahlung losses.
Moreover, large particle densities, together with ion viscous heating, should allow fulfilment of Lawson
criterion and provide effective screening of cyclotron radiation. We invoke both well-known, empirical
scaling laws of PF physics, Connor-Taylor scaling laws, Poynting balance of electromagnetic energy and the
balance of generalised helicity. We show that the evolution of PF hot spots is a succession of relaxed states,
described by the double Beltrami solutions of Hall-MHD equations of motion. We obtain some necessary
conditions for ignition, which are violated in most realistic conditions. Large electromagnetic fields in the
hot spot accelerate electrons at supersonic velocities and trigger turbulence, which raises electric resistivity
and Joule heating, thus spoiling further compression. Ignition is only possible if a significant fraction of the
Bremsstrahlung-radiated power is reflected back into the plasma. Injection of angular momentum decreases
the required reflection coefficient.’

Sincerely

Andrea Di Vita

[Lerner]

Like to see your paper. Can you send a copy to eric@lpphysics.com, please?

[krikkitz]

I’ve just read this paper through my subscription to Research Gate and it strikes me once again that of course, plasma dynamics are Chaotic. Di Vita, as with many others, assumes that when you see turbulence, it must be suppressed, but that is not possible in a Chaotic system without destroying the system you seek to preserve. A better approach would be to seek out those islands of stability that always appear in such systems and find a way to exploit them. Identify and exploit. You guys really do need to get in touch with Mitchell Feigenbaum, the mathematician who figured out how to predict these islands of stability in Chaotic systems. I wish I could assist you further, but I am no mathematician (understatement). Mitchell Feigenbaum can be found at the Laboratory of Mathematical Physics at The Rockefeller University. His email is Mitchell.Feigenbaum@rockefeller.edu. Seriously. Good luck.

[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

[krikkitz]

Thank you for responding to my post, M. Di Vita. Although to my knowledge plasmas have never been characterized formally as Chaotic, they do exhibit some characteristics that led me to think along those lines. For one, they show somewhat smooth transitions to doubling states, i.e., formation of sheaths, which reminds me of bifurcation in Chaotic systems. I understand your point regarding a few versus many degrees of freedom. However, in the presence of an emergent strong magnetic field, those degrees of freedom do essentially contract to just a few. The evidence of this is the behavior of the plasma itself in the DPF, in the way the “instabilities” form. This is order arising from chaos, a hallmark of Chaotic systems. Another characteristic of Chaotic systems is some mechanism of feedback. In the case of the DPF, for one, there is strong feedback from the magnetic fields produced by the plasma in the famous “like likes like” way that moving charges attract each other and organize themselves.

I am certainly not an expert in either Chaos or plasma physics (understatement). I simply know if plasma in the DPF is Chaotic, that efforts to suppress turbulence will not work. What I would really love to see is someone who is well versed in Chaos take a crack at characterizing plasma in the DPF with the view in mind that it just might be Chaotic in nature. If it is and someone could identify an equivalent of a Feigenbaum constant, that could save many headaches and a whole lot of money. It’s worth taking a look.

[Di Vita]

“Thank you for responding to my post, M. Di Vita.”

Thank you for your interest. Please, let me play devil’s advocate. For a hint of possible future developments, see the last lines of my post.

“Although to my knowledge […] Chaotic systems.”

Indeed, the so-called ‘edge localized modes’ (also known as ‘ELMs’, i.e., coherent oscillations observed in the boundary layer of tokamak plasmas) are currently described as ‘limit cycles’, i.e. as stable, spontaneously occurring, oscillating solutions of a system of simplified, non linear ordinary differential equations. The latter provide us with approximate desciption of mass, momentum ad energy transport in the plasma boundary layer. This approximate description works fine because of the relatively simple (axisymmetric) geometry of tokamak plasmas. (Unfortunately, simple geometries seem to play no role in the DPF). ELMs play a crucial role in the helium control strategy at ITER (if ELMs do not remove helium properly, duterium-tritium fusion keeps on storing helium inside the plasma, leading to unacceptable dilution of deuterium and tritium and stopping further nuclear fusion reactions). The mathematical theory of limit cycles is the same theory of chaotic systems (see e.g. Kutznezov’s textbook).

“I understand your point regarding a few versus many degrees of freedom. However, in the presence of an emergent strong magnetic field, those degrees of freedom do essentially contract to just a few.”

If only it were true… 🙂 Strong magnetic fields may justify simplification from fully three-dimensional geometry to two-dimensional geometry in a restricted class of problems. (Even so, most essential physics is lost: think e.g. of a magnetar). 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.

