Talk:Aneutronic fusion

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Notice: Elerner is banned from editing this article.
The user specified has been banned by the Arbitration committee from editing this article indefinitely. The user is not prevented from discussing or proposing changes on this talk page.

Posted by Thatcher131 03:01, 3 December 2006 (UTC) for the Arbitration committee. See Wikipedia:Requests for arbitration/Pseudoscience.

Talk:Nuclear fusion/Annotated bibliography of p-B11 fusion is a somewhat dated (1998) list of references with my (POV warning!) comments on them. It doesn't have a clear place in this article, at least in the present form, but I thought it might be useful enough to be pointed out here. --Art Carlson 10:16, 8 September 2006 (UTC)

Contents

[edit] Problems and proposed solutions

According to the Rider paper it seems that these fuels would work in a non-equilibrium plasma. [1] But the whole point of his paper is to prove that such things cannot realistically exist. Still, it should be mentioned as the reason why people pursue them. - Omegatron 02:56, May 12, 2005 (UTC)

The reason people pursue aneutronic fusion is that are green techies. They love science fiction and futuristic technology, but they also think small-is-beautiful and hate nuclear power. Then people come and rain on their parade and say aneutronic fusion can't be done for this reason or that, e.g. Bremsstrahlung. The natural and admirable reaction is to look for a way around the problem, e.g. non-Maxwellian electrons. Rider and I are saying, as much as we agree that aneutronic fusion is a dream that was worth dreaming, there is just no sign of a passage through the mountain range blocking the way. My point is that non-equilibrium plasmas are not anybody's reason to pursue aneutronic fusion but rather a last-ditch effort to save it. And there's not just one such obstacle, there are several: Bremsstrahlung, confinement requirements, power density, direct conversion, neutron production from side reactions. And if you ever found the miracles to solve all these, you would still have to ask whether it is not better to apply the miracles to a reactions with a cross section a thousand times bigger, like D-T. Art Carlson 08:15, 2005 May 12 (UTC)

Art, respectfully, many people working on aneutronic fusion aren't exactly green techies. This is pointedly biased. At the least, Sam Cohen, my advisor, who used to be fairly high up in the ITER hierarchy, and now works on confinement concepts which may turn out to be amenable to anuetronic fusion. There are potential answers to all of these problems: "Bremsstrahlung, confinement requirements, power density, direct conversion, neutron production from side reactions"
  • Bremsstrahlung: Heat ions preferentially, possibly using orbit resonances. Non-maxwellian electrons are another possibility. Run at a lower density. Achieve better confinement times...
Fusion products tend to heat the electrons more strongly because the velocity is more closely matched. Non-maxwellian electrons were considered in several forms by Rider. Bremsstrahlung power density scales with n^2, but so does fusion power density. If the Bremsstrahlung is higher than the fusion then all the confinement time in the world won't help you. On the contrary, with better energy confinement you will almost certainly have better particle confinement. The fusion products will build up and make your Bremsstrahlung more severe. This is almost a problem for D-T fusion (within a factor of three). I've never seen a calculation for p-B fusion, but I suspect it would be a show-stopper.
Okay, I didn't think of the velocity being more closely matched. You should be able to construct a region where the parallel velocity of the ions and the fusion products are matched more closely though, yes? This would at least help.
As I highlighted earlier, I think there might be a problem with Rider's claims, but I can't examine them in detail as of yet. at the least the more promising idea is to have a higher temperature for the ions than electrons, because electron-electron collisions are going to be quite imperative in relaxing the electron distribution to maxwellian. If I recall correctly, the time scale for the electrons to reach the same temperature as the ions is roughly M/m times larger than the relaxation time for electrons to maxwellian. One can think of there being a phase space flow which scales like this. Then the redistribution energy for ions being hotter electrons should scale around m/M times less, yes?
I'm pretty sure that Rider included this factor as it is rather obvious and standard. As a conservative simplification, you can assume that all the fusion energy goes to the ions (somehow), that the ions lose their energy to the electrons (only) classically, and that the electrons lose their energy (only) by bremsstrahlung. If you artificially cool the electrons so they don't radiate so much, the ions lose energy even faster. If you heat them so the ions stay hotter, then you have to pay a higher price to heat the electrons than you save from the ions. Take your time to read Rider, then we can get into details. (I'll chew on Rostocker in the meantime.) --Art Carlson 11:02, 5 March 2006 (UTC)
The problem with the build up of fusion products is an area of active research I think. Nat Fisch keeps talking about 'alpha channelling' in Tokamaks or mirror machines. The problem in FRC's is probably a bit tougher, but there should be some kind of flexibility. LDX also claims that they can get a higher energy confinement with a worse particle confinement.
  • Confinement Requirements: I'm not sure what exactly you're talking about here. Are you just saying hotter => faster diffusion?
No, simply that the Lawson requirement for p-B is 500 times higher than for D-T (which is already damned hard to reach).
  • Power Density: So the power density is much lower compared to D-T reactions. We're not concerned which power density, we're concerned with economics. It's still possible to make an economical reactor with a low power density. The sun has a low power density...
The sun? Not in my backyard! When the power density is a factor of 2500 lower, believe me, we are concerned about it. Assuming 10 billion dollars allows you to produce the same volume of plasma, then a factor of 2500 in power density is the difference between producing power for, say, 20 cents/kW-hr and 500 dollars/kW-hr.
Your first assumption is far from clear, though, and you also have to weigh capital costs versus maintainance. Granted, with these kind of numbers, a general statement is an easy one to make...
  • Direct Conversion: There have been operating direct conversion systems for some time now, at albeit much lower fluxes. What part of direct conversion do you regard as an impassible mountain range?
If you look at the plans for a fusion reactor with direct conversion, it is hard to find the plasma vessel because it is dwarfed by the convertor. Direct conversion is possible and is economical and elegant in principle, but it would be a major scientific and engineering effort to actually get one working at the many MW level.
I think direct conversion also admits the possibility of a smaller reactor. One on the range of KW. If you can shink your heating and driver systems along with the direct convertor, you might get a small reactor without as many maintainance issues as D-T reactors. Of course, that's also a tall order, since nobody is sure how to heat these things to 123 keV, but still...
  • Neutron production for side reactions: This is at the least a significantly less challenging problem than a D-T reactor must deal with. I recognize the problems you outline in potential neutron production, but it's not as if the neutron flux is impossible to deal with. You add shielding, you protect against hard x-rays. The lifetimes of materials will go up tremendously versus D-T plasmas, yes? That's good, right? I also think your 'simple calculation' is a bit sketchy on assumptions. The neutronic reactions are nearly all endothermic: thus having 0.1% of the reactions create neutrons does not imply that the neutrons have 0.1% of the energy: it's likely much less. Less energetic neutrons are easier on materials and easier to handle. I can't find the paper online -- I'll look in the library tomorrow.
That is all correct. I just want us to keep in mind that "aneutronic" just means a heck of a lot fewer neutrons, not none at all.
--Art Carlson 14:52, 4 March 2006 (UTC)
I don't think the characterization of non-Maxwellian plasmas as a 'last-ditch effort' to save aneutronic fusion is really correct. Or fair. The same basic ideas are being tried out in other areas of magnetic confinement. You have people working on alpha channelling, or heating up ions preferentially, or polarizing nuclei to improve cross-sections, or people trying to stem the high energy tail by various damping processes, etc. etc. These are all decent ideas. A successful implementation would help fusion in that device. It's hardly a 'last-ditch effort'.
You make the point that if these 'miracles' were discovered, why wouldn't you just use them on D-T fusion. Many wouldn't exactly be applicable (eg. direct conversion probably wouldn't help too much. Bremstrahlung is also much less of an issue...). But you're right, many would be applicable to D-T fusion. That's -good-. But -eventually-, aneutronic fusion might yield a more economical, compact reactor. You might be able to put it on planes, or submarines. Many of the proposed reactors could be much less of an engineering nightmare -- it's the physics that isn't developed enough yet to know if this is a decent path or not. It's not like the idea has no potential. I think that you have far too much conviction here. I don't entirely, but mostly, agree with the tone of the articles, but I may go over the calculations and edit a bit here and there. Is this ok? Danielfong 08:13, 4 March 2006 (UTC)

[edit] Cyclotron radiation, radiation dose, and suppression of bremsstrahlung

The Carlson argument about cyclotron radation is just plain wrong. If the plasma frequency is more than half the synchrotron frequency the radiaton can't escape except from a very thin surface layer. In the plasmoid of a plasma focus, radiation can also escape from the very small core area at the initation of the beam, but this loss is also small and brief. This has been discussed extensively for over 40 years in the plasma focus community. I also corrected the shielding part, which implies that workers are inside the reactor--that's absurd. Finally I corrected the part on my own work, which substitutes the factor two for the correct one of five--a significant difference.Elerner 01:01, 27 June 2006 (UTC)

[edit] Cyclotron radiation (1)

1) I suppose you are right about the plasma frequency. I would like to read about it. Could you supply a reference? I find the calculation of maximum beta useful anyway. I would want to put it back in, with mention of any appropriate restrictions.
try any standard textbook. The calcuation is not at all valid.68.39.247.3 02:47, 28 June 2006 (UTC)
The criterion ωp > ωc / 2; is equivalent to nkT/(B^2/2\mu_0)>kT/(2m_ec^2)=kT/(1\,\mbox{MeV}). Is it possible you meant \omega_p^2>\omega_c^2/2? That is what would make sense looking at the dispersion relation of the X wave (or the L wave). Either way, a substantial, but not obviously prohibitive beta would be required. Although this restriction might be somewhat more severe for aneutronic fusion because it generally requires a higher temperature, I think it is rather too detailed - and difficult to get the details right - to include on this page. Maybe I can put it under Electron cyclotron resonance, but even then... --Art Carlson 09:00, 29 June 2006 (UTC)
Your formulas are entirely wrong. Please refer to a text-book for the correct ones. What is right is that the magnetic field energy per electron is 1 Mev. kT can be anything.Elerner 01:05, 5 July 2006 (UTC)
Should I make an equally helpful contribution to this discussion? You are entirely wrong. Go read an (unspecified) elementary text book. (See below for a less emotional response.) --Art Carlson 09:05, 5 July 2006 (UTC)
1 MeV per electron is a really interesting number, too. In a perfect system, you first supply magnetic energy of 6 MeV for each p-B11 pair (one electron for p and 5 for B), plus a bit for thermal energy. When they fuse - and let's assume they all do -- each pair releases 8.7 MeV in the form of fast alphas. Now you have about 15 MeV of energy, partly in the form of magnetic fields and partly in the form of fast particles. This energy has to be extracted, converted to electricity, and reinserted with an total efficiency of 6/15 = 40% to break even. That includes the efficiency of the direct convertor, the efficiency of the capacitor banks and magnetic coils, the production of the plasmoid, bremsstrahlung losses, and losses due to heat conduction and instabilities. Oh, and I almost forgot, we want to have a little bit of electricity left over to sell! --Art Carlson 09:27, 6 July 2006 (UTC)

[edit] Radiation dose

2) I differentiated between operators and maintenance personell. Somebody will have to go into the reactor sometime, and they will have to worry about residual radiation from activated materials. You don't mention material damage or accidental release of inventory, so I don't know why you deleted that, too.
Activation is trivial. The beryllium electrodes after one year's use will have radioactivity equivlent to a class full of children--the radioactivity in thier bones. Material damage is similarly trivial.
Maintenance will require allowing several hours for decay of carbon 11(half-life 20.3 min) Carbon will be deposited as a solid coating--how can it escape?Elerner 02:49, 28 June 2006 (UTC)
As cited, we are talking about neutronicity on the order of 0.1%. A thousandth of an ITER is still a hell of a lot of neutrons. Even in ASDEX Upgrade (deuterium fill, density and temperature below reactor conditions, duty cycle < 0.01) we have to wear radiation badges inside the meter thick concrete walls for several hours after operation has stopped, and we wait a few weeks after shutdown before doing any serious maintenance inside the vessel. The biggest problems are usually from the activation of impurities in the materials, and materials on surfaces like to oxidize and become volatile, not to mention what happens in a fire or loss-of-flow accident. --Art Carlson 09:50, 29 June 2006 (UTC)
You are ignoring the difference between a huge device which absorbs nearly all the neutrons produced and a very small one, where only a tiny fraction of the neutrons will be absorbed before they hit the boron-10. A tokamak has very significant stored energy, while a DPF does not. TFTR used gigajoules per pulse while a DPF uses less than 100 kilojoules typically.Elerner 00:58, 5 July 2006 (UTC)
So let the amount of activated material per neutron be a factor of 10 or 100 or 1000 smaller. You will still need a license from the NRC. My statements are not exactly inflammatory. I clearly say that radiation is not a show-stopper and is a tiny problem compared to radiation with D-T fusion. Isn't that reasonable? --Art Carlson 08:43, 5 July 2006 (UTC)
I have tried to create a compromise on the radiation question.Elerner 00:38, 6 July 2006 (UTC)
I appreciate the effort to get specific and quantitative (although considering the speculative nature of fusion reactor design, I am not sure it is appropriate here). Some of the wording ("trivial", "classroom of children") is POV. The biggest problem is that I am still skeptical of the content and will need to see where the numbers came from.--Art Carlson 07:44, 6 July 2006 (UTC)

