Talk:Aneutronic fusion/Archive 4

Charged fusion products and ICF

Croquant has added a footnote with the blanket statement that the heating of the plasma by fusion products is not relevant for ICF. I believe it is relevant, but the point is rather subtle. Somebody - ideally somebody with experience in ICF research - should consider this question more closely and sharpen the relevant statements here and in related articles. --Art Carlson 08:35, 5 September 2006 (UTC)

Art, I am afraid there is some misunderstanding between you and me on the use of the term "ICF". In my footnote, I thought about X-ray ICF, as in H-bombs, laser or Z-pinch initiated fusion, in the conditions corresponding to the 4th chapter of the Lawson original paper (http://www.jet.efda.org/pages/content/news/2005/yop/dec05-aere-gpr1807.pdf), the "systems in which the desintegration products escape".

As the confinment method in a focus fusion device does not belong to this category, my opinion is the same as yours : heating of the plasma by fusion products is relevant to such a process.

Croquant 05:27, 6 September 2006 (UTC)

What bothers me is this: The Lawson criterion for ICF is ρR > 1 g/cm² (see here), but 1 g/cm² is enough to stop fusion products (see Lawson Sec. 5). Thus we have to expect that a significant fraction of the fusion energy is deposited in the plasma, and that must help keep the reaction going even as the plasma expands. I don't have a handle on how important this is in realistic reactor designs, but I hesitate to say that it is simply "not applicable". --Art Carlson 08:45, 6 September 2006 (UTC)

I may have some dust in the eyes, because I don't see anything in Lawson's paper about this 1 g/cm² "enough to stop fusion products"; I just see at the end of section 5, that, for 1 g/cm², "the assumptions that radiation and charged particles escape is justified". I agree with you that, if we are not in the escape conditions, my statement is wrong, but, when you say that these conditions are not fulfilled, you don't convince me. Croquant 09:23, 6 September 2006 (UTC)

"A figure of 1 gm/cm^2 for the range of the photons and of the reaction products is assumed. This is of the right order of magnitude at temperatures of the order of 10^8 degrees, ...." --Art Carlson 09:35, 6 September 2006 (UTC)

I don't see anything in this sentence which can justify a possible stopping of the fusion products. As English is not my native language, I may miss some subtlety. Could you explain more precisely the way you get to your conclusion ? Croquant 12:24, 6 September 2006 (UTC)

The mean free path of a particle through a material with number density n is λ = 1/(nσ), where σ is the interaction cross section. If the atoms of the material have mass M, then we can write the number density in terms of the mass density ρ: n = ρ/M or λ = M/(ρσ) or ρλ = M/σ. This is why Lawson can write the range of the fusion products, normally a distance, in units of g/cm². The conversion factor is the mass density. For a fusion pellet of mass density ρ and radius R, an alpha particle produced in the center has less than a 1/e chance of escaping if R > λ, i.e. if ρR > M/σ. The Lawson criterion for ICF tells us that we need R > (1 g/cm²)/ρ, and Lawson tells us that the range for fusion alphas in DT is about (1 g/cm²)/ρ. Therefore if we have conditions that can give us useful fusion, we also have R > λ, so most fusion products are stopped within the pellet. --Art Carlson 13:06, 6 September 2006 (UTC)

OK Art; I misunderstood the meaning of the word range. Thanks for the explanations. So, the strict escape conditions are not actually fulfilled. However, I'm wondering what physical method could be used to extract the alphas before they interact with the fuel ions : isn't it just a theoretical possibility, without practical ways to implement it ? Croquant 14:58, 6 September 2006 (UTC)

You're right. Once I went back and read the footnote carefully and in context, it made more sense. The fact that the alphas are contained (assuming my arguments from Lawson are still valid under scutiny) is important, because otherwise the neutron production with p-B11 ICF would be significantly lower than with p-B11 MCF. On the other hand, whatever it is in ICF, you're stuck with it. The only way I have ever seen suggested or can myself imagine to extract alphas apply only to magnetic systems: either have an open-ended system or else large field gradients that break adiabaticity. I have rephrased the sentence in the article. --Art Carlson 15:14, 6 September 2006 (UTC)

By the way, since you seem to be interested in the topic and not totally ignorant, it would be nice if you could hang around to pull me and Eric apart when we start bashing each other. --Art Carlson 15:18, 6 September 2006 (UTC)

Although it could be a hard work to put both of you apart :-), I'll do my best. Croquant 16:24, 6 September 2006 (UTC)

anon in Oregon

Art is slowly learning how to build your gadget Eric... lol!!! I was curious how you intend on replenishing the fuel within the reaction chamber between firings. It will obviously take some amount of time to purge the reaction products and fill the chamber with more reactants. Have you thought about the idea of running several gadgets in sequence, so that one could be firing while the rest go through various cycles of recharge?

