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Why Lawrenceville Plasma Physics Results are Not Even Wrong; a Detailed Analysis.

June 20, 2012

I recently responded to a claim from Lawrenceville Plasma Physics that they were close to a commercial fusion reactor.  I was annoyed that such claims were being made and even more concerned that such claims were not receiving a strong criticism from the scientific community.  I read the paper published in the journal – Physics of Plasma by Lerner and his colleagues.  The journal is a reputable peered reviewed publication. It was clear to me that the paper was not significant. Dense plasma focus devices are well understood and have been modelled in detail. The results quoted by Lerner did not show that the focus device which he has developed was significantly better than other devices and there was no evidence that a commercial fusion device was any closer.

I was dubious if the paper had achieved its claim of proving that fusion was the result of confined ions rather than beam ions hitting the pinch plasma (non-thermal fusion).  This would indeed be a new result and would contravene the well-known and well accepted current theories that exist. The key point is that Lerner’s device still follows the scaling laws of other devices even if he proposes a different interpretation of results.  The different interpretation does not increase the yield from his device nor does it bring him any closer to commercial fusion.

My conclusion was that Lerner had not built a novel device and had not proved or indeed disproved anything. He had replicated a standard focus device and the paper was not even wrong.  I was contacted by Lerner and asked to explain my position. So I have prepared a short paper to refute Lerner’s claims and justify my conclusion and explain to those who might be interested the reality behind Lerner’s claims. I also want to make it clear that I have no vested interest other than seeking clarity and the truth and I respect Lerner’s right to do experiments and make claims based on his results. 

To clarify the original claim I quote from the LPP web site

On March 23rd, 2012, we published in the journal Physics of Plasmas a report of the confinement of plasma with ion energy equivalent to 1.8 billion degrees C for a period of tens of nanoseconds using a dense plasma focus device. This achieved two out of three conditions—temperature and confinement time—needed not just for fusion energy, but for fusion energy using advanced, aneutronic fuels that have long been considered out of reach. We did all this with an innovative device costing less than one million dollars. If we are able to achieve the third condition, density, we could be on track to commercializing fusion within five years.

For background I will give a quick review of the concept of a dense plasma focus device. The key is that a high voltage is applied between an anode and a cathode. The electrodes have radii A and B, with A>B.  A gap exists between A and B and an insulator shields part of the anode from the cathode.  A plasma forms in the gap and is pushed along the anode by magnetic fields generated by the high discharge current. When the plasma reaches the end of the anode a pinch column forms where the anode had been and this has a very high density and temperatures. This focus is sometimes called a plasmoid.  The ion energy is such that in a deuterium gas, a significant amount of neutrons are produced from fusion reactions.

It is generally accepted that the main mechanism producing the neutrons is a beam of fast deuteron ions interacting with the hot dense plasma of the focus pinch column. The origin of the fast ion beam is a diode action in a thin layer close to the anode with deviations from neutrality generating the necessary high voltages. This mechanism has been modelled in detail based on a expression for fusion yield given below;

Yb-t      =     calibration constant x ni Ipinch2 zp2(ln(b/rp))σ/Vmax0.5

where Ipinch is the current at the start of the slow compression phase, rp and zp are the pinch radius and pinch length at the end of the slow compression phase, Vmax is the maximum value attained by the inductively induced voltage, σ is the D-D fusion cross section (n branch)corresponding to the beam ion energy and ni is the pinch ion density. The D-D cross section σ is obtained by using beam energy equal to 3 times Vmax, to conform to experimental observations. 

Data is available  for the neutron yield Yn from a wide range of machines and can be used to calibrate the model and also to establish a clear empirical scaling law.  It has been shown that the log of the neutron flux is linear with the log of the Ipeak.

Table 1 data from plasma focus devices

A comparison of data from a wide number of plasma focus devices worldwide

 The pinch current is higher for smaller diameters of anode, so a correction factor is required to convert Ipeak to Ipinch. In the case of LPP, I used 0.58 which is the factor measured for the NX2 device which is similar in anode dimensions to the LPP device.  

Figure 1, Data from a wide range of plasma focus devices world wide showing the standard scaling law.

Figure 1, shows a log-log plot of Neutron flux versus Ipinch, LPP best data point in red.