Calculation of long term radioactivity induced in Be electrodes

Be neutron x-sect 10^-28 cm^2 for broad range of neutron energy

50% of neutron encounter average 1 cm Be 9

sp. Gr. 1.85

1.2x10^23 atoms/cm^2

1.2x10^-5 abs rate

6.5x10^-3 neutrons per pB11 reaction

7.8x10^-10 Be10/reaction

5.6x10^4Be10/J

4.8x10^11Be10/s

1.4x10^19Be10/yr

1.9x10^5Bq (decays/s)

5 microCuries

1 microCurie/MW-year

So I am restoring my remarks.Elerner 02:28, 11 July 2006 (UTC)

Eric Lerner's version of the radioactivity story is unacceptable for two reasons:
  1. It is reasonable to expect a problem, and
  2. even if the problem could be eliminated, it is difficult to prove that.
If we have to start from scratch and are not experts, the most reasonable thing to do is to look for a similar system that has been analyzed by experts. The closest thing to an aneutronic fusion reactor is a "conventional" fusion reactor. The advantage of this approach is that the reference point has a high degree of realism, because people have taken a serious look into the details of the problem and have tried hard to fix as much as they can. There the biggest radiological problems are tritium (which we can ignore here) and activation and damage of materials by neutrons. The biggest single difference is that the fraction of energy carried by neutrons in an aneutronic reactor is approximately 1000 times smaller. Therefore the simplest estimate is that the problems in an aneutronic reactor are 1000 times smaller than in a D-T reactor of the same size. There may be some factors that shift this result. Eric mentions, for example, the low average energy of the neutrons. Since we normalized to neutron power, lower energy means a higher flux. It may help some to spread the energy over a larger number of neutrons, but I don't know how to quantify the effect.
The other approach to estimating the radiological problems is to do it ourselves from scratch. Eric made a first cut by considering neutron absorption reactions in the primary materials Be, Al, Cu, and W. He concluded that the most difficult reaction is Be9 (n,gamma) Be10, and that the radioactivity produced would be negligible. This is in blatant contradiction to the estimate above, so Lerner's method requires a closer look. Be10 has a half-life of 1.5 million years. To illustrate the necessity of going into detail, suppose there is an impurity in the beryllium or a minor structural material at a level of 0.1%, whose neutron absorption product has a half-life of 100 years. The activity due to this impurity would be 15 times larger than the activity of Be10. (Math available on request, if that went by too fast.) Among the questions that would have to be answered (An expert would certainly have a different list and probably a longer one.) are:
  • What are the weigth, pressure, and magnetic forces expected, and what are the structural materials used to contain them?

Once again you are ASSUMING that there are powerful magnetic fields that need to be contained by strong strcutural materials. Once again, decades of experience with the plasma focus show that the powerful fields are in the plasmoids and that the fields affecting the structure are much smaller.Elerner 18:41, 26 July 2006 (UTC)

  • What are the primary impurities in industrial sources of the matrials used (Be, Al, Cu, and W, at the least)?

Just out of curiosity, I looked up the imputities in ultra-high purity commercial Be. No long-lived(more than 30 y lifetime) impurity radioisotopes will contribute even 10% of the radioactivity of the Be-10. Cd112, 14 y lifetime, will about double the radioactivity initially. But the anode would still be well within NRC safety regulations and would not be considred as radioactive waste. It could be safely recycled into new Be products.Elerner 01:21, 28 July 2006 (UTC)

  • Have all (n,p), (n,alpha), (n,2n), and (gamma,n) reactions been considered?
  • Is isotopic tailoring of the boron fuel, the hydrogen fuel, the water coolant, or any of the solid materials required to suppress unwanted reactions?
This, of course, is getting into way too much detail for interested laymen writing an encyclopedia article. We should be trying to simply state the current state of knowledge, not trying to extend it. I would like to have a statement summarizing the current state of knowledge at the end of the section, but maybe we would do better to refrain. Maybe we need to get the opinion of an expert in materials and radiation. (Sorry Eric, you may have "credentials" in plasma physics or cosmology, but I don't believe you have ever been funded to do research on nuclear materials engineering.) Maybe we need a statement along the lines of this: While no radiological study of a detailed reactor design has been published, it appears that radiation will not present any problems that cannot be overcome. Make your own suggestion, Eric, but I won't let you leave your version as it is. I hope you now understand why. --Art Carlson 12:50, 26 July 2006 (UTC)

The difficulty only arises because you have devoted a large section of the article to trying to prove that radiation is a problem.Elerner 18:41, 26 July 2006 (UTC)

[edit] Suppression of bremsstrahlung

3) Your numbers for the 1.5 MA conditions are fusion/bremsstrahlung = 2.1 with suppression of bremsstrahlung by the field and 0.97 without. That is my factor of 2 (actually 2.16). Where does your factor of 5 come from? For that matter, the ratio of 0.97 with no quantum effect is suspect. Rider got a maximum ratio of 0.57. (If I recall, he also took credit for a monoenergetic velocity at the resonance and spin polarization, neither of which you claim.) Anyway, the bottom line is that you published a ratio of 2.1 (whether it is right or wrong).
--Art Carlson 08:05, 27 June 2006 (UTC)

Why don't we arrive at consensus offline by email-more effcient? Rider made a few mistakes, which are not really worthwhile correcting. I see where you got the factor of 2. But that was based on earlier calculations and an arbitrary T of 300keV. I am about to submit for publication simulations that show much higher T being reached.Elerner 02:49, 28 June 2006 (UTC)

At any rate, the key point is that ,without the magnetic effect, ignition is either not reached or barely reached, while with it, it is achieved by a good margin.Elerner 02:49, 28 June 2006 (UTC)

Another question, if I may: Is my impression correct that you do not envision any mechanism of confinement parallel to the field (other than inertial)? --Art Carlson 15:30, 27 June 2006 (UTC)
No, that's wrong. The plasmoid field is a force free toroid. The only escape is along the axis in the beam. Ions makes tens of thosuands of orbits before exiting in the beam.Elerner 02:49, 28 June 2006 (UTC)
A toroid in free space will rapidly expand. If you don't have another trick, your confinement won't be much better than inertial. --Art Carlson 09:10, 29 June 2006 (UTC)


Please Art, don't be a Joshua. You were once involved in the field--read the literature on plasma focus before making more changes. Force-free toroids are quite stable. This is not just theory--they have been observed for 40 years to have lifetimes tens of thousands of times longer than the Alfven velocity crossing-time. They are not formed by shocks, but by a kink instability in the vortex filaments. The critical parameter in whether or not cyclotron (synchrotron is more accurate even at 50keV) radiation escapes is the ratio of cyclotron frequency to plasma frequency, which is completely different than the ratio of plasma pressure to magnetic pressure. So everything you wrote was wrong. Please, check the literature before trying again. Why are you so intent on attacking this effort? Read up on it before you draw your conclusions.Elerner 00:58, 5 July 2006 (UTC)

1) It is a well-established and well-known result of magnetohydrodynamics - found in many textbooks - that any configuration of plasma and fields in a vacuum will expand on the Alfven time.

[edit] Cyclotron radiation (2)

2) The statement ωp > ωc / 2; is mathematically equivalent to nkT/(B^2/2\mu_0)>kT/(2m_ec^2)=kT/(1\,\mbox{MeV}). If you can't do the math yourself, you have disqualified yourself as a physicist.
According to the NRL plasma formulary, p.29, the ratio of electron plasma frequency to gyrofrequency is proportional to n^1/2/B. You have asserted, in your addition to this article, that the ratio is that of plasma pressure to magnetic field pressure, which is proportional to nT/B^2. Your error is that you have introduced a factor of T which does not belong there.Elerner 00:38, 6 July 2006 (UTC)
Look again. I also have a factor of T on the right hand side. Your mistake. --Art Carlson 07:49, 6 July 2006 (UTC)
Right, you can introduce T into any equation by multiplying both sides of the equation by T. We all learned this in high school. But that does not miraculously create a real physical dependence on T. If you take T back out, you can see that the criteria depends on the plasma density, not the plasma pressure. Different physical quantity. In dimensionless terms, the ratio is the square root of the ratio of the rest energy density of the plasma to the magnetic energy density.Elerner 00:21, 7 July 2006 (UTC)
I found it helpful to express the relation in terms of β and T. For some purposes, using n and B as the variables is more useful. The physics is always the same no matter what set of variables are chosen. You seem to realize that now, although before you refered to my "error" and wrote, Your formulas are entirely wrong. I don't expect it, and I won't hold a grudge, but a simple "I'm sorry I called you stupid" would seem appropriate here. --Art Carlson 07:55, 7 July 2006 (UTC)

You continually put back in the incorrect formula that the ratio of plasma frequency to cyclotron frequency depends on the ratio of plasma pressure to magnetic pressure or beta. But the first ratio is proportional to nT/B^2, while the second is proportional to n^1/2/B. Depending on T, beta could be high or low and still have plasma frequency exceeding cyclotron frequency. I took out the incorrect formula again.Elerner 03:20, 11 July 2006 (UTC)

[edit] Equilibrium and time scales

3) You're the one pushing the DPF. You must have current references (other than your own) supporting your positions. Just give them to me, instead of demanding me to do a literature search as if I were getting paid to do it.
Bostick, W.H. et al, Ann. NY Acad. Sci., 251, 2 (1975).
Brzosko, J.S. et al, Physics Letter A, 192, 250 (1994).
G.R.Neil, R.S. Post, Plasma Phys., 14, 425 (1988).
I.Volobuev et al, Sov. J., Plasma Phys., 14, 401 (1988)
Brzosko, J.S. and Nardi, V., Physics letters A, 155, 162 (1991)
Brzosko, J.s. et al, Phys. Plasmas, 2, 1259(1995)

Elerner 00:38, 6 July 2006 (UTC)

Thanks. I'll be back. --Art Carlson 07:49, 6 July 2006 (UTC)
OK. I looked through these papers (except the first one: the IPP library does not carry the Annals of the New York Academy of Sciences). I didn't find a single mention of the Alfven time (hardly any mention of magnetic fields), plasmoids, equilibrium, or the virial theorem. The times, dimensions, and temperatures mentioned usually seemed compatible with thermal disassembly. I found one phrase in Brzosko (1994) especially vivid. He refers to "the explosive decay of the magnetic structure of organized plasma filaments". So, having now "read the literature", I can see no support for your statements Force-free toroids are quite stable. This is not just theory--they have been observed for 40 years to have lifetimes tens of thousands of times longer than the Alfven velocity crossing-time. I guess I am now obligated to revert your edits. --Art Carlson 21:51, 6 July 2006 (UTC)

You can find substantially the same material in Colloques internationaux CNRS no. 242, p.129-138. Also J. Plasma Physics 8, 7(1972) To summarize the numbers reported in this work, which has been know for a very long time, B~10^8 G, radius~200 microns n `10^20/cc, plasmoid lifetime~10 ns. It is easy to calculate that for these numbers the Alfven velocity is about 1.5cm/ns and the crossing time is then 26 ps, 400 times shorter than the lifetime. (The plasmoids in the experiments we performed were a lot smaller, so the lifetime is thousands, not hundreds of times longer than the crossing time.) The later sources confirm the high density (in fact observe higher density) and the confinement times of tens of ns. I notice you did not reply on the pinch effect. That makes it no mystery why confinement times have no relationship to the Alfven crossing time.Elerner 00:21, 7 July 2006 (UTC)

Sorry, I could not find either of these references in the library or on line. Numbers like 200 microns, 10^20 cm^-3 (or higher), a few keV, and 10 ns showed up in several of the papers, apparently refering to simultaneous conditions in the hot spots, so we can play with those numbers for now (although a DPF discharge is a complex process taking place on several disparate time- and length-scales, so caution is in order). The number I haven't seen there is 10^8 G = 10 kT. At a radius of 200 microns, such a field could be produced by a current of 10 MA, which I guess is higher than the total current by an order of magnitude or so. I could conceive of the field getting this high in a sausage instability, but not staying that way for very long. Therefore: Please, Eric, send me an electronic copy of one or both papers, if you have them, and tell me whether the measurement of magnetic field is time-resolved and the high values persist for the 10 ns you mention. --Art Carlson 11:44, 7 July 2006 (UTC)

Even in the absence of magnetic field estimates, the data you correctly cited indicates that confinement is occurring for times much longer than the Alfven crossing time. The plasma energy density even with a few KeV (and some of the sources speak of tens of KeV) and 10^20/cc (and some speak of 10^21) is at least 5x10^11 erg/cc. So the confining magnetic field, even with a beta of unity, is at least 3.5MG. Even with this unrealistically conservative estimate, the confinement time is still at least 15 times the Alfven crossing time.Elerner 04:04, 8 July 2006 (UTC)

That's a round-about way to talk about the ion acoustic wave. You don't need either the density or the field for that calculation.
c_s = \sqrt{\frac{ZKT_e}{m_i}}
I have taken gamma_e=1 and assumed T_e>>T_i. For most fully ionized gases (e.g. deuterium) Z/μ is about 1/2. Then c_s at 1 keV is about 22 mm/μs (check my math) and the transit time of 0.2 mm is 10 ns. That fits the data real well, although calculations of this kind can have lots of factors of two flying around. --Art Carlson 11:26, 8 July 2006 (UTC)

I did check your math. That's 22cm/μs, so your calculation is off by a factor of 10. Factors of ten need to be watched even more than those pesky factors of two.;)Elerner 04:34, 9 July 2006 (UTC)