I'm posting anon for now sry, this just caught my muse in the right way and I felt obliged to comment... I'll prob. get a wiki account in the next few days.

-anon in Oregon (I know the ip doesn't say so, but I'm also in the process of a move)

Only a tiny amount of fuel is burned with each pulse. The device pulses rapidly enough to maintain the plasma in an ionized state. Gas slowly leaks into the chamber from a reservoir and the ion beam evacuates a tiny amount of fusion products with each pulse.Please visit www.focusfusion.org to chat about this.Elerner 02:32, 13 September 2006 (UTC)

Dispute between Art and Eric

Art and Eric, you clearly have two different points of view on the difficulty to get to ignition in a p-¹¹B fuel, and the risk of an "edit war" between both of you is very high. You use two different criteria, and I must confess that I have no final opinion on their correctness.

Let me summarize what I understood:

• Art: you use nTτ Lawson's triple product, and, from your calculation, you find it 500 times higher than for a D-T fuel. Furthermore, you introduce a "power density", not very clear to me, 2500 times lower than D-T; if it's a measure of the economic potential, as explained in Nuclear fusion, it seems to me that this criterion is not directly related to ignition.
• Eric: you use the "basic" Lawson's criterion (density-confinement time product), and your ratio is only 45; the fact that it doesn't take temperature into account may explain the discrepancy with Art's figures.

So, my first question is: is there a consensus in the fusion community about what criterion should be used in the various types of fusion processes? Specifically, can one legitimately use the same criterion for various reactants and density-temperature-time scales?

Croquant 14:26, 20 September 2006 (UTC)

My interpretation is that this particular argument is sufficiently novel that we really can't just interpret the old conventions and adapt them, the use of each criterion must be judged on it's own merits.

That said, I think that Eric needs to post some actual calculations and a list of assumptions before his calculations should grace the page. Art's calculation is very standard. Eric's, as far as I can tell, involves trickery and assumptions and all kinds of clever things which for the life of me I can't pin down! The Lawson criterion is by no means a lower bound of difficulty, and Eric seems to be trying very hard to show that it's not as bad as it looks at first glance. But I can't tell if he's honest or not because I can't see the calculations!

If and when Eric makes the calculations clear, I would not object to including Art's calculations as the 'base' measure of difficulty, and Eric's as the 'state of the art' version, with all assumptions that go beyond the pale explicit. Indeed, I think this would be the best outcome.

Art makes a useful distinction: is it possible vs. is it worthwhile. I'm not convinced that power density is the best measure of whether or not it's worthwhile. It's not clear at this point. But it's better than nothing.

I just see the recent discussion in Charged_fusion_products_and_ICF, which answers partially to my previous question. I read it completely, and come back later. Croquant 20:57, 20 September 2006 (UTC)

Concerning the "power density" figure of merit, it's a way to know if the energy production process is worthwhile; so, it seems to be an economic criterion. My opinion is that such an economic criterion should take into account the energy cycle as a whole, and not only the fusion process. (I'm sorry I have to go; I'll be back tomorrow). Croquant 21:19, 20 September 2006 (UTC)

The main difference I can see between your approaches is the fact that temperature should (Art) or should not (Eric) be taken into account in the criteria. My hypothesis (to be confirmed by both of you) is the following :

• Art's calculations are related to a process in which the entire plasma volume must be warmed up to the fusion temperature (as in a tokamak);
• Eric's calculations are related to a nearly-adiabatic process, in which ignition is initiated by "hot spots" (as in a focus device).

If I'm right, and as nobody can seriously consider fusion of an aneutronic fuel in a tokamak (at least in a foreseable future), and, according to Eric, of a D-T fuel in a focus device, there is no way to make a fair comparison using a single criterion. So, both of them should be set out, along with their validity area. Croquant 05:23, 21 September 2006 (UTC)

Thanks for your comments and questions.

