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A figure in a 23 Nov 2023 article on Optics.org shows that more energy was produced than delivered. That is, the area or the red region seems to represent the energy produced.

enter image description here

But a similar figure in another article on the Lawrence Livermore National Labs (LLNL) website could be interpreted as meaning that the measurement of "energy produced" includes the energy delivered. That is, the area of the red region plus the yellow region represents the energy produced.

enter image description here

I'd like to be able to reference an article from a reputable ground-truth source that unambiguously clarifies whether or not the numbers that were released for "energy produced" include the energy delivered.

If the "energy produced" is defined to include the energy delivered, then any experiment that fuses even a handful of atoms would "produce" more energy than is "delivered". By that definition, many experiments achieved ignition long before December 5th, 2022.

Update

There are a couple of sources of information that I think should be reviewed before answering...

####1####

Sabine Hossenfelder said in a recent video, referring to a December 2022 announcement...

They got about 50% more energy out of the fuel pellet than they shot in with the laser.

She also makes it pretty clear that she thinks that "Produced"=="Out Of Target" with the following graphic.

Image from Sabine Hossenfelder video

...and she characterizes the Second Ignition numbers in the same way.

####2####

This article on the Lawrence Livermore National Labs (LLNL) website says...

Fusion “ignition” refers to the moment when the energy from a controlled fusion reaction outstrips the rate at which x-ray radiation losses and electron conduction cool the implosion: as much or more energy “out” than “in.”

If "In+Produced=Out", this implies that if "Produced>=0", the requirement for ignition is satisfied.

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  • $\begingroup$ "Energy produced" does not involve the laser radiation energy used to ignite the fuel in any case of sane use of the English language, because the laser radiation energy is not produced in the fuel burn but comes from outside. Total sum (energy of laser radiation) + (radiation energy released from the reaction) would better be called "total radiation energy involved in the shot". $\endgroup$ Commented Mar 23 at 19:39
  • $\begingroup$ The chart on optics.org looks wrong because the ratio of numbers on the 3.88/2.05 disk does not correspond to ratio of the colored areas; perhaps someone has drawn these by hand, without checking the area ratio is correct. The chart on the LLNL website also looks wrong because the red area is supposed to show the energy produced, but is too small on the 2.4/1.9 disk, so again the ratio of areas is wrong; it seems the LLNL chart assumes "produced" means "total energy involved" which is erroneous understanding or misleading use of language. So both sources seem to have their charts wrong. $\endgroup$ Commented Mar 23 at 19:48
  • $\begingroup$ It is also interesting to check how LLNL defines "ignition". On their web page lasers.llnl.gov/science/ignition they say it has to do with rate of energy injected from fusion being equal or higher than rate of energy being lost by radiation emission and other channels - thus the condition of ignition seems to have nothing directly to do with the charts and numbers above. $\endgroup$ Commented Mar 23 at 19:55
  • $\begingroup$ Of course, some fusion reactions always happen even in much easier experiments (e.g. a fusor), so total energy released is always higher than the energy input; some fusion reactions happening does not mean ignition. I understand ignition this way: the fusion energy production has to overtake the energy losses from the reaction volume, at least for some short time. $\endgroup$ Commented Mar 23 at 20:11
  • $\begingroup$ That lasers.llnl.gov/science/ignition article says "Fusion “ignition” refers to the moment when ... as much or more energy “out” than “in.” ". If "In+Produced=Out", this implies that if "Produced>=0", the requirement for ignition is satisfied. But the part in the middle hints at a truer definition that isn't being reported on in the media. $\endgroup$
    – phil1008
    Commented Mar 23 at 20:17

3 Answers 3

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No, "energy produced" doesn't include the energy of the laser radiation used to start and maintain nuclear reactions in the fuel. But you are correct that ignition was achieved before Dec 5, 2022 (for the scientists' definition of ignition, there seem to be more of them, unfortunately).

Papers from people involved with these experiments usually use the term "fusion yield", denoted $Y_{total}$, to refer to energy gained from the fuel.

In the first reported experiment in LLNL that increased this yield to levels comparable to the laser energy used, Hybrid-E experiment N210808 on August 8, 2021, this yield was 1.37 MJ, while the laser energy used was 1.917 MJ. According to these papers, this experiment surpassed the generalized Lawson criterion, thus achieved "ignition", even though the energy produced was smaller than the energy input. [1][2][3]

[1] Kritcher et al., Design of an inertial fusion experiment exceeding the Lawson criterion for ignition, Phys. Rev. E 106, 025201 – Published 8 August 2022, paper pdf file: https://journals.aps.org/pre/pdf/10.1103/PhysRevE.106.025201

[2] Zylstra et al., Experimental achievement and signatures of ignition at the NIF, Phys. Rev. E 106, 025202 – Published 8 August 2022, accepted manuscript pdf file: https://link.aps.org/accepted/10.1103/PhysRevE.106.025202

[3] https://www.photonics.com/Articles/LLNL_Experiment_Moves_to_the_Cusp_of_Fusion/a67273

Later experiments in 2022-2023 increased the yield for similar energy input still more, surpassing the "scientific energy breakeven" condition, where the yield is greater than the laser energy used.