Shucks. I was afraid of that. (Excuse: I was tired and had a bad conscience because there are other things I should rather be doing.) That's close to your calculation and, admittedly, makes my position less comfortable. I need at least three factors of two, or two factors of pi. Faced with the choice between finding them and giving up the theory of MHD, I would rather dig around in rough numbers, experimental errors, and imprecise statements. A promising place to start would be the question of whether the size, time, and temperature quoted were really measured simultaneously. (Obviously not, in this case, since I fabricated the 1 keV temperature myself.) Of course, if you can offer solid measurements to back up your claim of a factor of thousands instead of a measly factor of ten, we would have a different discussion. I would also dearly love to see a discussion of these numbers by a scientist who is aware of the potential conflict with virial theorem and the consequences that would imply. --Art Carlson 08:16, 10 July 2006 (UTC)

I see that the one common element between your comments here and on plasma cosmology is the entirely un-scientific approach that theory trumps observation. Plato thought that too. But scientists believe in observation over theory. This is especially the case as you are appealing to an approximation of EM theory that is not relevant here. In MHD, you have, by definition, a collisional plasma in which force-free configurations get wiped out by collisions. But we are dealing with non-collisional plasma here and if you apply MHD to such plasma you get what Alfven called “pseudo-plasma”—hypothetical entities that don’t bear any resemblance to the real plasma. Also, if you were really right that all pressure gradients had to be balanced by the walls, there would be no pinch effect, since the filaments created are very far from walls. Where are the walls in the solar corona that confines those nice filaments in prominences? Elerner 03:20, 11 July 2006 (UTC)

4) Can we go back to a civilized tone now?
--Art Carlson 09:05, 5 July 2006 (UTC)
P.S. Point (1) can be proved quantitatively and in elegant generality, but there is also a Physics 101 version: Take any configuration of plasma and magnetic field that is confined to a finite volume. Expand all dimensions by a factor R, keeping the magnetic flux through any surface constant. Since the area goes with R^2, B must go with 1/R^2. The magnetic energy thus drops with B^2*V ~ (1/R^2)^2*(R^3) ~ 1/R, and, of course, with adiabatic expansion the plasma energy per particle drops, too. That is, expansion is energetically favorable and can only be prevented if the boundary resists it, that is, exerts a pressure approximately equal to the energy density of the configuration. (If you follow me this far but don't believe that the disruption time is close to the Alfven transit time, I can continue the calculation.) --Art Carlson 14:42, 5 July 2006 (UTC)
Reference added in proof: In a PPPL report, Hammett, Jardin and Stratton, citing both Shafronov and Freidberg, write One common use of the virial theorem is to take the inner product of this equation with the position vector x and integrate over all space to show that an isolated MHD equilibrium can not exist by itself (unless there are physical coils or gravity to provide overall force balance). (In case anybody thinks I'm just making this stuff up.) --Art Carlson 12:36, 10 July 2006 (UTC)

First, the MHD approximation is not appropriate in non-collisional plasmas where the gyrofrequency greatly exceeds the collision frequency. Alfven, the inventor of MHD approximation, pointed this out repeatedly, including in his Nobel address. Second, it would be incorrect to describe a force-free toroid as strictly isolated, since the magnetic field lines, and current runs along the axis out to large distances. Elerner 03:20, 11 July 2006 (UTC)

In the well-known pinch effect, the magnetic field created by electric currents through a plasma creates inward-directed forces which confine the plasma. While pinches can be disrupted by instabilities, they can also remain stable for far longer than the Alfven crossing time. An example familiar to all is a lightning stroke, where plasma heated strongly by the lightning current is also prevented from expanding by the pinch forces of the current for an appreciable fraction of a second, much longer than the Alfven crossing time. Thunder occurs when the heated plasma suddenly expands after the current ends.

In a DPF, a kink instability within the pinched filament creates the plasmoid, which is then metastable for ns to tens of ns, far longer than the Alfven crossing time of the order of 1 ps. The plasmoid is confined by the pinch forces of the current flowing through it.

A good description of the pinch effect and the formation of force free-filaments (in an astrophysical context) is in Alfven and Falthammar, Cosmical Electrodynamics, p. 192-199. This book is out of print, but available in any physics library. Force-free configurations are minimum energy configurations.Elerner 00:38, 6 July 2006 (UTC)

(Sorry. I overlooked this section before.) The question is the boundary conditions. A pinch provides radial confinement but not axial. If you pinch a toroid off a filament, it may have confinement in the minor radius, but it will expand in major radius. (The toroidal currents on opposite sides of the loop will repel each other.) The "force-free-configurations" in a Reversed field pinch or a Spheromak are confined by a conducting wall. (I will check out your experimental references.) --Art Carlson 08:24, 7 July 2006 (UTC)

In a force-free toroid, there is a strong component of the current running along the axis, which provides a confining force against expansion of the major radius, perpendicular to the axis. There is escape along the axis. This is in the form of an accelerated beam which leads to both the heating and eventual evacuation of the plasmoid. But this takes a great deal longer than an Alfven crossing time.The toroid is metastable, not stable, but lasts quite long.Elerner 04:04, 8 July 2006 (UTC)

Sorry, doesn't fly. Won't give you a net radial j×B. --Art Carlson 10:50, 8 July 2006 (UTC)

In a force-free configuration there never is a jxB force. J is always colinear with B. That's what makes it force-free. The ions travel along the lines of force.Elerner 04:25, 9 July 2006 (UTC)

That is quite a trick of yours: In a force-free toroid, there is ... a confining force. No j×B, no force, no confinement. --Art Carlson 08:47, 9 July 2006 (UTC)

If there is stable confinement, of course there is no net force. If a particle, however, hit by a collision, moves radially,it has to move across the field lines and then there is a jxB force until it returns to the direction of the field lines.Elerner 22:29, 9 July 2006 (UTC)

Sometimes I almost start to take you seriously, and then you come up with something like this that makes me wonder if you understand anything about plasmas. You probably don't mean "stable confinement" ("stable" means there is a restoring force on a perturbation, "confinement" refers to any mechanism that slows down loss of energy or particles) but "equilibrium", which is the lack of net forces. That lack of net forces refers to the sum of jXB and pressure gradients. If you claim that there is neither a net force nor a jXB force in a DPF equilibrium, then you are claiming that there is no pressure gradient. That means either you have no pressure at all - not a very interesting situation - or the pressure at the wall is the same as the maximum pressure, in which case the pressure you claim is not compatible with limits of consturction materials. j is always the macroscopic current density. If you want to talk about individual particles without having to face uncomfortable singularities, it is better to talk about the Lorentz force qv×B. It also sounds like you think that this force tends to restore motion parallel to the field. It doesn't. If you are only talking about gyro-motion, that, in the absense of a pressure gradient, does not result in a macroscopic current density. I am willing to overlook sloppy language, but only if I can detect physical understanding behind it. --Art Carlson 07:43, 10 July 2006 (UTC)

See above on walls, etc.Elerner 03:23, 11 July 2006 (UTC)

[edit] More magnetic field effects

Eric, I see that Todd Rider on p. 135 discusses (briefly) magnetic fields, concluding: Unfortunately, detailed studies of this issue [55, 82, 83] revealed that magnetic fields actually increase the energy transfer rate. (He also mentions the issue of synchrotron radiation.) Is he talking about the same effect as you are? If not, did you include this negative effect in your calculation along with your positive effect? --Art Carlson 13:52, 6 July 2006 (UTC)

I don't have a complete copy of Rider at my office. What are the references?Elerner 00:21, 7 July 2006 (UTC)

"once suggested":
  • J.R.McNally, Jr., Physics of Fusion Fuel Cycles, Nuclear Technology/Fusion 2, 9-28 (1982).
  • J.R.McNally, Jr., Simple Physical Model for the Effect of a Magnetic Field on the Coulomb Logarithm for Test Ions Slowing Down on Electrons in a Plasma. Nuclear Fusion 15, 344-346 (1975).
"detailed studies":
  • J.D.Galambos, Effects of Nuclear Elastic Scattering and Modifications of Ion-Electron Equilibration Power on Advanced-Fuel Burns (Ph.D. thesis, University of Illinois at Urbana/Champaign, 1982).
  • J. Galambos and G.H. Miley, Effects of Enhanced Ion/Electron Equilibration Power on Cat-D Tokamak Ignition. Nuclear Technology/Fusion 4, 241-245 (1983).
  • S. Ichimaru and M.N. Rosenbluth, Relaxation Processes in Plasmas with Magnetic Field. Temperature Relations. Physics of Fluids 13, 2778-2789 (1970).
--Art Carlson 07:42, 7 July 2006 (UTC)


No authors other than I have considered the quantum version of the magnetic field effect in fusion applications because they were all looking at tokamaks, where the fields are enormously lower. The quantum effects were only studied in the context of neutron stars.

The classical effects studied in, for example, Galambos and Miley, are quite small—less than 15%, compared with the 20-fold decrease in the quantum case, and deal with fields that are several orders of magnitude less than those I focused on.

My calculations, and those in the neutron star studies I partially relied on, integrate over all the relevant velocities, so provide an accurate picture of the net effect.Elerner 04:04, 8 July 2006 (UTC)

What you say about the other studies seems rasonable. I am still surprised that you claim a quantum effect much larger than about a factor of two because the energy levels parallel to the field are not constrained. Still, it could be right since most collisions in a plasma are small-angle and in a super-strong field the direction of motion of the electrons cannot be changed. If only collisions near 180 degreees are effective, then the energy transfer might be suppressed by a factor up to something like the Coulomb logarithm (10 to 20). Is this the right way to think about it? I reserve the right to be skeptical, but maybe only at level yellow, not level red. What would give me some confidence in your result is if neutron star calculations also talk about a factor of 20 (although it is quite a stretch to compare a DPF with a neutron star!). Do they? --Art Carlson 10:13, 8 July 2006 (UTC)

Yes, they do. The difference is that the ion energy there is 1000 times higher and the B field also 1000 times stronger, so the dimensionless T is about the same.Elerner 04:25, 9 July 2006 (UTC)

After giving the problem some more thought, I have identified processes that are equivalent to small-angle scattering, so I would like to call back my suspension of disbelief expressed above. That apparently puts me at odds with the neutron stars theories. Could you give me a reference to check this out? --Art Carlson 07:51, 10 July 2006 (UTC)

G. S. Miller, E.E. Salpeter, and I. Wasserman, 1987, Deceleration of infalling plasma, ApJ, 314, 215 Elerner 03:20, 11 July 2006 (UTC)

For the record: This paper gives an example where "[t]he stopping length in the B = 0 case is then ~y = 4.3 g cm^-2", while "increasing the field to B = 7 × 10^12 G gives us y = 52 g cm^-2". This is a factor of 12, so Eric is right here that quite large reductions in the transfer of energy from ions to electrons are possible. The paper goes into some detail explaining the physics behind the effect, but I couldn't follow it. --Art Carlson 08:02, 12 July 2006 (UTC)

[edit] End of the road

Sorry, Eric. All your latest comments either don't speak to the real issues or illustrate a lack of any real understanding of plasma physics. After this lengthy exchange I must conclude that you will never allow yourself to be convinced that you are wrong, even by the best physical arguments. I imagine you will say exactly the same thing about me. The depth of the problem is illustrated by the fact that you reverted all my last edits, even those I thought we could compromise on, like reducing the detail on cyclotron radiation since we both agree that is not a fundamental issue here. My ideal solution is that you just disappear. More likely is a revert war. Better would be if one of us could bring in outside expertise, though I'm not sure that would help. --Art Carlson 07:52, 11 July 2006 (UTC)

Right, Art, you really know more plasma physics than Alfven, who I was quoting. You did not answer anything that I wrote, so you just go back to the same games of reverting that Joshua played.Elerner 23:13, 11 July 2006 (UTC)

Art is still reverting without responding to my arguments. It is particularly egregious to continually bring up radioactive waste when I demonstrated that the waste produced is insignificant. To claim that waste comparable to the radioactivity in a human being must be "desposed of" is unprincipled scare-mongering. Art has not pointed to any errors in my calculations above. Nor has he responded to my arguments about magnetic confinement.Elerner 23:35, 12 July 2006 (UTC)