• Figures of merit that compare reactions without reference to a specific machine are of necessity zero-dimensional, in the sense that they take no account of spatial or temporal differences. A real device will have, so to speak, both a geography and a history. That said, the Lawson criterion and power density (divided by pressure squared) are still remarkably useful. They can be applied to pulsed as well as steady-state devices and also to strongly inhomogeneous plasmas (with "hot spots"). The worst that can happen is that you have to be careful about exactly how you define the energy confinement time.
• Some comparisons are obviously unfair. For example, if I design a reactor for D-T fuel and then replace D with p and T with B, keeping the temperatures constant, the aneutronic fuel would look a hell of a lot worse than it already is. Eric and I agree that you have to adjust both the fuel mix and the temperature to be (in some sense) optimum for the reactants being used. Unfortunately, power density also depends on number density, so you have to decide how to treat that. When switching from one fuel to another, you have the choice of leaving the density the same, leaving the pressure the same, or keeping any other function of density and temperature constant. (You can't keep both density and pressure the same because we already decided that we have to change the temperature, remember?) I clearly state that it is best to keep the pressure constant for present purposes because it is most useful, most common, and most natural. Eric seems to plead for keeping the density constant (but actually he finds any quantitative comparison at all uncomfortable).
• We all agree that p-B11 is a no-starter in a tokamak, but it is nonsense to rule out use of D-T in a DPF. In the first place, the confinement might be good but not really as good as Eric extrapolates, so that p-B11 fizzles but D-T does just fine. Second, even if the confinement is good enough to burn p-B11, I might still want to make the device more compact by using D-T, D-D, or D-He3.

--Art Carlson 08:02, 21 September 2006 (UTC)

My question was not: is the Lawson's criterion useful?, the answer being obviously: yes. I just note that there are two versions of this criterion (the double and the triple products), the triple product being generally considered as the best one, and two versions of the reactivity curves. However, Eric uses the versions which don't take the temperature into account; why? Without any evidence of dishonesty, the only hypothesis I can think of is that the DPF ignition process may be adiabatic (no heating power, contrary to a tokamak), and consequently taking temperature into account in the criterion may not be pertinent (or at least less pertinent) for a DPF. What is your opinion about this hypothesis?

I confess that I don't clearly understand the consequences of keeping density constant vs keeping pressure constant; are there on power density only, or is the Lawson's criterion affected as well?

Croquant 11:19, 21 September 2006 (UTC)

I thought I answered those questions, but apparently I didn't do a very good job. First, Eric actually does take temperature into account implicitly, even it it is not obvious because the result is expressed as a limit on simply nτ. Second, whether the fusion products are used to keep the plasma in steady state by heating it, or the plasma is brought to fusion conditions and then allowed to burn out, doesn't matter. Eric has to invest energy to create a plasma hot enough to produce fusion, then he has to hold it together for a certain time while fusion occurs. The Lawson criterion is about balancing the fusion he manages to produce against the investment he had to make. I don't see a fundamental difference between a one-time energy balance and a steady-state power balance. --Art Carlson 12:20, 21 September 2006 (UTC)

OK Art. I understand you disagree with my hypothesis. From the text you wrote in Lawson_criterion#The_.22triple_product.22_neT.CF.84E, I understood that the triple product was rather a power efficiency criterion, and the double product a minimum criterion for ignition, but probably both things are closely related, and trying to deal with them separately is not pertinent. Am I right? So now, let's wait for Eric's point of view, in order for me to understand the reasons why he didn't take explicitly temperature into account in his calculations (they lead to a ratio of 45 instead of 500 with yours, so I think it's worth going into this question). Croquant 13:35, 21 September 2006 (UTC)

The question that is supposed to be answered in this section is “how difficult is pB11 fusion”? That is what I am trying to answer. But Art is confusing this with a different question: is pB11 fusion economically worthwhile? He then compounds the confusion by using his “power density” parameter, based on wrong physical assumptions, to come up with an invalid measure of economic viability.

I have no problem with saying that pB11 needs a much higher temperature than DT. That is said in the paragraph before the disputed one. As a further compromise I have included the temperature AGAIN in the latest version of the disputed paragraph.