“The evidence of this is the behavior of the plasma itself in the DPF, in the way the “instabilities” form. This is order arising from chaos, a hallmark of Chaotic systems.”

Indeed, it is a hallmark. But not of Chaotic systems; just of what plasma physicists call ‘relaxation’, i.e. ‘spontaneous evolution towards a stable, organised configuration’. Relaxed states are often described with the help of variational principles, i.e. with wordings like: ‘as its own relaxed state, the plasma selects the state which minimises magnetic energy among all possible configurations with the same twistedness of magnetic field lines’. This is the so-called Taylor’s principle, formulated in 1974. In DPF pinch, hot spots seem to be realisations of Taylors’ principle. Numerically, it has been shown that relaxation to states described by Taylors’ principle is the outcome of the competition between heat transport processes on one side and magnetohydrodynamic turbulence on the other side. Turbulence, not chaos.

“Another characteristic of Chaotic systems is some mechanism of feedback. […] themselves.

Spontaneous filamentation, a common feature of many turbulent plasmas both in the lab and in space, is a well-known example of such self-organisation. Again, it is not necessarily due to Chaos. In the DPF, filamentary plasmas have been described with the help of the so-called Turner’s principle, a generalisation of Taylor’s principle.

“I am certainly […] will not work.”

This is certainly true. Even in conventional fluid dynamics (I mean, with zero magnetic field), nobody has yet achieved full suppression of turbulence in high-speed flows. (As you may know, sharks seem to be equipped with a particularly wrinkled skin which lowers turbulence-related drag -my dear friend Professor Bottaro at Genoa University in Italy is a renowned expert in the field. But reduction is no suppression). A fortiori, as far as I know nobody is able to tame magnetohydrodynamic turbulence today. (Admittedly, it is possible to raise the shock front angle in hypersonic plasma flow with the help of a magnetic field, as recently observed in a laboratory at Pisa, not too far from the Leaning Tower). In my opinon, the appeal of DPF lies precisely in the fact that it requires no turbulence suppression.

“What I would really love to see is someone who is well versed in Chaos take a crack at characterizing plasma in the DPF with the view in mind that it just might be Chaotic in nature. If it is and someone could identify an equivalent of a Feigenbaum constant, that could save many headaches and a whole lot of money. It’s worth taking a look.”

You are perfectly right. Indeed, I wonder if a simplified system of equations like the system quoted above in the discussion of ELMs may hold also for a DPF. Once the system has been written down ‘on the back of the enevelope’, then standard mathematical techniques (including e.g. the so-called ‘continuation analysis’, a tool available even in MATLAB) may find both ‘an equivalent of a a Feigenbaum constant’ and all islands of stability, provided that they exist. In turn, simplification forces us to give up any complete description of the system. Then, it requires knowledge of both a) the equations of motion of a plasma and b) the relevant quantities to be computed (such quantity should differ in ELMs and PDF, as both temperature, chemical composition and geometry are different). Since a) are well-known, the difficulty is to find out b). Of course, once the answer is known, it can be tested also on other plasmas, not just on the DPF. Then, the problem affects both the quest for nuclear fusion and the fundamental research.

[Alex Pollard]

Di Vita, what do you make of Hannes Alfvén’s Nobel acceptance speech, repudiating magnetohydrodynamics wherein magnetic fields are assumed to be “frozen” into plasma?

[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.

[Di Vita]

“Di Vita, what do you make of Hannes Alfvén’s Nobel acceptance speech, repudiating magnetohydrodynamics wherein magnetic fields are assumed to be “frozen” into plasma?