A competent reader will recognize that it is the other way around. You have written some things in after I did, but what you wrote does not challenge the validity of my arguments.
For the sake of anyone entering the fray, the brief summary is this:
  • Radioactivity: Eric believes that radioactivity in a p-B11 reactor will be negligible, I believe it will be manageable. He presented a calculation for the reaction Be10 + n -> Be11. I insist that a serious calculation must include a concrete engineering design, consider many materials including isotopes and impurities, and calculate many reactions in addition to neutron capture.
A plasma focus device, unlike a tokomak, does not require a large variety of materials. The main unavoidable material inside the neutron shield is beryllium for the electrodes. Given the low energy of the neutrons from side-reactions, there is no energetically possible reaction with Be-9 other than neutron absorption and there is no other naturally occurring isotope. Other than the electrodes and the thin Be vacuum chamber, the only other structure inside the neutron shield is the x-ray conversion device, which includes extremely thin layers of aluminum, copper and tungsten, each with a total thickness of a fraction of a mm. After passing through a final aluminum wall, the neutron enters the water shield to be moderated and then the boron-10 absorber. No long-lived isotopes can be produced in the aluminum wall. Thus my calculation is right. Art would have to point to some concrete way that waste that is orders of magnitude more radioactive would be produced before there is enough to need “management.” Our bones contain long-lived radioactive materials, but no one talks about the need to “manage radioactive waste” at a cemetery. To say that radioactive waste is a problem for pB11 DPF reactors is not only wrong, it is scare-mongering.Elerner 14:53, 14 July 2006 (UTC)
I am not qualified to do a radiological analysis. I only know how difficult they can be. Has a detailed radiological analysis of a p-B11 reactor design ever been published? The easiest, maybe the only way out of this disagreement is to leave behind original research and to find verifiable sources. --Art Carlson 08:35, 17 July 2006 (UTC)
When a rough calculation shows that the radioactivity is orders of magnitude too small to be a problem, it is up to you to prove that there is a problem.Elerner 15:07, 17 July 2006 (UTC)
I would interpret that to mean that you know of no radiological studies that are published or otherwise verifiable. Is that correct? --Art Carlson 19:14, 17 July 2006 (UTC)
If someone wants to say, in a wikipedia article, something as absurd as "pB11 reactors will create enough radioactive waste as to require management" then is is they who need verifiable studies. No one would do a study to prove something that scarcely needs proving. Scientific studes of the sun rising in the East are a bit scarce too. I might add that much of what you have writtten on this page is not cited to verifiable sources, either. The page might be considerably shorter, and better, if we stuck to the verifiable source rule.Something to consider.Elerner 22:35, 17 July 2006 (UTC)
I realize that certain facts cannot be expected to be stated in the peer-reviewed literature. I would be satisfied with a simple statement by someone with credentials in the business. Do you know anyone? (BTW, can you learn to indent? It's hard enough keeping track of comment and response as it is.) --Art Carlson 07:46, 18 July 2006 (UTC)
  • Confinement: Eric believes that megatesla fields can be produced and maintained in a DPF for times that are relevant for fusion power. I believe that any configuration of particles and fields with a pressure much higher than the surroundings will disassemble in a time close to the Alfven transit time.
This contradicts the existence of plasma filaments, which are "configuration(s) of particles and fields with a pressure much higher than the surroundings" and which have been observed and analyzed in hundreds if not thousands of papers. They last far longer than the Alfven transit time. Examples are lightning strokes, and filaments in solar prominences.Elerner 13:56, 14 July 2006 (UTC)
Example of pinch confinement of solar coronal loops: magnetic fields about 100 Gauss, particle density around 10^10/cc, radius of filaments about 5,000 km, Alfven velocity 2,000 km/s. This means the Alfven crossing time is a few seconds. But the lifetimes of loops is typically thousands of seconds—-thousands of Alfven crossing times.[[User:Elerner|Elerner]
This is a good example of a plasma which is not confined. There is radial confinement, sure, but the loop as a whole expands at millions of km/h. --Art Carlson 13:23, 15 July 2006 (UTC)
He cites papers that, at least on first blush, give lifetimes that are 10 or 15 times longer than the acoustic transit time (which is closely related to the Alfven time). I cite the virial theorem as a general proof and some toy models involving magnetic energy or jXB forces as paedogogical aids. Eric seems to think that the virial theorem depends in some way on the velocity distribution or the collisionality. It doesn't. The one point which might bear some discussion to tie up the argument is the surface integrals in the virial theorem.
  • There are other arguments, too. The one that most efficiently demolishes his credibility as a physicist is his refusal to recognize that ωp > ωc / 2 is mathematically equivalent to nkT / (B2 / 2μ0) > kT / (2mec2),
The problem is that Art, in his version of the article, says that the ratio of plasma pressure to magnetic pressure, beta, is equivalent to the the ratio of plasma frequency to cyclotron frequency. That is wrong. That would be true if kT appeared only on the left of the above inequality. But kT appears on both sides of that inequality, so Art's statement in his version is wrong. The correct way to state the inequality is to cancel out the common term on both sides, kT. In that case the correct English translation is "If the magnetic field energy per electron does not exceed twice the elctron rest energy, cyclotron radiation is trapped in a plamsa." Elerner 13:56, 14 July 2006 (UTC)
Do you or don't you acknowledge that ωp > ωc / 2 is mathematically equivalent to nkT / (B2 / 2μ0) > kT / (2mec2)? --Art Carlson 13:11, 15 July 2006 (UTC)
but his claim that you can confine a plasma without a jXB force comes close. I will re-engage in the discussion if someone new shows up or if Eric shows any sign of coming to reason. When I find time I also plan to extend the article on the virial theorem to cover charged particles in electromagnetic fields in detail.
--Art Carlson 09:58, 14 July 2006 (UTC)
I stole some time from more important things and added the magnetic field version to the virial theorem article, including the estimate that the expansion time is equal to the acoustic (or Alfven) transit time. --Art Carlson 13:23, 15 July 2006 (UTC)


Loops tend to kink, which is the first stage in forming plasmoids in a DPF. I had forgotten, but good description of the formation of plasmoids at much lower densities and larger scales than in a DPF is at http://ve4xm.caltech.edu/webpub/hsu03prl-preprint.pdf. , http://arxiv.org/PS_cache/physics/pdf/0411/0411089.pdf and especially http://ve4xm.caltech.edu/webpub/yeebellan.pdf

The first two papers by Hsu and Bellan show experimentally the formation of a magnetically confined plasmoid, with no external confining magnetic field. (They refer to the plasmoid as a spheromak configuration.) The third paper by Yee and Bellan study the stability of the plasmoid. The fact that it is magnetically confined can best be seen from their data that shows that the plasmoid is moving at a velocity of about 8cm/microsecond but is expanding at a velocity of 0.5cm/microsecond. The Alfven velocity of this plasmoid with 800 G magnetic field is around 17cm/microsecond. So the expansion time is about 30 times longer than the Alfven time.

It should be added that in this experiment the plasmoid is not trapped within the axial current of the device, while in a plasma focus, the axial current continues during the whole plasmoid lifetime, which contributes to the stability of the plasmoid against expansion. As I emphasized above, it is incorrect to view the plasmoid as entirely self-contained because of the current running along the axis, which extends much beyond the plasmoid radius. This is ONE reason why Art's simple-minded appeal to the virial theorem is wrong. But in any case, the experimental results are clear and theory never can be used to contradict experiment, only the other way around..Elerner 15:00, 15 July 2006 (UTC)


Still no response from Art Carlson justifying his reverts on radioactive waste and confinement.Elerner 22:19, 16 July 2006 (UTC)

perhaps he's realized he's already wasted too much time on your nonsense?--Deglr6328 16:35, 17 July 2006 (UTC)
It's more that I don't like repeating myself, especially when nobody is paying attention anyway:
  • "A promising place to start would be the question of whether the size, time, and temperature quoted were really measured simultaneously."
  • "That is, expansion is energetically favorable and can only be prevented if the boundary resists it, that is, exerts a pressure approximately equal to the energy density of the configuration."
  • "[A] strong component of the current running along the axis ... [w]on't give you a net radial j×B."
I have wasted too much time on his nonsense, but I'm not sure I've realized that yet. --Art Carlson 19:39, 17 July 2006 (UTC)
Actually, supposing that Eric actually wants to give a serious response, I would suggest that we try to clear up the theoretical issue before tackling the experimental one.
That is exactly the opposite of the scientifc methodElerner 22:35, 17 July 2006 (UTC)
Eric, would you please help me understand your point of view by answering these simple questions?
  • Do you agree that nature in general and the DPF in particular are adequately described by Maxwell's equations and the Lorentz force?
  • Do you agree that the virial theorem is a correct mathematical derivation from these equations?
  • When the virial theorem is applied to the special case of the DPF, do you believe that the conclusion that the expansion time is on the order of the Alfven time is improper?
  • Can you specify what you believe the DPF configuration to be in sufficient detail to check this claim mathematically?
Thanks very much. --Art Carlson 20:08, 17 July 2006 (UTC)
Plasmoids have been studied for decades, both theoretically and experimentally, in many contexts, even if Art is ignorant of all this. He should start by reading and replying to the references above(Hsu, Yee and Bellan). But while he is looking those up, I will get some more. Some of this will be integrated into this and other articles shortly.Elerner 22:35, 17 July 2006 (UTC)
I should have stuck to my "end of the road" resolution. Not only do I not know why Eric thinks an azimuthal j and an azimuthal B produce a radial j×B force, I can't even figure out if he believes there is such a thing a j×B force! --Art Carlson 07:56, 18 July 2006 (UTC)

Unfortuntately I know very little on this subject. But isn't it just a matter of finding some suitable references that support one side or the other? After all, we shouldn't be debating the issue, but describing it. --Iantresman 13:01, 18 July 2006 (UTC)

I agree with Ian. It is ridiculous to be debating this back and forth. It is absurd that Art asks for evidence from “someone with credentials in the field” and obviously excludes me, even though I’ve been funded for years by two governments to do research in this field and have given invited presentations on it at international fusion conferences. The whole article needs to have all unverifiable (unsourced) material eliminated from it. That will take some work, but will happen in time.
Art, I entirely disagree with your method. In science, you can’t use theory to refute observations. Many researchers have observed long-lived plasmoids for decades. If you can prove theoretically they don’t exist, you’ve just proved that your use of theory is wrong. And, I’ve explained several times that your use of the viral theorem is wrong since force-free toroidal configurations are not confined within a surface. The force fee lines have larger and larger radii of curvature as they approach the axis until they run along it. But leakage out along the axis is limited to the beams, which evacuate the plasmoid in a time much longer than the Alfven crossing time.Elerner 14:27, 18 July 2006 (UTC)
Thanks, Ian. Relying on verifiable sources is neither as easy nor as desirable as it sounds, but it is certainly the ideal. How can you even start to get an article on plasma physics right if you don't know how to calculate j×B? On the radiation issue, Eric doesn't have an verifiable sources, so he resorts to calling my position "absurd" (twice). On the equilibrium issue, it is verifiable that the virial theorem is commonly understood to imply that all plasmoids are unstable on an Alfven time. We should report this. If it is verifiable that a significant minority of experts believe that this conclusion is false in the case of the DPF, then we should report that, too. Do you think you can suggest some appropriate language? --Art Carlson 15:19, 18 July 2006 (UTC)

Art, the thing you seem not to understand is that the fields and currents of a force-free toroidal plasmoid are not contained in a surface and therefore the surface integral is never zero. I mentioned this above, but you never replied to it. This is the mathematical reason your derivation about plasmoids on the virial theorem page is wrong. Your definition of a plasmoid is not the one everyone else uses. The fact that plasma is confined in a finite space is not at all the same as saying that the field lines and currents are also all confined in the same finite space. They are not.Elerner 13:35, 20 July 2006 (UTC)

I should add that Art's over-enthusiastic application of the virial theorem also would forbid the existence of solids and liquids, which are held together by purely electromagnetic forces. Help, I'm exploding!Elerner 14:20, 20 July 2006 (UTC)