My calculations for the figures that I give have been presented in the discussion above and are repeated here: for DT the triple product minimum occurs at 26 keV and is 4.42x10^16 keV-sec/cm^3. For pB11, the minimum is at 238keV and is 1.177x10^18keV-sec/cm^3. In each case, the triple product for burn-up is T/<vs.>. The ratio is 26.6. The no for burn up is just 1/<vs.>. The nτ for fusion energy/thermal energy=1 is T/<σv>E, where E is fusion energy per reaction. The ratio of T/<σv> is 26.6 and the ratio of E is 1.68. Multiply then together and you get 44.63, rounded up to 45.

The power density at a given pressure is NOT a measure of technical difficulty, which has to have something to do with what you have to achieve. It is also not a good measure of economic viability, because it assumes that higher pressures need more money. That is clearly false. The low-pressure tokamak is enormously more expensive to build than the ultra-high pressure DPF.

It’s perfectly OK with me to put in a sentence about the tokamak not being suitable. I’ve tried to do that.Elerner 14:51, 21 September 2006 (UTC)

Why do you consider nτ to be a better measure of overall technical difficulty than nTτ? --Art Carlson 15:39, 21 September 2006 (UTC)

Do somebody know when and why the nTτ triple product was created? I'm trying to find out if it was originally planned for a different purpose than the nτ criterion, or as a replacement of it. A reference would be welcome. Croquant 18:33, 21 September 2006 (UTC)

I don't have much information on this. Only this. I know the guy who wrote it and he works nearby, so I could ask him where he got this, if it would help. --Art Carlson 19:31, 21 September 2006 (UTC)

I just found, as an historical reference, that the nτ criterion is still used in Introductory Nuclear Physics, K.S. Krane, 1988, p. 542. Croquant 18:49, 21 September 2006 (UTC)

The difference is that nτ is really an invariant while nτT is not. If you vary n and τ but leave nτ the same you get the same amount of burn at a given T. But if you vary T and leave nτT the same, you will not get the same amount of burn, because the reaction rate is always non-linear in T. That’s why the difficulty with nτ and with T should be listed separately, not multiplied together. Elerner 01:17, 22 September 2006 (UTC)

From Art's reference (this) and Eric's explanation about non-linearity in T, may I presume that the triple product is a fairly good approximation in the nearly-linear part of the reactivity curves in the range of the moderate temperatures used in a tokamak, while an extrapolation to another range of temperatures is not valid, reactivity being no longer linear in T? Croquant 08:18, 22 September 2006 (UTC)

Sorry, but I think you don't have it quite right yet, presumably because you were misled by Eric. His argument is circular because it depends on his choice of variables rather than on physics. To illustrate, let me use exactly the same words to defend the use of nTτ (which, of course, is equal to pτ, while nτ is just equal to pτ/T);

The difference is that pτ is really an invariant while pτ/T is not. If you vary p and τ but leave pτ the same you get the same amount of burn at a given T. But if you vary T and leave pτ/T the same, you will not get the same amount of burn, because the reaction rate is always non-linear in T. That’s why the difficulty with pτ and with T should be listed separately, not divided by each other.

Do you see the problem? It might also help to think of the graphs of nτ vs. T and of nTτ vs. T. If I show you one or the other with the units covered up, you wouldn't be able to tell which one it is. So my question to Eric remains unanswered:

Do you any physical or technical (not notational) reason to consider nτ to be a better measure of overall technical difficulty than pτ?

(In addition, it is not clear, what Eric means by "amount of burn". Can we agree to talk about "energy gain factor", G, the fusion power (or energy) produced in a volume divided by power (or energy) lost out of that volume?)

--Art Carlson 09:38, 22 September 2006 (UTC)

So, do we have to get to a consensus about which product is invariant, nτ or pτ (nTτ), or is the invariance a false problem? I have to confess that I am really puzzled about this point. Croquant 10:43, 22 September 2006 (UTC)

The invariance is a false problem. Mathematically, both figures are on an equal footing. I argue that the pressure is physically and technologically a more important quantity than the density. I don't think Eric has gotten past the mathematics. I do recognize that nτ is also often used as a figure of merit, even though it may be less telling, so I have no objection to also reporting its limits in the article. --Art Carlson 11:32, 22 September 2006 (UTC)