Alfven’s speech provided Witalis and Turner with the physical basis of their dismissal of conventional magnetohydrodynamics (MHD) for plasmas whose linear size is smaller than the collisionless ion skin depth (the ion equivalent of the London depth in superconductors). Should a macroscopic description apply to such plasmas, it would rather be provided by the so called ‘extendend MHD’ (EMHD), which is known also as ‘electron MHD’ or ‘Hall MHD’. Ohm’s law is the fundamental difference between MHD and EMHD. If collisions are negligible, then MHD Omh’s law -together with Faraday’s law- predicts the magnetic field lines to be frozen to the velocity of the plasma, where the plasma is made of ions and electrons moving together. In contrast, if collisions are negligible then EMHD Ohm’s law and Faraday’s law predict the magnetic field lines to be frozen to the velocity of the electrons, which may differ from ion velocity. In other words, electrons and ions are much more decoupled in EMHD than in MHD. Remarkably, Stenzel’s experiments and Gekelmann et al.’s experiments have independently shown that spontaneous filamentation occurs in EMHD even without the triggering due to thermal instabilities predicted by Haines (in UK) in Z-pinch on the basis of MHD. Spontaneous filamentation is a well-known phenomenon in plasma guns like the magnetoplasmadynamic thruster (MPD), currently investigated in Japan, USA (prof. Choueiri) and Italy (prof. Andrenucci) for space electric propulsion. And, of course, it is the foundation of DPF operation, including LPPX. The very structure of DPF pinch is filamentary, as reported by Jakubowski et al. (in Poland) and by Bostick et al. (in USA). But the real amazing thing is tha DPF pinch filaments may collapse into relatively stable hot spots, which are non-filamentary, point-like, ultra-dense plasma structures. Nardi (in Italy) suggested that hot spots may indeed be just relaxed plasmas described by Taylor’s variational principle, according to which magnetic energy attains a minimum with the constraint of magnetic helicity (a quantity related to the twistedness of magnetic field lines). Unfortunately, Taylor’s principle provides no information concerning plasma density, while the only thing we know for sure about hot spots is that the density of electrons attains values near to the liquid water at room temperature and 1 bar. Finally, according to Brzosko (a Polish physicist working in the USA I met long ago in Dubrovnik), nuclear reactions occur spontaneously in hot spots and produce radionuclides. Qualitatively at least, old measurements of Harries in the USA agree with Brzosko’s measurements. These observations support LPPX roadmap towards fusion. Trouble is, occurence of such reactions within hot spots imply the magnetic field achieves locally values unheard-of so far on Earth. In turn, generation of such field is well understood in the framework of MHD. Indeed, Taylor’s principle is a matter of MHD, not of EMHD. But hot filaments and the resulting hot spots are definitely a matter of EMHD. If a macroscopic description of such structures is feasible (Nardi would disagree), then the role of electrons should be properly taken into account. This is precisely what Lerner’s original papers fail to do (according to my opinion). I have tried to take also electrons into account. Today, I think electrons dissipate a certain amount of energy initially stored in the ions. (After all, collisions are not negligible at high density). This dissipation, unaccounted for by Lerner, spoils fusion. However, I suggest there is some way to solve the problem: just recycle a fraction of the energy lost by the plasma through radiation, and fusion becomes again possible.

[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.

[Di Vita]

SECOND PART OF MY ANSWER TO KRIKKITZ

“Regarding relaxed states. All of physical reality seeks for it’s lowest energy state. […] though… ”

This is an all-too-common example of misunderstanding in physics. Physical systems seek for their lowest energy state provided that they are isolated. Look e.g. at an old light bulb. Once unplugged, it is switched off, and is isolated from the grid; if it is switched on, it gets warmer, it is not isolated, and its energy content is obviously larger. Note that the bulb is in steady, stable state in both cases; if you shake it gently, it will remain in its original condition, whatever it is, i.e. it relaxes down to its original state after a small perturbation. Both the switched-on and the switched-off bulb are therefore in relaxed state, but the energy content of one state is larger than the energy content of the other state. Should the bulb seek fot its lowest energy state, you’d never be able to switch it on. As for DPF plasmas, they may be relaxed, but are definitely not isolated (as LPPX people working on electrodes are painfully aware… 🙂 )

“The principles of least action […] across scales…”

The principle of least action rules mechanics. But mechanics provides full description only if the system lacks dissipation. Neglecting dissipation is a weak point in Lerner’s original papers, in my opinion.

“Regarding your last paragraph, […] cannot.”

Let us hope we shall be blessed with a view of our final goal, a burning plasma.

[krikkitz]

Regarding lightbulbs and processes seeking their lowest energy state:

You said, “This is an all-too-common example of misunderstanding in physics. Physical systems seek for their lowest energy state provided that they are isolated. Look e.g. at an old light bulb. Once unplugged, it is switched off, and is isolated from the grid; if it is switched on, it gets warmer, it is not isolated, and its energy content is obviously larger. Note that the bulb is in steady, stable state in both cases; if you shake it gently, it will remain in its original condition, whatever it is, i.e. it relaxes down to its original state after a small perturbation. Both the switched-on and the switched-off bulb are therefore in relaxed state, but the energy content of one state is larger than the energy content of the other state. Should the bulb seek fot its lowest energy state, you’d never be able to switch it on.”

This is the common mistake of many physicists, that all problems must be simple and linear. I did specifically state that the path to the lowest energy state is often “bumpy.” Turn the bulb on. Now turn it off. Now turn it on. Now turn it off. Now turn it on. Now turn it off… Eventually you will reach a point where you can no longer turn it on because the filaments have burned through, i.e., they have reached their current possible lowest energy state. And it will have done so by the quickest possible path, given the parameters of its local system. In your example, you seem to assume that last part does not matter in accounting for a system seeking its lowest energy state, “given the parameters of its local system.” I never said everything seeks it’s lowest energy state by a direct linear path disregarding all other factors! Also, I never said it will always FIND its lowest absolute energy state, only that it seeks it. Energy, after all, is bound into matter, and matter is bound to its local system’s interactions, which constrain it in wonderful ways.