Hey, maybe this discussion will get interesting after all. I am pleased to learn, Eric, that you do not question the virial theorem per se or its fundamental applicability to the DPF. Good move. It's your best shot. And since you're a special friend, I'll give you another tip. The surface integral is only one place to look for a loophole in the virial theorem. The other - and the more promising one - is in the difference between mean values and maximum values. I have a lot more to say about this, but won't have time to go into details before next week. (Besides, some of it is probably crossing the line to original research.) The question about solids and liquids is good, too. I remember thinking about it and answering it to my satisfaction several years ago. Unfortunately I don't remember what that answer was. I promise to give it some thought. --Art Carlson 20:12, 20 July 2006 (UTC)
References are not so hard, they just take a bit of time. How about letting this stand until Friday and hitting the library in the meantime? I have already found some relevent papers.Elerner 23:58, 18 July 2006 (UTC)
Art, it is fortunate that we don’t have to strain our brains about this, since the problem has been studied by others for the last fifty years. An examination of my files and notes and a quick trip to the library gives the following results:
In 1958, S. Chandrasekhar and L. Woltjer showed that force-free stable configurations can exist in space. They concluded that ”...the maintenance of a stationary state requires the appearance of surface currents at the boundaries” of the configuration. They showed that this condition leads both to no contradiction to the virial theorem and no necessity for expansion. (Proc. Nat Acad Sci., 44, 285) (Since it is not possible to have force free surface currents without also having some currents that cross the boundary, this is connected with my point that the current system is not bounded.)
It doesn't matter for the current version of the article, but for the record, you have not read this paper carefully. They do not consider a solution where "some currents ... cross the boundary" but explicitly note (at the top of page 287): In solving equation (9) we may certainly use the vanishing of the normal component of the current, j.dS, as a boundary condition. Furthermore, they explain that the surface currents are required to counteract the universal tendency of a magnetic field configuration to expand (i.e. the virial theorem), that is, the force on the current is outwards and must be taken up by something outside the system. One possibility they mention explicitly is that an asymptotically uniform external field could provide this containment. --Art Carlson 08:58, 28 July 2006 (UTC)
My parenthetical comment relating to my own arguments above is, as you say, incorrect, but that does not affect the overall conclusion. Chandrasekar and Woltjer’s solution is for, as they describe, an ”isolated spherical plasma”—one surrounded by nothing. You have misquoted the paper. The paragraph mentioning asymptotic fields begins ” We can avoid surface currents on a plasma with a force-free magnetic field by fitting suitable external fields.” External fields are explicitly posed as an ALTERNATIVE to the surface currents that maintain stability for a totally isolated sphere. The surface currents contain an ISOLATED plasma with no need for external fields.
There are two ways I can try to explain this to you. The first is to understand why the authors speak of an (apparent) "paradox":
1) There are, by assumption, no forces on the plasma inside the sphere. (j×B = 0)
2) There are, by assumption, no forces outside the sphere. (j = B = 0)
3) And yet, by the virial theorem, there must be an outward acceleration.
The resolution is that there are forces on the surface, neither inside nor outside the sphere, and these forces, to resolve the paradox, must obviously be in the outward direction required by the virial theorem.
The second way to explain this is to look directly at the fields, currents, and forces. We have a sphere, with no field outside, and a surface current j.
1) In what direction is the field just inside the sphere? (Answer: in the direction of r×j, by Ampere's Law)
2) In what direction is the Lorentz force? (Answer: in the direction of j×B ~ j×(r×j) ~ r, that is, outwards)
It doesn't get any clearer than that. --Art Carlson 21:11, 28 July 2006 (UTC)
The Chandrasekhar and other references describe "stable", non-expanding plasmoids.Elerner 05:44, 29 July 2006 (UTC)
Do they? The way I read it, Chandrasekhar et al. describe "stationary" states within a finite volume, and go to great efforts to point out that such states can only exist if currents or fields are imposed outside that volume (possibly in the surface). If the system of internal currents plus surface currents were force-free, then you could just draw the boundary a bit farther out and you would have no surface currents!
You don't have anything at all to say about my two physics arguments here (or the physics arguments I have given before relating to this point)?! I get the impression you are not too comfortable talking about physics. --Art Carlson 11:24, 30 July 2006 (UTC)
It is absurd for you to argue that “external forces” are needed. What external forces are needed to stabilize an atom? Or do you think atoms are inherently unstable because of the virial theorem?
This argument does matter for the article, because you persist in inserting sentences that imply only solid objects can contain plasma. I am again removing this un-physical idea.Elerner 14:12, 28 July 2006 (UTC)
I think it is important to point out that a megatesla is the mother of all magnetic fields, not just the garden variety. Two numbers that we can agree on to describe the conditions are the magnetic pressure and the electron density. Since few people have a feel for MPa and number densities, I thought it was a good idea to give them a quick reference point. This, and not the idea that you have to put a plasma in a bottle, was my primary motivation to mention the strength of steel and the density of solids. With this background, are you willing to put the statements back in? Do you have an alternative suggestion to help the reader understand the conditions we are talking about? --Art Carlson 16:35, 28 July 2006 (UTC)
The relevent comparison is to what has been obtained in the lab. I provide that now. We don't need "wow" comparisons and we can leave mother out of it.Elerner 05:44, 29 July 2006 (UTC)
I'm not entirely happy with the section, but I can live with it. As a compromise, I put the info on pressures and densities into footnotes. That might not be a bad idea anyway: I feel we are getting into too much detail for a general article on aneutronic fusion. Some of these things (and other things I want to say but haven't had time to) might better be placed in Virial theorem or Dense plasma focus. If you can live at all with the idea that information in footnotes will not irrevocably poison the minds of youth, please leave it alone. Wouldn't it be cool if we actually had a stable version for a few weeks? Oh, and one more thing: Do you think you can provide footnotes for the fields produced by lasers and DPF? --Art Carlson 11:31, 29 July 2006 (UTC)
However, I am glad to see some progress on the radioactive issues.


Much later, in 1987, D. Wells and L.C. Hawkins showed mathematically that self-confined quasi-force-free plasma configurations do have a confining force, and put this explicitly in the context of explaining experimental results where hot plasma are confined for many Alfven transit times without an external magnetic field (J. Plasma Physics, 38, 263)
The most interesting statement in this paper is the following: It has been observed experimentally that plasmas with very high ion temperatures and densitites can be contained for times corresponding to many Alfven transit times by the use of magnetic fields. In some experiments, magnetic pressures too low to support the corresponding plasma pressure are recorded. It is a shame that the authors do not elaborate or give references to support either of these statements! It is obvious that they want to say that there are plasmoid configurations that are isolated and do not expand. As far as I can tell, they don't actually say that. They do deduce the existence of "non-zero containment forces" and "finite containment forces". (What distinction are they trying to make between the two?) It is not at all clear whether they really derive the sign of these forces, i.e. whether they are inwardly-directed/containing or outwardly-directed/disruptive. This paper be a good starting point to follow up on references, but it is not a good citation to support the hypothesis of isolated plasmoids that don't expand. --Art Carlson 11:42, 30 July 2006 (UTC)
There are still other approaches. In 2000, L. Fadeev and A.J. Niemi demonstrated mathematically the existence of stable knotted self-confined configuration of plasma filaments could exist(Phys. Rev Lett 85,3416 and arXiv:physics/0003083). They argued that the use of the pressure term in the standard virial theorem argument was incorrect, and that nonlinear effect that arise from the interaction of individual particles with the electromagnetic field lead to an entirely different conclusion, namely that self-confined plasma configurations are possible.
This is probably the most interesting paper. In particular, the assumptions and limits of the standard derivation and of this one are laid out in some detail. The authors, if I understand them correctly, argue that there are special configurations with statistical properties not captured by the averages used in the derivation of the virial theorem. What is not entirely clear is whether they are talking about strictly isolated plasmoids. See p. 3418 (my emphasis):
The field ρ is a measure of the particle density in the bulk of the plasma. If its average (asymptotic) value <ρ²> = ρ02 becomes too small, .... Consequently we select the averge ρ02 so that it aquires a sufficiently large value in the medium. ... From this we conclude that |ρ(x)| never vanishes; it is bounded from below by a nonvanishing positive value.
I don't see any way to read this other than that the plasmoids being discussed are - indeed must be - imbedded in an infinite plasma. It is the current and field "fluctuations" that exist only within a bounded region. (In addition it is not always clear whether the structures considered are bounded in three dimensions or only in two (helical filaments), but as I read it the authors are not only talking about structures of infinite length.) The authors admit that it is not clear to what extent their solutions exist or can exist in the real world. My prejudice is that collisions and instabilities in actual plasmas will quickly destroy the correlations required to maintain such a state, but of course there can be no proof of such a statement.
I believe that special correlations of the type considered in this paper are also the reason that Eric Lerner (unfortunately?) does not explode. (See the first paragraph in the right-hand column on p. 3417.) The standard derivation assumes the particles react with the macroscopic fields resulting from macroscopic charge and current densities. Momentum transfer through collisions is not a problem either. In condensed matter, however, there are microscopic correlations between charges that cannot be ignored. As Faddeev and Niemi point out, "at high enough temperature the bound state degrees of freedom decouple" and a plasma description becomes appropriate.
--Art Carlson 13:02, 30 July 2006 (UTC)
I did not check anybody’s math, but Chandraskhar and Woltjer did have a remarkably good reputation for getting things right. In any case for wiki purposes, I surely don’t have to. What is key is that there is an abundant peer-reviewed literature showing 1) that self-confined plasmoids are possible and, more importantly, 2) that they are experimentally observed to exist for periods much longer than the Alfven crossing time. Therefore you and your pal Delgr really have no excuse to continually revert to your paragraph that states:” A magnetic field of this magnitude cannot, however, be maintained for an appreciable time in practical devices”. Even if you two think you are so much smarter than Chandraskhar, you can’t put your unsourced personal opinions in when they contradict stuff in the literature.Elerner 03:39, 21 July 2006 (UTC)
Thanks for the references. I've printed them out and will chew on them. (Please be a little patient.) --Art Carlson 14:18, 26 July 2006 (UTC)

Until you have, don't keep eliminating perfectly vaid, verifiable phsyics from the article.Elerner 18:41, 26 July 2006 (UTC)

  • I'm sure you can use yourself as a source, though conflicts of interest would require them to be publishsed in reliable sources, tedious to find perhaps, but probably necessary for particularly contenious issues.
  • As for j×B calculations, they may or not be relevent depending on the context. One thing I've learnt about plasmas is that they do some weird, wonderful and often unpredictable things; but at least these should be documented somewhere. --Iantresman 08:58, 19 July 2006 (UTC)
Hahaha! wow, next thing you know we'll be hearing arguments such as "F=-g((m1*m2)/r^2) may or may not be relevant to understanding gravity but who cares since it does some weird/cool stuff!".--Deglr6328 20:32, 19 July 2006 (UTC)
Art, you are reverting even though you have no reply to the references I've cited.Elerner 15:16, 23 July 2006 (UTC)
I didn't revert the article, for a change, I blanked it. Even if your references say what you think they do, your version is not acceptable for a number of reasons.
What reasons?Elerner 18:32, 23 July 2006 (UTC)

I thought leaving the sections out for a few days until we agree on a neutral, verifiable version would be a way out of the silly revert war.

We don't have to agree. We just both have to cite verifiable sources.Elerner 18:33, 23 July 2006 (UTC)

If you prefer simple reversions, I can oblige. --Art Carlson 16:08, 23 July 2006 (UTC) (P.S. I'm sorry I can't deal with this faster. I have a daytime job.)

Art, you have yet to answer the references on the virial theorem and self-contained plasmas, yet you continually revert to your version on this. While we try to settle the radioactivity question you should at least leave my version of the magnetic effect alone. You have no excuse not to.Elerner 14:24, 27 July 2006 (UTC)

[edit] Conditions observed in DPFs

Eric, you referenced the observation of magnetic fields of 0.02-0.04 megatesla to Bostick, W.H. et al, Ann. NY Acad. Sci., 251, 2 (1975). As I already mentioned, this journal is not in our library. Do you have an electronic or scanned version you can send to me? Do you have another reference for this value in a more accessible journal, or even online? Have fields close to this value been measured and published more recently than 30 years ago? Could you tell me what measurement technique was used? --Art Carlson 12:40, 31 July 2006 (UTC)

I cited alternatives above:Colloques internationaux CNRS no. 242, p.129-138. Also J. Plasma Physics 8, 7(1972). My own paper cited in the refs is far more recent and we observed 0.4 GG.Elerner 20:14, 31 July 2006 (UTC)
And I already told you that these sources are not in our library. Since you are either unable or unwilling to send me a copy and are either unable or unwilling to tell me in detail what they say, let me ask another question: What is the highest field in a DPF ever reported in a journal that is available in the large library of a major plasma research institute?
As for your own paper, you state in the abstract: "While fields of only 0.4 gigagauss have so far been demonstrated with the DPF, scaling laws indicate that much higher fields can be reached." And on page 23: "If we use (4) to predict Bc we obtain 0.43 GG, in excellent agreement with the observed value of 0.4 GG." That is, you do not report the "demonstration" or the "observation" in this paper, but only refer to it, and you do not cite any source, directly or indirectly. This is not the first time that you have claimed a paper says something that it does not. That forces me to question whether the evidence for fields of this strength is really strong enough that we can report this claim in Wikipedia. --Art Carlson 08:13, 1 August 2006 (UTC)
J. of Plasma Physics is not in your library? All of the references are in PPPL's library. As to my paper, if you follow the link on arXiv, you will get to it. The whole first half of the paper describes the experimental results. Just read it.Elerner 14:32, 1 August 2006 (UTC)
I've got egg on my face. I did a search on "0.4" and "gauss" and "gigagauss" in your paper. I found the two sentences I mentioned, but of course missed the mention of "4x108 G". I just found "Journal of Plasma Physics" in the online catalog, so I must have somehow overlooked it on the shelfs. I'll pick up that article tomorrow. (The online catalog confirms that the other two journals are not carried, though.) --Art Carlson 16:00, 1 August 2006 (UTC)
Just read the paper. It's always a good idea to read something you are commenting on, not just search it.Elerner 22:15, 1 August 2006 (UTC)
In the J. of Plasma Physics paper there is a plethora of detail on spatial and temporal structure and a good deal on energy. I can't find a word about measured maximum magnetic fields or densities. Can you point it out to me, or were you mistaken? (Of course, I might have overlooked something in the 14 pages. Unfortunately I can't search it electronically to be sure ... ) --Art Carlson 08:07, 3 August 2006 (UTC)
I have reread your paper, Eric, particularly the experimental part. I couldn't find any major flaws. (And believe me, I would not hesitate to say so if I could.) There are two things that still puzzle me. One, which we are not likely to resolve anytime soon, is the apparent discrepancy between your observations and the virial theorem. The other is the fact that the D-T neutron pulse is 5 times shorter than the D-D neutron pulse. Do you understand how that can be? I can't think of any explanation that would not imply a density at least 5 times higher than the value you report. --Art Carlson 13:51, 3 August 2006 (UTC)
The more I think about it, the more the short DT neutron pulse bugs me. If I recall correctly, you also mention the fact that the short pulse, which would be even shorter if the response time of the detector was taken into account, indicates a small spread of velocities along the line of sight. You interpret that as a small speed perpendicular to the magnetic field, but the field must twist around in several ways, and I doubt that you can maintain a significant non-Maxwellian distribution very long. Is there any chance of getting at look at the whole scintillator trace, from before the discharge to after the DD neutron pulse? Or at least hearing your best estimate of the triton temperature perpendicular to the line of sight? --Art Carlson 19:51, 4 August 2006 (UTC)
First, the DT pulse has to be shorter that the DD because there has to be time for the tritium to accumulate. Second, the trace is really flat as it is shown in the figure from the end of the gamma ray pulse to the beginning of the DD pulse except for the peaks shown.