Please remember that Wikipedia does not publish original research. Everything on the page needs to be referenced to a third party source. If you can't find a reference for the results of a calculation, it probably shouldn't be here. If you find conflicting references for calculation results, and neither is obviously better than the other, write about both. It's acceptable to include simple, straightforward calculations that haven't been published elsewhere, but only if they deduce something that can easily be shown to be true from published sources. But as soon as there's a dispute, we revert to including absolutely nothing that can't be attributed to another publication. — Omegatron 01:06, 23 November 2006 (UTC)

Table comparing D-T with p-B11

I am thinking we might want a table with three rows (D-T, p-B11, and the ratio between them) and several columns (T, nTτ, nτ, power density at a given pressure, ...). I would put a range of values in the boxes to cover various assumptions (T_e=T_i vs. T_e=0, for example), with the details explained in footnotes. I think this would be clearer than just running text and would allow us to include everybody's favorite number. What do you think? --Art Carlson 11:32, 22 September 2006 (UTC)

Basically, I think it's a good idea. However, I'm not sure that disputes will not arise when we get to the explanations: for instance there may be no consensus on the exact meaning, use and limits of the various figures of merit. Furthermore, do you think that enough reliable data can be found in order to fill this table? In any case, if Eric is OK with this idea, it's worth trying. Croquant 12:27, 22 September 2006 (UTC)

Eric and I don't disagree as much as it might appear on what data to start from and how to calculate the various figures of merit from them. There are some disagreements about the most reasonable assumptions to make, but I hope we can deal with that by writing ranges. Where I anticipate trouble is deciding which figures to include. The irreducible minimum, I believe, will be T (which is the least clear-cut number of them all), nTτ, and nτ. I think it is important to say something about power density for a given pressure. Eric may try to strike that, or he may suggest adding power density for a given density. (Too bad he's in another time zone. Or maybe it's better that way.) --Art Carlson 12:38, 22 September 2006 (UTC)

One of the problems I can see is that there are so many dimensions (n, p, T, τ, type of fuel), not completely independant one from another, and just a reduced set of measured or calculated data. So, instead of a set of curves, we merely have a few figures, which doesn't make understanding very easy (at least for me...), but it's better than nothing. Croquant 12:55, 22 September 2006 (UTC)

Another question, I asked already in a different way: is it possible to make a clear separation between the "possible" and the "worthwhile" figures of merit, or are these notions so closely related that they share the same figures? Croquant 13:06, 22 September 2006 (UTC)

This isn't finished yet (obviously), but you can see which direction I'm thinking. The numbers aren't right yet or are missing altogether, and the footnotes are missing, too. Mostly I'm experimenting with the format so far.

fuel	optimum temperature	minimum required for ignition		maximum power density		minimum required for 1 MW/m³
		nTτ	nτ	at p = 1 bar	at n = 1×1021 m-3	pressure p	density n
D-T	13-66 keV	2.76×1021 m-3 keV s	1.5×1020 m-3 s	xx-yy MW/m³	xx-yy MW/m³	xx-yy bar	xx-yy m-3
p-11B	125-600 keV	1.37×1024 m-3 keV s	xx-yy m-3 s	xx-yy MW/m³	xx-yy MW/m³	xx-yy bar	xx-yy m-3
ratio	10	170-500	15-45	830-2500	x-y	50	x-y

Art’s arguments are wrong precisely because they ignore the physics. In a plasma, you can’t take particle pressure as an independent variable and no one does. Pressure is the product of the two physically independent variables, particle density and average particle energy or , for a Maxwellian distribution , temperature. Since it is technically difficult to increase particle density and to increase temperature, but the difficulties are not the same, it makes physical sense to list the need to increase both separately, not to multiply them together.

Art keeps using pressure because he refuses to abandon the physically incorrect notion that magnetic fields have to be balanced by solid-state structures. He is also not trying to reach a compromise, but keeps edit warring an just reverting to his version which never changes. I’ve changed my version several times to reach an agreement.

I am changing the article back again, since Art’s version is still misleading.