Neither you or I are dim bulbs, Da Vita.

[mchargue]

Di Vita: Thank you very much for sharing your expertise here. I appreciate the insight, and the chance to expand my understanding of the subject.

[Alex Pollard]

Di Vita, thank you very much for your response.

The key issue seems to be the validity of macroscopic MHD. This in turn has profound implications for cosmology, wherein for instance, cosmic filamentary structures are not predicted, yet are abundant and are poorly explained using gas laws and gravity with some unexplained magnetic fields thrown in. The crisis in physics only deepens, now with the laughable fiction of “magnetic reconnection”.

My attraction to LPP has from the outset been motivated by Lerner’s challenge to the clear failures of mainstream cosmology, which is completely blind to the overwhelming importance of electrical forces in space.

The main reason why LPP has not received anything like the funding of Tri-Alpha or ITER is exactly this divisive question, the validity of mainstream plasma theory.

So for me it is a matter of intuition. Mainstream cosmology is wrong, therefore LPP could be correct in spite of mainstream opinion, and is in fact the only fusion concept with any realistic prospect of success, because it is not misled by false understandings of plasma behaviour.

[Di Vita]

Newbie, you wrote: “This is the common mistake […] linear”

On the contrary, physicists are the first ones who mistrust excess of simplification, because they are doomed to simplify everything. On his very first lesson, Arago used to tell his pupils : “Sirs, you want to scientists. Scientists are observers, Please, observe!” Then he stepped away from the classroom. After a while, he came back to his amazed pupils and asked: “What did you observe? Please report!”. Clearly nobody could spell a word, and he was therefore eager to explain that no observation is meaningful if there is no theory to support it, and no theory is possible without simplification. A XVIII-century American would say: ‘no explaination without simplification’; actually, Galileo said (in old Italian): ‘Difalcar l’esperienza’, i.e. ‘make your experience free of all unnecessary things”. The selection of what is ‘unnecessary’ is as arbitrary as your hypotheses; both are to expected to lead to experimentally testable predictions.

“burned through […] energy state” Indeed, some fraction of your filaments gets vaporised, which is scarcely a ‘minimum energy’ state. Even if the vapor cools down, it is not likely to come back to its original filament in any solid form. Your minimum energy state is rather a maximum entropy state.

“And it will have done so by the quickest possible path, given the parameters of its local system.”

Believe it or not, this is perhaps one of the most least understood propositions in physics. Many researchers postulate you are right -look for ‘Maximum Entropy Production Principle’ or ‘MEPP’ in Google. According to MEPP, systems relax to their final state following ‘the quickest path’, i.e. the entropy of the Universe increases during their relaxation in the quickest way, or equivalently with the maximum erate of entropy production. MEPP supporters’ sanctuary is the open-access journal ‘Entropy’. Indeed, the most famous counterexample to MEPP is precisely the filament of a bulb. Back in the XIX century, in fact, Kirchhoff has proven that heat dissipation in a resistor with constant resistivity minimizes the amount of entropy produced per unit time. The simplest example of Kirchhoff’s resistor is the filament of a bulb.
Kirchhoff’s proof relies on Ohm’s law and Maxwell’s equation of electromagnetism, and has therefore nothing in common with the discredited approach of Prigogine, de Groot and Mazur to non-equilibrium thermodynamics, based on Onsager symmetry relationships. As for myself, I believe that MEPP has no general validity. For details, see A. Di Vita, Phys. Rev. E 81, 041137 (2010).

Why does Kirchhoff matter to people interested in Dense Plasma Focus fusion? Because Kirchhoff’s result may be generalised to some Hall-MHD plasmas like the Dense Plasma Focus, leading to filamentary structures which may evolve towards hot spots depending on the electron density – see A. Di Vita Eur. Phys. J. D 54, 451–461 (2009). The paper of mine at the beginning of the present thread, A. Di Vita Eur. Phys. J. D (2013) 67: 191, is an application of these results to the LPPX scenario.

In a nutshell, I think LPPX plasma -as well as other plasmas- show filaments and hot spots precisely because it does NOT follow the ‘quickest path’.

“Neither you or I are dim bulbs, Da Vita.”

You are right. But -as I hope to have shown- we are not even sure of what happens to a dim bulb. There is still a long way, before we are allowed to generalise our conclusions to you and me.

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