Since the FWHM was 8 ns at both detectors, I cold only put an upper limit on the perpendicular temperature based on a 1 ns spread between them. This would be somewhere around 14 keV. That would not imply an extreme difference between axial and radial velocities. However it is only an upper limit.Elerner 22:21, 4 August 2006 (UTC)


From previous comments, I gather that the record density reported is a few times 10^26 m^-3, which makes it about 10,000 lower than that required to simultaneously suppress bremstrahlung and synchrotron radiation. Correct? --Art Carlson 12:40, 31 July 2006 (UTC)

Again your math is a bit off. The density required for trapping at 10GG is 2.4x10^30 m^-3 and the peak density observed is about 3x10^27 m^-3, about 800 times lower, not 10,000.Elerner 20:14, 31 July 2006 (UTC)

[edit] additions to page

[edit] Direct conversion and economics

I have added new sections on direct conversion which is the main advantage of aneutronic fusion and on current research in the field. I took portions of "energy balance" and reorganized it into a new section on technical challenges. I hope to add needed references over the next day or two.Elerner 18:09, 7 August 2006 (UTC)

Well, well, well. We've been busy, haven't we? You will not be surprised to learn that I take umbridge with many of your changes. I do see some logic to the new structure, so I will try to deal with the content within that form, rather than (shudder!) resorting to massive reversions. It may be next month before I have much time for this, though. --Art Carlson 20:44, 21 August 2006 (UTC)
Can I take that back? A section on direct conversion makes sense here because it is a subject that is important to aneutronic fusion and only of marginal interest to conventional fuel cycles like DD and DHe3. The section should explain what direct conversion is and what the advantage is (efficiency, mostly), and list/describe the major proposals, whereby a reference for each of these would be very helpful. However, its place of honor at the beginning of the article is predicated on the correctness of the assertion that direct conversion is "the principle advantage of aneutronic fusion", which I do not believe is tenable. My impression of the literature is that most people think the principle advantage of aneutronic fusion is that it is aneutronic. The fact that direct conversion is possible is welcomed in order to have any chance at all of making the energy balance positive.
The other major problem with the current version is the discussion of economics. The statement that "about 80% of the capital cost of a typical electric power generating station is in the thermal conversion equipment" is not true except for fossil fuel plants, possibly only for natural gas power plants. (That is why gas plants are used for peaking and emergency power: They are so cheap that you can afford to leave them idle most of the time.) For any design of a tokamak power plant, the cost of the turbines and generators is a very small fraction of the total cost. Since the cost of fusion power depends on the captital cost of producing the fusion, the capital cost of the energy conversion, and the recirculating power fraction, it is not possible to make sweeping statements about "sharply reduced costs". Furthermore, the current version states that direct conversion is as a rule easy, compact, and cheap, but many proposals that have been made have high technological risk and are both voluminous and expensive. Direct conversion is not even necessarily efficient. (Think of solar cells.) This section needs major revisions. Would you like to have a go at it, Eric, before I come back with my sledge hammer? --Art Carlson 10:45, 22 August 2006 (UTC)
While there have been no extensive analysis of direct conversion costs, it is very reasonable to state that the potential exists for great cost reductions. To give one example, technology exists for conversion of pulsed charged particle beams into elctric power--high power microwave generators. MW generators that are now produced on a one-of-akind or few-of-a-kind volume already cost about the same as turbines of the same capacity which are mass-produced in large volume. Since it is a well-know manufacturing rule of thumb that mass production leads to cost reductions of at least a factor of ten over small-volume production, it is perfectly defensible to say that there is a potential for major cost reductions. Also this is stated as a motivation for the apporach, which it certainly is.Elerner 18:17, 31 August 2006 (UTC)
Art Carlson's introduction to the direct conversion section is a non-sequitor. Instead of talking about direct conversion, it talks about the Lawson criterion, which belongs in the section on technical challenges. I have again moderated the language of my introduction and clarifed the 80% figure, which does refer to fossil-fuel plants, which have the lowest capital costs over all, so are the reasonable comparison on thsoe costs.Elerner 18:26, 31 August 2006 (UTC)

I've changed the economic comparison paragraph. I put in a new version of my old graph, which, I think is more accurate. I think that Art's paragraph is very close to incomprehensible by the average reader. Let's try nto to get into reverts, but edit instead.Elerner 01:08, 13 September 2006 (UTC)

I agree that my version is incomprehensible. There is nothing directly false in either version. But I find your version misleading. While the rest of the world is debating whether aneutronic fusion is even theoretically possible, and has postponed the question of whether it would be cheaper or more expensive than D-T fusion, you have jumped at least two orders of magnitude in the price projections and raised the question of whether aneutronic fusion would be cheaper than electricity from natural gas plants, if the natural gas were free! You may think that is a reasonable question, but it does not accurately represent to the readers the current state of the debate. We either need to make clearer the assumptions and background involved, or - better - we need to eliminate the discussion of economics altogether. It would, of course, help if we could find some serious, verifiable discussion of the economics of direct conversion. I will not delete the material until you have had a chance to propose a better version. --Art Carlson 08:58, 13 September 2006 (UTC)

[edit] Power density and Lawson criterion

OK. I fixed up the discussion of direct conversion and economics. The next worst thing about the August edits is the elimination of the information that, "for p-11B compared to D-T, the triple product nTτ required for ignition is 500 times higher and the power density is 2500 times lower." If that's not a "technical challenge", then I don't know what is! Change coming soon. Comments before? --Art Carlson 15:07, 28 August 2006 (UTC)
Yes I will get back to this shortly. I made it clear that higher nt and T are required. The power density is simply wrong. That depends on many variables such as density and T. The power density in a pB11 plasma focus is much higher than that in a DT tokamak.Elerner 02:58, 29 August 2006 (UTC)
I deleted the power density discussion, which is just wrong. You can’t compare the two fuels “at the same pressure” without specifying the temperature. Reactivity at the same pressure and different temperatures can vary widely. If the two fuels are compared at 600keV, the power density of pB11 is 60% that of DT at the same pressure. If they are compared at 66keV the power density of pB11 is 150 times less than DT at the same pressure.
The only valid apples-to-apples comparison is comparing the optimum conditions for the two fuels, which I did. The Lawson criterion for optimal burn is a factor of 30 times more for pB11, a substantial difference.Elerner 19:04, 31 August 2006 (UTC)
What? This strikes me as wrong. This completely ignores feasibility! I think that in such a circumstance it's an error to say such things. Ideally the power density section should include a graph versus temperature at different pressures. Do you agree? Danielfong 22:12, 31 August 2006 (UTC)
Dear Daniel, welcome to the discussion! Eric and I get in each others' hair a lot, so if you are interested, I think it would help a lot to have a third party around. The article is rather specialized, so it helps that you are a nascent plasma physicist, but on the other hand, if you don't understand the our technical arguments, then they must be too subtle for a general encyclopedia. I'm not asking you to take sides, just to comment on which formulation is more understandable, which arguments make more sense, and where external references are needed. Thanks. --Art Carlson 14:48, 5 September 2006 (UTC)
Dear Art, I'll make an attempt, but at the moment everything looks like a spaghetti argument on the talk page. I can't detect any real problems with the article, except the neutronicity argument could use some embellishing. It's my feeling that the advantage of 'aneutronic' fusion won't really be the lack of shielding, you'll just be able to get away with less of it, and you will have a replace it at a much lower frequency (meaning there will be much less expensive waste disposal). I would like to see some estimations on the savings you'd get with regards to shielding, if so possible. I'd also probably like to see some of the arguments shift towards D-He3 (which won't be totally aneutronic, but will cut neutron emissions by a bundle). Danielfong 17:03, 13 September 2006 (UTC)
Eric, I have presented my calculations in detail here. In particular, I do clearly specify the temperature in my calculation as being that which yields the highest power density for the reaction at hand. You have not pointed to any mistake in these calculations, nor to any other set of assumptions that would be more instructive. You seem to have something of the sort in mind, but I have not been able to fathom what it is on the basis of what you have written. Maybe you can talk in complete equations? In short, my version is the only one which is documented. In addition, no flaws in it have been pointed out. So let's use it. --Art Carlson 11:57, 5 September 2006 (UTC)

Rather than get into reversions on this, I would like to ask Art to give his calculations defending the figures of 600 and 2500 in the power density paragraph. I can't duplicate them. And, may I point out, Art has posted a few arithmetical errors on wiki.Elerner 01:12, 13 September 2006 (UTC)

Once again, my calculations can be found here. If you still have trouble following some step, then I need to clarify the calculation in that article. --Art Carlson 09:03, 13 September 2006 (UTC)
If I am understanding you correctly, you want to use fusion power density / pressure squared as a figure of merit for fusion reactors. Now, I don’t think that is a good figure of merit, because some reactors, like the DPF may have plasma pressures orders of magnitude greater than a tokamak. In the article you reference, you say that this figure of merit is a measure of economical viability, but it clearly is not—actual power density is.
I'm not sure sure we are on the same wavelength. I calculate two figures of merit. The first is the Lawson criterion in the triple-product form. This is used all the time and should not be controversial. The second is the (relative) power density at a given pressure. (These have in common that the optimum temperature is that which maximizes <σT>/T²). Since the power density depends on the density and temperature as well as the fuel cycle, you have to specify the other conditions. I compare the power densities of different fuel cycles at the same pressure. I think you are comparing the power density of D-T at the pressure attainable in a tokamak with the power density at the pressure (you think) attainable in a DPF. That is not fair. My figure of merit would apply (at least within a factor of two or so) to a D-T tokamak compared to a p-B11 tokamak, or to a D-T DPF compared to a p-B11 DPF. Remember we are not discussing alternative confinement concepts here, but alternative fuel cycles. --Art Carlson 20:49, 14 September 2006 (UTC)
I don't agree at all. You can't separate fuels and devices--some fuels are more suitable to some devices. The article already points out that extremely high magnetic fields make things more favorable to pB11. Such fields can't be reacehd in a tokamka. A neutron-rich fuel like DT would blast apart a compact device like a DPF. The material damage rate would be pretty spectacular. So I don't see your figure of merit as a valid one at all. It does not relate to anything practical. The Lawson criterion gives an idea of technical difficulty. But then it should be the minimum triple product for complete burn-up, not for ignition. Ignition depends on the energy loss rate, which is device-dependent for both fuels.Elerner 02:04, 15 September 2006 (UTC)
It seems you agree that my math is right (this time), and that the results as I state them in the article, with the assumptions made there, are correct. That's a good start. Can we at least agree that the Lawson criterion has a place here? First, it is the figure of merit "everybody" uses, so we can't leave it out. Second, it is the best you can do to order the difficulty of various fuel choices before you start to discuss the confinement device. And third, it is a minimum requirement: If the DPF is the sooper-dooper device you believe it is, then it is so far above the minimum requirement that it doesn't matter any more. But the place to start is with Lawson. The role of the confinement concept comes into play when we take a closer look at the τ in nTτ. --Art Carlson 08:43, 15 September 2006 (UTC)
OK, I've added another comparison, which includes the fact that DT is more energetic. Hope this is OK with you now.Elerner 13:37, 18 September 2006 (UTC)

---Continuing dialog but restarting indentation---

Fine, why don't we include the minimum lawson criterion for burn-up and drop your pressure-based figure?Elerner 23:19, 15 September 2006 (UTC)

I'm glad we have agreed on the importance of the Lawson criterion as a measure (not the whole story!) of the technical feasibility of producing net energy. The next natural question after whether it is possible, is whether it is worthwhile. As you yourself have already pointed out, a very valuable figure of merit, commonly used in every area of energy technology not just fusion, is the power density. Since the reaction rate is proportional to the square of the density, the density or some function of the density and temperature has to be held fixed to compare different fuels. Since most, perhaps all, confinement concepts have a pressure limit, the natural choice is to compare different fuels at the same pressure. (Taking the same density is less common but might be a defensible alternative.) It is also of interest to note that the nTτ form of the Lawson criterion, as opposed to nτ or even nτ/T, is also justified on the basis of maximizing the power density for a given pressure.) The usefulness of this figure of merit is immediately evident if we consider burning p-B11 in a tokamak: Even if we could get it to burn, and even if we found some tricks to improve the performance of the fuel and the device, the power density is so low that an economic aneutronic tokamak is out of the question. One reason to include this number is to point out that, if aneutronic magnetic fusion has any chance at all, it will be in conjunction with an "alternate concept". --Art Carlson 10:40, 16 September 2006 (UTC)
In addition, your penalty factor assumes equal ion and electron temperatures, which is not a justifiable assumption.
It is correct that I assume equal ion and electron temperatures, which I believe to be justifiable from the literature. If you can succeed in supressing the transfer of energy from ions to electrons, of course, it's a new ball game. I have added a footnote to this effect. Can we postpone this fight until we have settled the one above? --Art Carlson 20:49, 14 September 2006 (UTC)
It is not justifiable from the literature. Just the x-ray loss alone make the electron temperature lower, and the high magnetic field effect can lead to temperatures that are an order of magnitude or more lower.Elerner 02:04, 15 September 2006 (UTC)
With "justifiable from the literature" I mean that most publications dealing with fusion either make the assumption or conclude from detailed considerations that the temperatures will be nearly equal. Admittedly, most publications also deal with tokamaks, but the article should try to reflect the state of the discussion as it is, not as some editor thinks it should be. We can get into exceptions later in the text. Remember, too, that radiation loses will selectively cool the electrons, but energy transfer from fusion products will under many conditions of interest selectively heat them, so the electrons are not automatically cooler than the ions at all, much less negligibly cold. --Art Carlson 08:52, 15 September 2006 (UTC)
Finally, I don’t even get the exact same numbers as you do. I find the maximum value for pB11 is 4.8x10^-27, not 3.0, but that is a minor point compared to the fact that the real measure should be power density, not power density/pressure squared.Elerner 15:20, 14 September 2006 (UTC)
I didn't give a reference for my number in the article, and I don't remember for sure where it came from, but I suspect from R. Feldbacher and M. Heindler. "Basic Cross Section Data for Aneutronic Reactor". Nucl. Instrum. & Meth. in Physics Research A271 (1988). Pp. 55-64. What is your reference? --Art Carlson 20:49, 14 September 2006 (UTC)
My reference includes better and more recent data "Thermonuclear Cross Section and Reaction Rate Parameter Data Compilation" Larry T. Cox, 1991 Phillips Laboratory report AL-TR -90-053Elerner 02:04, 15 September 2006 (UTC)
Thanks. I'll check it out. --Art Carlson 08:53, 15 September 2006 (UTC)
It looks like I don't have easy access to the original, but the formulas and coefficients in Talk:Nuclear_fusion#Optimum_fusion_temperatures apparently come from there. Can you verify that? The rest is just a bit of math. --Art Carlson 09:11, 15 September 2006 (UTC)
All right. I did the math. The results are on Talk:Nuclear_fusion#Optimum fusion temperatures. In particular, I get 3.0x10^-27, not 4.8, for p-B11. Your turn, Eric. --Art Carlson 14:03, 15 September 2006 (UTC)