As to the table, I’ve said before that “ignition” is a bad criterion, since it involves lots of assumptions. Power density at a given pressure is not a technically relevant comparison and not a measure of the technical difficulty of reaching economical operation.Elerner 23:07, 24 September 2006 (UTC)

Eric, which criteria are you considering more pertinent than Art's ones? Croquant 11:09, 25 September 2006 (UTC)

SOS

Help! The danger of a revert war between me and Eric is higher than it has been since the #End of the road. Optimist that I am, at some point I thought it might be possible to reason with Eric. He has again blasted past my rational arguments with a breathtakingly simple assertion: In a plasma, you can’t take particle pressure as an independent variable and no one does. Pressure is the product of the two physically independent variables .... You certainly can, and competent physicists certainly do, when it is helpful to the problem at hand. I suppose Eric thinks differently because you can get by thinking that in undergraduate physics courses. It's like thinking velocity is more fundamental that momentum because the concept of velocity is introduced first and momentum is introduced as the product of mass and velocity. When you take a course in quantum mechanics, you learn that there is nothing more "physical" about the velocity, and in fact that it is much more convenient and insightful to treat momentum as the fundamental quantity. If Eric has not learned this by now, I suspect he never will. In any case, it is not my job to teach it to him. (The whole story is strongly reminiscent of the fact that he never recognized, or at least never acknowledged, that $\omega _{p}>\omega _{c}/2$ is mathematically equivalent to $nkT/(B^{2}/2\mu _{0})>kT/(2m_{e}c^{2})$.) So what can I do??? Patiently revert and hope to get some outside help, I guess. --Art Carlson 08:33, 25 September 2006 (UTC)

I'm sorry I don't have a sufficient knowledge of the topic to pull both of you apart efficiently. It's a pity that people highly interested in the same topic don't find a way to get at least to a consensus on the editorial process. I don't understand why both of you are not able to build a strong basis, by limiting the article to consensual information. When points of view are different, don't you think it may be too sharp for an encyclopedia? Croquant 10:58, 25 September 2006 (UTC)

I strongly believe that an encyclopedia benefits when experts write articles using their special knowledge. Taking advantage of expert knowledge, especially in a wiki environment, raises difficult issues of deciding who is and who isn't an expert and resolving disputes between experts. Writing an informative and understandable article is an art that sometimes makes it hard to separate good communication from original research. If we are forced to leave behind our hopes of producing a really good article by such disputes, it will be a real pity. What we will be left with is a least-common-denominator article based on verifiability, which could just as well be written by people who don't have any special knowledge of the subject. If you've got some time you can try it yourself. Google "Lawson criterion" and pick several results at random. Some will talk about n*tau, some will talk about n*T*tau. Here are two examples that use the triple product and the pressure, instead of n*tau and the density.

This:

We can characterize the fusion power (the rate of heat production) in terms of the plasma pressure, since higher pressure allows more plasma density, and more density means more fusion power. Also, the temperature must be high enough--about 100 million degrees Celsius for DT fuel; but pressure includes temperature, pressure being the density multiplied by the temperature. Then, as we are using it here, the Lawson number is just the number we obtain by multiplying the plasma pressure by the energy confinement time. When this number is large enough--that is, when it reaches the Lawson criterion--the fusion power can keep the fuel hot enough to burn. It does not matter whether we achieve this criterion by having a very large confinement time (excellent insulation) or a very high pressure, or any combination of the two. The number obtained by multiplying the pressure and the time is all that matters.

And that:

Notice that nτE is a function of plasma temperature. For D-T reactions, nτE has a minimum around 300 million degrees - however, in magnetic confinement facilities it is easier to achieve higher nτE at lower temperatures. The optimal trade-off appears around 100-200 million degrees. In this rather narrow temperature interval the triple product nτET sets a constant condition for fusion ignition (Q -> infinity), see figure.

If you don't want to use your understanding of physics and technology, then all you can say is that both criteria are used, so both should be mentioned in the article. It is Eric who does not want to mention the commonly-used n*T*tau criterion. You can guess as well as I what it is he's afraid of. (I'm sorry for the long-winded reply, but it is so frustrating trying to get through to Eric! Or even to get him to stop messing up the article.) --Art Carlson 12:51, 25 September 2006 (UTC)

I asked Eric if he can suggest criteria he considers as pertinent. If he has some more to give, I hope it will be possible to build a more consensual table. Croquant 14:01, 25 September 2006 (UTC)

I made one last effort to compromise, including the pressure-confinement time ratio. Note that ALL the efforts at compromise have come from me. Art just keeps reverting to the same paragraph. If this does not work, I am going to challenge Art's paragraph on the grounds that it is original research, unless he can find citations that analyse pB11 the way he does.Elerner 16:15, 25 September 2006 (UTC)

Although you use different words, it seems to me that you nearly agree on most of the criteria; however, you still disagree on the power density, Eric having cut off Art's sentence: "Furthermore, the power density of a p-¹¹B plasma will be 2500 times lower than that of a D-T plasma at the same pressure, when the fuel mix and temperature are optimized for each reaction." Is the use of that criterion worth going on fighting about this section? Croquant 17:09, 25 September 2006 (UTC)

I'm glad that Eric finally sees the necessity of including nTτ. It does leave a bad taste in my mouth that he presents himself as the king of compromise when he throws out other parts of my version without even mentioning their existence.