I have included the best result reported by Lerner, which is 1.1Ma and 1.5 1011   neutrons.  It is clear from the paper that other shots at 1.1Ma had a lower yield. Figure 2, in Lerner’s paper shows three points at the highest ion energy ( highest Ipeak) and the spread is at least a factor of 3.  So Lerner’s result fit exactly with all other Plasma Focus devices. What is different is that he drives a large current into a small radius anode, but the device scales just as expected. No new physics here I am afraid.  I have to commend his team on making a solid job of measuring everything and proving that they have a standard plasma focus device, they could have got the calibration of some of the instrumentation wrong and then we might have had less clarity.

I would be interested to hear comments from you on whether you consider this an issue in science today and the role of the web in publishing “Facts” that might mislead.

For more information on the modeling of plasma focus devices and as a reference source for the data used here please see,

Neutron Scaling Laws from Numerical Experiments, S Lee & S H Saw, Journal of Fusion Energy,  2008.

  1. P Liddi permalink

    Great blog, Mike. The net is full of new ideas and claims but people never hear first hand from experts. Best of luck to LLP and anyone pursuing fusion power, but lets keep it real.

  2. Alvaro permalink

    But is focused fusion a device fundamentally capped in its possibilities?
    Could you ilustrate a bit on the history of it and why you think it cannot succeed?

  3. Wooaa neddy. According to the legend of the graph above (and accompanying text) this whole piece is an “annoyed” rebuttal based as it is on LPP results seeming to fit somewhat neatly on a plot of neutron yields from typical DPF experimentation into deuterium+tritium fusion.

    While on first glance that all seems sensible, if in fact the LPP red dot for neutron flux was generated by a side reaction of LPP’s aneutronic fusion of p+B11 (and NOT a principally neutron-yielding deuterium-tritium reaction) then this article runs the risk of missing the point to an alarming degree.

  4. Gavriel State permalink

    Does the CCHEN nanofocus device fit this linear scaling? Looking at and they are showing ~10E3 neutron production for a device that has a peak current of 15 kA. With a similar calibration factor to the other devices in your list, that seems to put their neutron production well above your line, at least according to my crude on-screen estimates.

    Could there not be a possibility of similar higher output from LPPs device, given that they too are pushing larger currents through a smaller electrode geometry?

  5. Dennis T permalink

    Never mind my question. I just learned that Coulomb interactions are electrostatic interactions, not electromagnetic.

  6. The empirical factors you refer to may be due impurities in the fusion fuel such as vaporised electrode. LPP has confirmed copper ions are present. The empirical factors may be common to all prior DPFs but probably not to LPP when they install their tungsten electrodes, which should resist vaporisation much better than their current copper electrodes.

  7. As Dr. Mike Hopkins is not posting his criticism in peer-reviewed journals, reply coming from the Indiegogo Crowdfunding QA:
    >On the Web, links lead to an analysis by Mike Hopkins calling your results “not even wrong.” What is your reply?–3?show_todos=true
    Dr. Hopkins’ analysis misses the whole point of our July 2012 paper, which was about our demonstrating record-breaking temperatures in our confined plasma. Hopkins complained that we had not demonstrated record-breaking fusion yields. But yields depend not only on temperature but on densities as well and we were not claiming any superior density or yield. The paper was about the record temperatures. It was demonstrating that this temperature—sufficient to ignite hydrogen-boron fuel, was indeed confined in a small plasmoid that made our paper the most-read one of 2012 in Physics of Plasma, the leading journal in our field. Evidently a lot of our colleagues got the point, even if Dr. Hopkins missed it. As to densities, we expect to greatly improve them and achieve record fusion yields as well in our next series of experiments.”

  8. I would be interested in your reply to breakablec, Dr Hopkins. I would also be interested in your opinion on the recent arxive paper on plasma confinement by a Polywell device (

  9. Andrea Di Vita permalink

    Admittedly, LPP paper focussed on temperature, not on DD neutron yield. However, Dr. Hopkins s right when invoking well-known scaling laws in assessing LPP performances. The interested reader may find further discusson in A. Di Vita, Eur. Phys. J. D (2013) 67: 191. In my opinion, Lerner’s arguments neglect the adverse role of Joule dissipation, and lead therefore to overoptimistic predictons. Few strategies in order to overcome this problem are also discussed in the paper. . ,

    • I’ve been researching fusion since grade school and came to the conclusion that solar flares/CMEs provide the data points humans will need to understand, interpret, and refine to our environment a suitable method to facilitate power production through dense plasma fusion. In school I called it ‘kinetic fusion’ due to the momentum of the ions and the added heat due to friction of ion interaction. That said, I know I will throughly enjoy reading all of your papers. A new set of thought experiments from another’s perspective is always exciting.