I hope I am not starting another edit war here. But you are not using valid comparisons. First of all, getting ignition depends on many factors other than fuel, as I have explained several times. Second, ignition in no way guarantees for either fuel or for any device, that the fuel will then burn up completely. If ignition causes your plasma to become unstable, you may burn very little.
However, the requirements for burning the fuel entirely are much less ambiguous. The triple product is the minimum product of pressure and confinement time needed to burn the fuel entirely. Twenty seven is not a small factor and makes clear that pB11 is much, not a little more difficult. But we avoid totally invalid comparison that make the task seem impossible.
My calculations are as follow: 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/<σv>. The ratio is 26.6.
If you still disagree, Art, maybe we can call in Croquant?Elerner 20:31, 17 September 2006 (UTC)
Eric, would you mind telling me finally how you come up with these numbers?! What's the idea of saying "My calculations are as follows" and then just stating your results (without even giving any units)?! My calculations and the assumptions underlying them are laid out here and here and here. I find the optimum temperatures to be 13 keV and 125 keV, and the minimum triple products to be 2.76×1021 m-3 keV s and 1.37×1024 m-3 keV s. --Art Carlson 20:59, 17 September 2006 (UTC)
Sorry, see corrected version above.Elerner 21:44, 17 September 2006 (UTC)
That's still pretty sketchy, but I think I can piece it together now.
First, your numbers. Your temperatures are higher than mine because you are looking at the temperature that maximizes <σv>/T, and I am maximizing <σv>/T². Your values for the two fuels are closer together because you leave out a factor of T/E_ch that is in these formulas, and because you leave out my factor of three penalty. Your values for both are higher because of (apart from the cm to m conversion) that factor T/E_ch, mitigated by the factor of 12 in the Lawson formula. I haven't checked your math, but I assume your numbers are correct given your assumptions.
Second, your assumptions. You seem to be taking the burn-up fraction as the figure of merit. This is an unconventional choice, and for good reason. Recycling un-burned fuel is not a big deal. Energy is the name of the game. Just think about it. Of two reactions that had similar burn-up, would you take the one that produced 100 MeV per reaction or the one that produced nothing? It is true the derivation in the Lawson criterion article, except for the ICF section, makes the tacit assumption that the fusion products are confined and keep the plasma hot. If all fusion products are lost, you can still make a reactor, but it will be driven, not ignited. The relevant figure of merit then is the gain. The optimum is still where <σv>/T² is maximum, but you need to use the total fusion energy, not just the fusion energy released as charged particles. This would make D-T another factor of 5 more favorable over p-B11.
--Art Carlson 08:39, 18 September 2006 (UTC)
The nτ for burn up is just 1/<σv>. 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.
And since the temperature needed for p-B11 is ten times higher, the triple product is a factor of 500 higher. The limits on both nτ and nTτ are refered to in the literature as the Lawson criterion. My experience, at least in the tokamak world, is that the triple product is considered to be a better measure of technical difficulty. (See, for example, this). The triple product also follows naturally from any analysis which includes a pressure limit. There is no such natural motivation for choosing nτ as the figure of merit. For these reasons, I argue that we should in any case include the triple product in the article and let the chips fall where they may. (Note that trying to make aneutronic fusion look bad was not one of my arguments, and it is not one of my personal aims.) I have no objection to including the limit on nτ as a second figure of merit.--Art Carlson 09:07, 19 September 2006 (UTC)
The pressure comparison just does not make sense, since you MUST make further assumptions about electron temperatures.
Do you mean comparing the power density at given pressure? Of course you have to make an assumption! If you have been listening, you will know that I have stated in the articles that I am assuming equal temperatures for electrons and ions, like most authors do because most fusion devices have this characteristic. Since, later in this article, we consider systems with cold electrons, I am willing to also report the numbers using this assumption. All these alternatives are getting cumbersome, but I think an intelligent reader can find his way.--Art Carlson 09:07, 19 September 2006 (UTC)
Can we try to compromise, or do you just want to edit war like Joshua?Elerner 02:47, 19 September 2006 (UTC)
I don't want an edit war. What I want is an accurate, understandable, helpful, and neutral article. On that I am not willing to compromise. As a I say above, I am not willing to replace my figures of merit with others, but I am willing to supplement them. Feel free to add to the article, or just wait a few days until I have time to do the numbers carefully. --Art Carlson 09:07, 19 September 2006 (UTC)
Look, your calculations are "original research" unless you can cite them somewhere in the literature. The assumptions you use are just wrong and unsupported. And your arguing that power density at a given pressure is a valid measure of economic value, independent of device, is also unsupported in the literature. If you want to say pB11 requires higher pressure, that would be OK. But otherwise, find this analysis in the literature. Other wiki articles are not citations.Elerner 22:03, 19 September 2006 (UTC)
I don't understand what you are asking for here. Do you want citations that nTτ is used as a figure of merit for fusion reactions? Do you want citations that power density is used as a figure of merit for fusion reactions? Since some assumptions have to be made to compare the power density of different fuel cycles, are you proposing holding something other than pressure constant? What assumption of mine do you consider to be "just wrong" (as opposed to useful only under some circumstances)? Since I do say that p-B11 requires higher pressure (50 times higher), why do you not consider my version to be "OK"? --Art Carlson 20:55, 20 September 2006 (UTC)
Maybe this (p.6) will help:
Power Density. At fixed plasma pressure, and accounting for the greater a/p –ash fraction expected at similar ash pumping efficiencies (i.e., similar tp*/tE) in a D-3He burn, the fusion power density in D-3He is about 100 times less than that of D-T. Hence, a factor of ~10 increase in the plasma pressure is required to achieve fusion power densities in D-3He similar to that anticipated for the D-T fuel cycle.
Sounds an awful lot like my approach. --Art Carlson 21:06, 20 September 2006 (UTC)

I wrote some comments in the Dispute_between_Art_and_Eric section of this page (I began my comment before seeing this part of your discussion, which explains my creation of a new section). Croquant 05:41, 21 September 2006 (UTC)

[edit] 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)

[edit] 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)

[edit] 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. Danielfong 18:59, 20 September 2006 (UTC)

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)

[edit] 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)

[edit] 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 ωp > ωc / 2 is mathematically equivalent to nkT / (B2 / 2μ0) > kT / (2mec2).) 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)

[edit] Consistent data set

Independent of the blood being shed on the front, I would like to come to an agreeement on the data we use, starting with <σv> as a function of temperature. The numbers I use are verifiable, but I think they come from multiple sources and may not be entirely consistent. Can we agree to use the functional form and coefficients given in

Cox, Larry T., Thermonuclear Reaction Bibliography with Cross Section Data for Four Advanced Reactions.,
AF-TR-90-053, Edwards Air Force Base: Phillips Laboratory Technical Services Office, 1991

and reproduced here? I'm open to other suggestions. --Art Carlson 08:19, 27 September 2006 (UTC)

[edit] New proposal for power density

(To avoid confusion, please limit comments in this section to the proposal above. Comments on other content should be put in the appropriate section. --Art Carlson 08:40, 3 October 2006 (UTC))

In every published fusion power plant design, the part of the plant that produces the fusion reactions is much more expensive than the part that converts the nuclear power to electricity. In that case, as indeed in most power systems, the power density is a very important characteristic. If the power density can be doubled without changing the design too much, then the cost of electricity will be at least halved. In addition, the confinement time required depends on the power density.
It is, however, not trivial to compare the power density produced by two different fusion fuel cycles. The case most favorable to p-B11 relative to D-T fuel is a (hypotheical) confinement device that only works well at ion temperatures above about 400 keV, where the reaction rate parameter <σ'v> is equal for the two fuels, and that runs with low electron temperature. In terms of confinement time required, p-B11 would even have an advantage, because the energy of the charged products of that reaction is two and a half times higher than that for D-T. As soon as these assumptions are relaxed, for example by considering hot electrons, by allowing the D-T reaction to run at a lower temperature, or by including the energy of the neutrons in the calculation, the power density advantage shifts back to D-T.
The most common assumption is to compare the power densities at the same pressure, with the ion temperature for each reaction chosen to maximize the power density, and with the electron temperature equal to the ion temperature. Although confinement schemes can be and sometimes are limited by other factors, most well-investigated schemes have, not surprisingly, some kind of pressure limit. Under these assumptions, the power density for p-B11 is about 2100 times smaller than that for D-T. If the device runs with cold electrons, the ratio is still about 700.

Are there specific objections to (1) the factual accuracy, (2) the point of view, or (3) the editorial style of this version? I tried to do justice to the complexity of the issue without being long-winded. Inline citations would be desirable. Footnotes could be used to add information or to reduce the length of the main text. We can talk about the exact values I used for the numbers. --Art Carlson 08:48, 2 October 2006 (UTC)

To make myself perfectly clear, I consider this expanded version to be adequate reply to Eric's objection that the two-sentence version did not do justice to the complexity of the issue. I will leave it here for a few days, during which time I consider Eric (or any other active editor) obligated to detail any objections. If no comments or suggestions are made (in enough detail that they can be responded to), I will consider this the consensus version, put it on the live page, and defend it against unargued or blanket reverts. --Art Carlson 09:48, 2 October 2006 (UTC)


Sure, Art, there is a lot wrong with that factually. First is the assumption that in any fusion device the cost is dominated by energy production, not conversion. That is the case for tokamak, but not, for example for the DPF. A tokamak without energy conversion that is capable of producing a GW of energy will, by any estimate I know of, have a capital cost in excess of $2/W, probably a lot in excess. A DPF, without energy conversion equipment, that is capable of reaching the breakeven conditions outlined in my own published research costs about $150,000 with current low production rates of components such as capacitors and fast switches. (This figure can be easily verified since I have priced the components myself.) It would be capable of producing 5 MW of net power, so has a cost of about $0.03/W. In that case the total cost is dominated by the cost of conversion, which would be around $0.80/W for thermal conversion, but probably around $0.10/W for direct conversion, again based on low-volume production.
A careful reading of what we both wrote shows that there is no disagreement on the facts. Since you evidently misunderstood me, we obviously need to work on the clarity. I first point out that the costs in published fusion power plant designs, like the tokamak designs you mention but not limited to them, are dominated by the nuclear island. I do not doubt that you have made some estimates for a DPF plant that are dominated by the balance of plant.--Art Carlson 21:18, 3 October 2006 (UTC)
Second, the power density of the reacting plasma does not have a direct link to costs. In the DPF, the reaction takes place in a volume that is tiny compared with the total size of the device and in a time that is a small fraction of the pulse repetition time. Therefore comparing power density in a DPF to that of a tokamak would give an estimate of relative cost that would be many orders of magnitude in error.
In other words, a DPF can produce enormously higher pressure per dollar than a tokamak. But the cost of power is not in the same ratio, although the DPF would be about two orders of magnitude cheaper.
It is tempting - but, as you point out, invalid - to estimate the output of a fusion plant by multiplying the fusion power density with some volume such as that of the reaction chamber. This is one of many reasons that, as we both agree, power density figures are totally useless to compare different power plant concepts like tokamaks and DPF. That is why I have never done so. My text specifically compares "two different fusion fuel cycles". So again, on a careful reading, we do not disagree on the facts.--Art Carlson 21:18, 3 October 2006 (UTC)
So altogether, the paragraphs are not accurate. Nor is the paragraph that you have, for the same reasons, so I am going back to my paragraph, which is accurate.Elerner 02:29, 3 October 2006 (UTC)
Now that it is clear that the problem lies more in understanding what I wrote, perhaps you can suggest a version that you find clearer? --Art Carlson 21:18, 3 October 2006 (UTC)

It has now been 9 days since I posted this proposal and 8 days since the last comments were made. Therefore I have incorporated it into the article. Improvements are welcome, but blanket reverts are out-of-place, --Art Carlson 08:06, 11 October 2006 (UTC)

[edit] Eric's justification for his reversions

Since Eric seems to have difficulty focussing on detailed arguments, I have created this section to give him a leg up. Specifically, he has several times made a reversion essentially identical to this one. I provide space here for him to explain why he made each of these changes. --Art Carlson 20:56, 3 October 2006 (UTC)

1. It is better not to provide a wiki link to the Lawson criterion when discussing the Lawson criterion because ...

2. It is better not to provide a wiki link to a calculation of the confinement requirement for D-T vs. p-B11 when discussing the confinement requirement for D-T vs. p-B11 because ...