• As Croquant points out, the power density is still an important point.
• Why does Eric remove the wiki link to Lawson criterion for those who want more detail?
• Does he mean to suggest by omission that laser pellet fusion might be a viable route to aneutronic fusion?
• The difference between 405 and 500 may not be much, but rather than go to the trouble of following my derivation, he makes up his own, which is wrong because he uses the temperature that minimizes nτ, not that which minimizes nTτ.

Wrong--that is what I did.Elerner 00:02, 26 September 2006 (UTC)

Really? It's not what you said you did. As I read your version, you found the T that minimized the nτ required, then you multiplied the minimum of nτ by this temperature and claimed this was the minimum required triple product nTτ. If this is not what you did, then you need to express yourself more clearly. If you don't understand the difference, then you are in bigger trouble than I thought. This may be close, but it's not mathematically correct. The true minimum of nTτ occurs at a temperature a factor of 2 or 3 lower and the value of the minimum is 1/3 to 1/2 lower. --Art Carlson 11:19, 26 September 2006 (UTC)

And as for his threat, what exactly does Eric want by way of citations? That authors consider power density to be an issue? That I know how to do calculus? Is something like this (top of p.15) relevant?

In terms of reactor relevance it is not β itself that is directly the critical parameter. It is instead the absolute magnitude of the plasma pressure since the fusion power density is proportional to p2 ∼ β2B4. Power balance and economic considerations indicate that the volume averaged power density of a fusion plasma (alphas plus neutrons) must typically be on the order of 1 MW/m3 in a reactor. This corresponds to a pressure of approximately p ≈ 0.8 MPa ≈ 8 atm.

I guess I'm still a little upset with Eric, but he has budged a bit. If he is willing to engage constructively on the remaining questions, maybe a consensus can be reached eventually. --Art Carlson 20:02, 25 September 2006 (UTC)

But YOU are not willing, Art, you just keep reverting. What is the point of discussion if you prefer an edit war? Why don't you make specific changes? And why are you not willing to compromise on anything????Elerner 00:02, 26 September 2006 (UTC)

Get a grip on reality, Eric. I've been making compromises all the time. When I read through the article, I'm afraid I made too many. You once restructured the whole article, and it still suffers from that, but I started working with your version anyway. When I reread the section on residual radiation I get a bad feeling because a casual reader is likely to misread a "negligible occupational dose" as no radiation issues at all. In the last several days my version has added information on the hot-ion mode, the product nτ, the pressure required for a given power density, and the signicance of these number for aneutronic fusion devices. Those changes are not specific? And what have you compromised on? Leaving out the triple product was absurd all along. Adding the mention of laser pellet fusion was not a compromise on your part, just a proof that you didn't even read my text. When you finally notice that a wiki link to the Lawson criterion is essential here, will you call that a compromise, too? And then there's the power density issue. I admit (a tactical mistake!) that the case for including the power density is not as strong as that for including the triple product (which is atomic-bomb-proof). But what is the case against it? When I look back over the discussion, you say a number of things, to which I have always replied, giving my reasons that I don't find your arguments convincing. Then you drop it. Does that mean you see the weakness of your arguments? Maybe it would help if you would cogently state once more your strongest arguments for not mentioning the power density. I'm not going to drop it without good arguments, just because you say so. And please distinguish between the usefulness of the power density as a general figure of merit for a power plant, alternative ways to calculate the power density, and confinement concept as opposed to fuel cycle issues. --Art Carlson 12:12, 26 September 2006 (UTC)

Art, if I'm not wrong, the reference (this) is related to plasma physics in a "toroidal magnetic confinement". Are you absolutely sure that your citations can be extended without any change to other confinement methods ? Croquant 04:40, 26 September 2006 (UTC)