    • In your paper you suggest reflecting Bremsstrahlung energy may help things considerably. How feasible is this? Also, you contributed to the LPP forum. Did Lerner engage with you about these issues at all?

      • No I did not. You must have confused me with someone else

      • In reply to mikehopkins above, actually I was replying to Andrea.

      • Thanks for clarifying. I have not been keeping up with the site much lately. Thanks for the interest. – Mike

      • Andrea Di Vita permalink

        @ marcus H. I had a rather long discussion with Lerner. He observed the scaling laws I have adopted in my paper include no information concerning atomic weight of ions. Basically, in his point of view such laws may scarcely describe the decaborane plasma he’s going to use after fixing present problems with LPP anode. Admittedly, people used to work with isotopes of hydrogen, and available scaling laws refer to plasmas made of hydrogen and/or deuterium.

        I replied that Lerner has overlooked the role of electron-related Joule dissipation due to anomalous resistivity triggered by turbulence. Such resistivity has been observed in the Eighties, and has been consistently referred to since then by many researchers. Of course, anomalous resistivity raises Joule heating, thus spoiling useful energy. Nonetheless, Lerner discusses its impact nowhere.

        As for Bremsstrahlung, a friend of mine, an optical engineer well acquainted with laser technology, suggests suitable mirrors coud do the job. The question is twofold: a) as for physics, it is not clear how many Bremsstrahlung photons reflected by these mirrors may be reabsorbed in the plasma (should the whole system work e.g. as an hohlraum?) b) as for funding, these mirrors are quite expensive, Moreover, it is not at all obvious that these mirrors can withstand many shots (i.e. how much their required replacement may impact costs). Defiitely, LPP lacks adequate funding. They’re stil engaged with anode. Pity, as their work is far from being junk.

        Too many questions remain open. This is why I strongly recommend further funding of LPP research, even if based on shaky grounds.

  10. It sounds like Dr. Hopkins is simply pointing out that the LPP method follows long-established scaling laws for plasmas. This implies that getting usable amounts of power require scaling up to the sizes of “conventional” fusion plasma machines. We likely will still need an ITER-scale machine costing $billions, even if dense plasma focus fusion works.
    In the bigger picture, it appears that we have forgotten the knowledge hard-won by the professional nuclear physicists and engineers of the 1950’s and 1960’s. This a case where six years in the lab saves six hours in the library!

    • Even in such a scenario, LPP’s focusfusion will opt out better since ITER is nothing but a big water boiling teapot that is even unstable at best and still providing potential radioactive pollution if anything goes wrong. And it is far more expensive too.

      And since you are mentioning 50’s and 60’s physicists, there are quite some theories out there which was developed back then and later proved wrong or has been adjusted. One should not forget that. So when Mr. Hopkins states that “Dense plasma focus devices are well understood and have been modeled in detail.” and uses that “model” to disprove the work of LPP, he is doing nothing else than what Mr. Lord Kelvin once said when stating that “All there is to know is known, its just a matter of resolution” (slightly rewritten). He was wrong and so are Mr.Hopkins.

      Mr. Hopkins also fail to reply to the fact that the plasma field in the old dpf was contaminated by copper evaporating from the copper electrodes. The new tungsten electrode will most likely eliminate that…. He also fail to understand what LPP is trying to do. As Mr.Lerner is well educated into dense plasma physichs my guess is that he knows very well where in Mr. Hopkins plot he lays. But this is not the point. Mr. Lerner needs a well functioning DPS and all Mr. Hopkins has provided is a proof that LPP has exactly that. A well working DPS. Thank you for your support Mr. Hopkins! But other devices does not use radial anodes and thus LPP introduces something new here aswell.

      I do not say that the LPP team won’t meet new and challenging problems but the only persons that finds new pathways are does that dear go on further. The others will only see the pathways already known, believing it is the whole world they see.

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