On Dec 5, 2022, an experiment at NIF using 2.05 MJ of laser radiation energy achieved fusion yield energy 3.1 MJ, which is greater than the laser energy used, thus surpassing the condition of "scientific breakeven". [4]

[4] H. Abu-Shawareb et al. (The Indirect Drive ICF Collaboration), Achievement of Target Gain Larger than Unity in an Inertial Fusion Experiment, Phys. Rev. Lett. 132, 065102 – Published 5 February 2024, paper pdf file https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.132.065102

Strangely enough, the LLNL website https://www.llnl.gov/news/ignition (and thus also secondary sources like optics.org) claim that first ignition was achieved on Dec 5, 2022, which is much later than the experiment from 2021; they refer to the fact that in 2022, fusion energy yield surpassed the laser energy input. But this is not the scientific definition of "ignition" used in the papers above, but is the definition of "scientific energy breakeven", which is a different thing. So the science communication / PR department at LLNL seems to be using terminology differently than their scientists do (and it seems to me, incorrectly).

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  • $\begingroup$ The second reference says "The NIF experiment N210808[7] produced a fusion yield of 1.37 MJ, 8× higher than its predecessor, passing scientific criteria for ignition[8]." The third reference says "In the Aug. 8 (2021?) experiment, which LLNL reported today, scientists achieved an energy yield of 1.3 MJ — more than the agreed-upon threshold for the onset of ignition". These just show that "Ignition" is defined in lots of different ways (as you said). Do you have any hard proof that "energy produced" equals (or not equals) "energy out" for results starting on Dec 5th, 2022. $\endgroup$
    – phil1008
    Commented Mar 24 at 10:17
  • $\begingroup$ @phil1008 I'm not sure what you're asking. How do you define "energy out"? $\endgroup$ Commented Mar 24 at 23:11
  • $\begingroup$ I would define it as Energy Out = Energy In + Energy Created By Fusion. But there seems to be some evidence that others define it as Energy Out = "Produced" = Energy In + Energy Created By Fusion. Which, I agree, is weird. $\endgroup$
    – phil1008
    Commented Mar 25 at 1:50
  • $\begingroup$ Both definitions you gave are the same, energy in + energy produced by the fuel. "Energy produced" certainly does not include the laser energy, I don't see any good reason to define "energy produced" that way. If some news article does use the term as if laser energy was part of it, it's weird and misleading use of language, maybe due to the article writer misunderstanding the topic or an oversight. Check the papers I linked above - the word "produced" is used always in conjunction with fusion energy yield. $\endgroup$ Commented Mar 25 at 15:57
  • $\begingroup$ Sorry, to clarify, in one definition "Produced" = "Yield" = "Energy Created By Fusion". In the other definition, "Produced" = "Energy Out" = "Energy In + Energy Created By Fusion". We're on the same page about the first definition making the most sense. What I'm looking for is hard proof that on Dec 5, 2022, the yield was 3.15 MJ and not 3.15 - 2.05 = 1.1 MJ. $\endgroup$
    – phil1008
    Commented Mar 25 at 18:29
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The numbers are energy from fusion (in the red obscured circle or the red crescent), and laser energy put on target in the yellow circle, according to S.Hoff's post today: https://www.youtube.com/watch?v=8XRSBA9elm8&lc=UgwIWoVG1qO9JycxOHR4AaABAg.A1KqiEWGIEQA1LSlD6AwnD

I think the biggest takeaway is that they originally shows the output in a circle, which is the obviously and natural interpretation of the figures to showing it as just the areas subtended by the crescent (https://en.wikipedia.org/wiki/List_of_two-dimensional_geometric_shapes), which is a deceptive presentation of the results.

I wonder if any actual scientists/engineers dissented on this presentation, because nothing goes public from a national lab or FFRDC without going through a technical review, and a trip to the public relations office. I would think even the director might have to sign-off for something this high profile, but that's just speculation.

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The person who made the first plot either made it misleading on purpose or made a simple geometry error.

To the main question - "delivered" is the energy from the lasers that reached the capsule (as people often point out, it doesn't include the inefficiency of the lasers). "Produced" is the energy released by fusion reactions. No, produced is not just "energy in the plasma" which might include delivered; if that were the case, "produced" would be by definition bigger than "delivered." It is not. It is an accomplishment that delivered is greater than produced. It's slightly misleading that delivered is inside of produced, I can see how it made you think this.

As for the difference between the two plots, in the first plot, the radius of the circle is proportional to the energy. This is just clearly the wrong way to plot it. It makes "produced" look a lot bigger than it should.

enter image description here

The second plot is done correctly. The area of the circle is proportional to energy. Note that one should interpret the red circle as lying behind the yellow one, so the total area for "produced" should include the area of the yellow circle plus the visible area.

enter image description here

I'm happy to see that the correct plot is on LLNL's website, and the wrong one is on optics.org. But the similarity between the two pictures leads me to believe that the following is very likely how this happened. LLNL used to have the wrong picture on their website; optics.org copied it, then someone at LLNL realized the mistake and made a change.

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