That wasn't the point. At this paragraph in the article we are trying to say what we can about the choice of fuel, independent of any particular confinement concept, whether tokamak or DPF. The quote illustrates that experts in the field sometimes use pressure instead of density as an independent variable, in particular that they calculate the power density in terms of pressure, and that they consider power density to be an important economic criterion. The threshhold of power density that is considered economically interesting will vary with the confinement concept, but it will always be important. The citation was just a stab in the dark anyway, because I can't figure out what Eric wants me to verify. Can you? --Art Carlson 12:22, 26 September 2006 (UTC)

Croquant, can’t you PLEASE try your hand at writing your version of this paragraph? This is taking far too much time and energy.

As I have explained many times here, power density at a given pressure is not a valid measure of economic performance. It does not have any relation to the cost of electricity produced. You have to take into account the device cost, optimum power density for the given device and fuel, pulse repletion rates and so on. Also, Art’s paragraph is too long, poorly written and hard to follow. It also has no citations, so is his original research. (If you say the same is true for mine, fine—I’d agree at this point to eliminate both versions. Neither is needed, since the basic point is made in the preceding paragraph.)

So either Croquant writes a version or we take out both versions.Elerner 13:14, 26 September 2006 (UTC)

"power density at a given pressure ... does not have any relation to the cost of electricity", emphasis mine. Obviously device cost, repetition rate, and other factors also play a role, but to say power density does not have the slightest relation to the cost of electricity is one of the silliest things I've heard in a long time. The simple gedanken experiment for slow learners is this: Design a power plant, the best you can. Then imagine what would happen if you could boost the power density by 1% without changing anything else. Well, you'd have 1% more electricity to sell, or more if you take recirculating power into account. (Do you follow me, Croquant? More fusion, more electricity, more money earned.) Now, if you want to say there is a better figure of economic merit, or that we should calculate the power density differently, I'd be more than willing to listen, but the claim that power density is irrelevant is no argument at all. I'm reverting. I'm sure you would more than happy to take out the paragraph completely so that readers, although they will be told about the temperature requirement and bremsstrahlung issue, would remain blissfully ignorant of the Lawson requirement in all its forms as well as the power density issue. My suggestion is to leave the reader with all the information since the numbers and statements are correct. If we can't agree on the significance of the numbers, then the neutral thing to do is to let the reader decide. --Art Carlson 13:53, 26 September 2006 (UTC)

I'll be out for a couple of days. When I come back, if both of you are still alive :-), and if you haven't changed your mind, I'll try writing my own version. However, I think it's just a poor answer to the problem. Croquant 19:36, 26 September 2006 (UTC)

Chicken! ;-) -AC-

Eric, would it help if we separated the two sentences on power density into a separate paragraph? It would give us an opportunity to go into some of the details on the issue that you, with some justification, consider so important. Equally important, it might allow you to notice some of the other things you are regularly reverting that I don't see as controversial and that you have never argued against. These include the cross references to Lawson criterion and Nuclear fusion#Neutronicity, confinement requirement, and power density, and the footnote about the hot ion mode (which I added as a compromise). You also propose a different wording in many places, and if we ever agree on the content, then we can settle issues of style. (Also, if you would pay closer attention, you would see that you reverted - presumably unintentionally - the addition of a citation concerning absorption of bremsstrahlung in ICF plasmas.) --Art Carlson 08:19, 27 September 2006 (UTC)

I'll even go farther. I'll delete those two sentences myself, with the understanding that we will confront the issue in a few days. --Art Carlson 11:24, 27 September 2006 (UTC)

If two editors argue for two competing versions, it is in general difficult to decide objectively which version is better or which version should be the reference version until consensus is reached. (Subjectively it is easier - My version is better!) But if one editor lists specific reason that he finds his version better, and the other editor makes no arguments on the talk page, then it is clear that the version with the arguments stated must be the reference version. Do you wish to argue against this as a principle, Eric? --Art Carlson 07:31, 2 October 2006 (UTC)

The only point in my recent edits against which Eric has argued here, is the inclusion of information on the power density. (With just one flimsy argument, but that's not the poiint right now.) Three paragraphs above I list four specific points, where I feel my version is more informative. Therefore I am reverting to the last version discussed here. (Of course I welcome, I long for comments and proposals from Croquant.) --Art Carlson 07:31, 2 October 2006 (UTC)