3. It is better not to provide a footnote explaining the hot ion mode, even though two of the three mechanisms discussed later for achieving p-B11 ignition use this mode, because ...

4. It is better not to provide a reference for the idea of bremsstrahlung absorption in pellet fusion because ...

5. It is better not to disambiguate the wiki link Pascal to Pascal (unit) because ...

This argument is not worth the time devoted to it. I have merged part of your paragraph with part of mine. I will narrow my objection to the fact that your claim that one measure is most imortant is totally unsourced and is your own original opinion, so does not belong there. Find a citation for it and then say "according to so and so..." other wise drop it.Elerner 18:33, 9 October 2006 (UTC)
I can live with that. Speaking of dropping it, I guess you saw the light about points 4 and 5. I'm still looking forward to hearing your reasons for maintaining points 1 through 3, though. --Art Carlson 19:14, 9 October 2006 (UTC)
oh, put them back in yourself without reverting and let's end this!Elerner 20:58, 9 October 2006 (UTC)
Glady. Just for the record, there were eight rounds of reversions due to these differences, which you now concede without having once justified them. I hope we can work more efficiently in the future. --Art Carlson 21:18, 9 October 2006 (UTC)


[edit] edits by EngineerScotty

You may not be aware of this, but aneutronic fusion has been studied in the laboratory for decades. The fact that it produces the bulk of its energy in charged particles is vaidated by thousands of experiments. To portray, as you do, known, undisputed physics as the opinions of a minority is a gross distortion. I don't want to get into a revert war again, but I think you should do a bit of research before piling in on this. I stronlgy suggest you rever the changes yourslef until you look a bit at the field.Elerner 00:41, 10 November 2006 (UTC)

Got your note--I have an interesting perspective on the article that you might consider--it might explain better the reactions of some on Wikipedia (and outside as well).
Adding references to the article would be good--inline references would be better. At any rate, processes or technologies which have been proposed--even if studied in detail--but which haven't been built, probably should use the subjunctive voice. I'm not at all equating the topic with perpetual motion machines (as WAS 4.250 did on the arb page), but many agree the technical hurdles are immense.
I should let you know that my professional line of work (a software engineer) has long taught me to be skeptical of claims which are based entirely on theory and not on practice (here being empirical research)--with exceptions granted for things like mathematics.
I'm not doubting the scientific claims at all, nor am I agreeing with them. I have no intellectual basis to do so, not being a physicist. I pretty much left them alone. However, when the article ventures forth from the purely theoretical, into questions of "how can we build a device which uses this far-off technology, how much will it cost, and what will other properties of this thing be", it crosses a big bright line from theoretical science into engineering--my turf. Discussing engineering parameters of device which we currently have no idea how to harness the underlying technology of, and speculating on its properties, while using the present tense--strikes me as highly inappropriate.
My preference for this article, after much reflection, would be to remove most if not all claims concerning the properties of a powerplant based on aneutronic fusion. Such engineering analyses are far too speculative to include in an encyclopedia at this state of the underlying technology (infancy), regardless of the soundness of the underyling science. The information on the underyling physics--the various reactions and their properties, what aneutronic fusion is--certainly should stay. The science parts of the article aren't bad (better sources would be nice), but the detailed commentary regarding how a reactor and energy conversion device might work are simply pie-in-the-sky at this point. If you were to get a multi-billion-dollar grant to study this, Eric, I suspect you'd be at least a decade away from having a laboratory reactor up and running, let alone being able to prototype a powerplant (let alone being able to build one that is cost-effective). To make claims--even couched as speculation--as to how efficient such a beast would be, is simply not appropriate here. And--not to be rude--it does look like a sales job.
Thoughts from others?
--EngineerScotty 01:24, 10 November 2006 (UTC)
I'm following this, and thinking about it. Fred Bauder 01:50, 10 November 2006 (UTC)
Might it become a principle in the case? :) --EngineerScotty 01:52, 10 November 2006 (UTC)
But your edits are flat-out wrong. Of course aneutronic fusion reactions have been produced in the laboratory. It is not a proposed form of fusion power--it is a well-known form.
Again, you're intermingling the raw science, with the technical application. Aneutronic fusion is certainly a well-known form of fusion; but it remains a "proposed" form of fusion power--nobody's built a functioning powerplant that operates using aneutronic fusion.
If you are trying to say that it has not produced net energy, that is true of all forms of fusion energy.
From the article, the only mention of an actual aneutronic reaction being produced is this passage: "In 2005, a Russian team produced hydrogen-boron aneutronic fusions using a picosecond laser[13]. However, the number of the resulting α particles (around 103 per laser pulse) was extremely low." Never mind being able to recover positive net energy--has anybody even sustained a chain reaction yet?
Fusion reactions are not chain reactions. You are thinking of fission--that is a different process. Please learn just a bit of the physics before chopping up the article.Elerner 02:10, 11 November 2006 (UTC)
Yet fusion engineering is an active field of study--there are whole departments devoted to it at some universities. It is not theory that aneutronic reactions produce almost all their energy as charged particles--it is undisputed laboratory findings for decades past.
That appears to be by definition.
If you eliminate from this article all discussion of engineering problems, you would have to knock out 80% of the article on fusion power, which deals with engineering problems of tokamaks.
A better solution, I think, would be to separate the aneutronic fusion and aneutronic fusion reactor--one could focus on the science, the other could focus on efforts to harness this sort of reaction.
Again, this article was gone over with a fine-toothed comb by Art Carlson, who is no friend of aneutronic fusion. Please don't take a bull-in-china-shop approach. Again I offer to provide review articles so you can see what the state of the field is.
Please. Also please note that you and Art do not constitute a consensus. While your work to improve the article is appreciated; many of us think it could be improved further.
Also we do not need a half billion dollars because the devices cost less than $300,000 to build. Many have been built--this is not theory this is ongoing experimental work dating back decades.Elerner 02:00, 10 November 2006 (UTC)
Which devices, exactly? And with what properties?
--EngineerScotty 17:55, 10 November 2006 (UTC)
Dense plasma focus is one device that is very cheap to build and has been researched experimentally for over forty years. This is not a new field--it is an ongoing program. Elerner 02:10, 11 November 2006 (UTC)

Elerner 02:00, 10 November 2006 (UTC)

I don't get this, "power," to me, means sustained output. This is a reaction, but not power. Fred Bauder 02:42, 10 November 2006 (UTC)
This is not correct. Power in science and engineering has a very specific meaning—energy produced per unit time. Fusion devices can produce power either continuously ( which has never been achieved, but is theorized as possible with some devices) or in pulses that are repeated. Aneutronic fusion is just another form of fusion energy from the more commonly studied DT reaction. It is no more theoretical than DT and has been studied experimentally very extensively. Fusion power has been produced in many devices and aneutronic fusion power has also been produced.
You are confusing “power” with “net power production”. That is very different. This is when you get more power out of the device than you put into it. This has not been achieved for any controlled fusion device
If you look at the “fusion power” article, you will see power is correctly referred to. None of the devices mentioned come at all close to producing “net power production”: more power produced than electricity than is needed to run the device. But they all are correctly described as producing power.Elerner 03:52, 10 November 2006 (UTC)
Still confusing. I know the Amazon is a "stream", but I don't think that's even mentioned in Amazon River. Fred Bauder 13:00, 10 November 2006 (UTC)
Did you look at the fusion power article? Rivers have nothing to do with this, but fusion power does. Please look at it and see the correct use of the terms.Elerner 02:10, 11 November 2006 (UTC)
I think the best approach to this article is that I will provide, over the next few days, additional verifiable references to everything that I can. Then you can get rid of things that are not cited? How about that?Elerner 02:10, 11 November 2006 (UTC)
I'm not very happy either with a lot of the edits by EngineerScotty. Unfortunately I won't have time before Thursday to go through them in detail. --Art Carlson 18:03, 11 November 2006 (UTC)

[edit] I think this section is wrong...

In the candidate area I found this passage:

"The next two reactions are usually treated as a chain in the hope of attaining an enhanced reactivity due to a non-thermal distribution. The product 3He from the first reaction..."

I believe this needs to be fixed. The first reaction has no 3H3 product, nor does the first reaction on the list. I think this needs to be re-arranged.

Maury 22:28, 16 November 2006 (UTC)

The reactions in question are
p + 6Li → 4He (1.7 MeV) + 3He (2.3 MeV)
3He + 6Li → 2 4He + p + 16.9 MeV
Add them together and you get
2 6Li → 3 4He
I suspect you were confused about which reactions I meant. Would it be better to number the reactions? --Art Carlson 09:09, 17 November 2006 (UTC)
I made some changes that might make things clearer. --Art Carlson 09:27, 17 November 2006 (UTC)
Yes, much better now. Maury 13:21, 23 November 2006 (UTC)

[edit] References in section on "Technical challenges"

We now have 12 inline references in fifty-some lines of text in Aneutronic fusion#Technical challenges. Do we still need the {{References}} template? --Art Carlson 10:00, 17 November 2006 (UTC)

[edit] Contradiction?

In every published fusion power plant design, the part of the plant that produces the fusion reactions is much more expensive than the part that converts the nuclear power to electricity.

This equipment is sufficiently expensive that about 80% of the capital cost of a typical fossil-fuel electric power generating station is in the thermal conversion equipment.[citation needed]

Not really a contradiction, but the latter seems irrelevant. — Omegatron 00:46, 23 November 2006 (UTC)

Actually I think with some re-wording this is actually useful information. If the second sentance is correct, and I believe it is, then it would seem the capital costs of a fusion plant would be very different, and that seems to be worth mentioning. That said, I'm not sure this is the proper article to do it in! Maury 19:04, 23 November 2006 (UTC)

[edit] Odd question, but...

I realize this might not be the right place to ask this, but it seems to be getting everyone's eyeballs, so...

Why is Bussard pushing aneutronic fusion? And for that matter, why does it seem that everyone with a "non-conventional" design (of which there are only a few, admittedly) always push aneutronic devices? Don't get me wrong, there are major advantages here that are evident to all, but given the fact that we're nowhere near ready to commercialize any design, wouldn't it be prudent to test using D-T to start with? Any of the reactions mentioned here are much more difficult to get working, so it would seem to me that any machine capable of supporting aneutronic fusion should be able to generate much higher rates using D-T, at least for a short time (embrittlement, etc.)

Is there some feature of the alternative designs that precludes this? As far as I am aware the initial fusion experiments in both the fusor and the migma used D-T, so I don't see any problems there. I don't fully understand Bussard's new design, but it doesn't seem to have any major differences that would require higher mass ions or anything that obvious like that.

Is there some sort of economic or legal issue here? Or is it, as it appears to these untrained eyes, a way of avoiding having to demonstrate the machines actually work at a small scale before moving on to the full-sized devices?

Maury 19:01, 23 November 2006 (UTC)

I never understood that either. There is certainly no compelling technical reason. (Psychologically, I suppose once you start divorcing yourself from reality there is no reason not to go whole hog.) When I brought up the advantages of using D-T in a dense plasma focus, Eric Lerner reacted very allergic. --Art Carlson 08:42, 24 November 2006 (UTC)
Bussard's experiments are D-D fusion, and he talks about burning up conventional nuclear waste in the neutron flux from D-T fusors. He also talks about retrofitting conventional power plants by tying the steam lines to external boron-blanketed D-T fusors. I don't understand why everyone's so hard on him when they clearly haven't paid any attention to what he's actually doing.
He clearly states that his proposed demonstration prototype would cost $150M for D-D or $200M for p-B11 and that the Navy is more interested in p-B11 for electric boats. He definitely likes the idea of aneutronic fusion (as anyone would), but it doesn't sound like he's being irrational about it to me.
He also emphasizes that the resulting alpha particles could be neutralized by grids to generate DC directly instead of the inefficient heating things up with neutrons and boiling water. I don't know if that's possible with other reactions. — Omegatron 23:34, 24 November 2006 (UTC)

[edit] p+6Li fusion efficiency?

The second paragraph doesn't give a very convincing explanation why this reaction chain is impractical:

p + 6Li   → 4He (1.7 MeV) + 3He (2.3 MeV)
3He + 6Li → 2 4He + p + 16.9 MeV
3He + 3He → 4He + 2 p

All it says is that the non-thermal distribution of 3He provides an insufficient enhancement to the later stages. Is the cross-section of 3He+6Li too low? Does electromagnatic repulsion require too high a reaction temperature? Can someone elaborate or reword this section a bit? --Dgies 21:04, 4 December 2006 (UTC)

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