# Talk:Inertial electrostatic confinement

The refs of course trace back to you, then from there to Todd Ritter. I am curious about what was wrong, the problem as a whole, or the explaination of why it happened? Or has something happened to fundamentally change his conclusions?

Maury 5 July 2005 21:42 (UTC)

The text I reverted is this:

Even if the materials needed were to become available, there is a more fundamental problem that appears to make the IEC approach impossible. Unlike "mainstream" systems like the Tokamak, the fuel in an IEC system is not at thermal equilibrum. The hot fuel in the center of the reaction chamber is always cooling through radiation losses, while hotter ions are injected after being accelerated by the grids (or separate accelerators).
As these high-velocity ions collide with their counterparts in the reaction area, they loose energy through bremsstrahlung. Due to the large differences in velocities (temperatures) this process is maximized in any non-equilibrum system like IEC. Current calculations suggest that radition losses will greater than the enegy added to the fuel at temperatures near the fusion triple point, and that achievable reaction rates are far below those needed for net energy production.

My objections are

1. Although IEC is usually envisioned to be non-equilibrium, and must be so if certain potential advantages are to be realized, I don't think this is an essential characteristic.
2. If a non-equilibrium distribution is contemplated, it is not a two-temperature distribution, but a mono-energetic distribution.
3. Bremsstrahlung occurs in every plasma, not just for hot ions in a cold abckground.
4. I don't know what the bit about maximized bremsstrahlung losses is supposed to mean.
5. "fusion triple point" seems to be a misuse of the "triple product" that plays a role in the Lawson criterion.

That seemed like enough reasons for a revert. Rider made two points, one that the bremsstrahlung losses for advanced fuels (which are often but not necessarily connected with IEC) are too large for a reasonable energy balance. This is covered under Nuclear_fusion#Bremsstrahlung_losses. The other point (his really creative contribution) is that a non-Maxwellian distribution requires infeasibly large recirculating power. This point is covered, albeit briefly, in Farnsworth-Hirsch_Fusor#Thermalization_of_the_ion_velocities (and is mangled in the articles on Fusion rocket and Cold fusion). We could discuss, if you like, whether other places are more appropriate for this information, or whether it should be expanded or duplicated. Art Carlson 2005 July 6 07:16 (UTC)

## Pressure confinement

Ok, back to you now...

1) I am unaware of any IEC system in which the fuel is not being continually showered into the interior. I suppose if one could create a system with a high enough containment time it might be possible, but I can't even see people suggesting this. Are you being overly piquane here, or do you really feel that a long-containment system is a real possibility, and that in such a system Ritter's concerns will not hold?

The point of the calculations by Rider (and others) is that it is impossible to maintain a useful degree of dis-equilibrium. If the containment time is so short that the ion energy distribution is non-Maxwellian, then the configuration is totally uninteresting for energy production. Art Carlson 2005 July 7 07:05 (UTC)
Why are they uninteresting? Keep in mind that these articles are for laymen as well as fusion scientists, so we should not be afraid to mention things that are useless, untrue but commonly believed, or uninteresting, and then explain why they are useless, untrue, or uninteresting. - Omegatron July 7, 2005 13:45 (UTC)
Agreed. In this case the concept dies already at the most basic level: Even assuming it works perfectly, it can't confine enough pressure. I have only cheated a little by not defining "pressure" and "temperature" precisely. I would prefer to keep the pure physics in IEC and relegate specifics including misconceptions to fusor. Art Carlson 2005 July 7 14:31 (UTC)

2) I am not sure what you mean here. Under the fusor the new ions arriving via acceleration are at a higher energy than the average within the containment area. Fusion products are likewise. As I understand it, generally there is a lot of fairly cool fuel and a small number of much higher temperature fuel. Is this not the case?

If only fresh ions are energetic, and most of the ions hanging around are cold, then you won't have much fusion. This is essentially a beam-target configuration, and it can be shown that the cross section for slowing down is much greater than the cross section for fusion. A configuration that works like that is not relevant for energy production. Art Carlson 2005 July 7 07:05 (UTC)

3) If (2) is correct the acceleration seen by the typical high-speed particle will be much geater on average. Under an equilibrium system the average particle will generally interact with one of roughly the same energy (given a distribution, of course). Under a non-equilibrium system it will generally interact with one that is much cooler.

Actually we're talking about the wrong thing here. The ions do not lose (much) energy to bremsstrahlung. They equilibrate with the electrons through collisions, and then the electrons lose the energy through bremsstrahlung. Art Carlson 2005 July 7 07:05 (UTC)

4) See (3).

5) Yes

If I have scrambled the two (bremsstrahlung vs recirculation), then considering that the second of his points is still valid for all known IEC approaches, shouldn't that be placed in this article? Even a short note, pointing back to the link you provided would seem appropriate.

Both points are mentioned in the Fusor article. I'm not entirely happy with having two separate articles, considering that the fusor is practically the only IEC system anybody ever talks about. I think the rationale for putting the recirculation info over there is that, as I argue, a non-equilibrium distribution is not possible to achieve with IEC, but IEC with an equilibrium distribution is possible. It's only the fusor folks that need to have their heads straightened out. The bremsstrahlung argument has nothing to do directly with IEC or fusors but with advanced fuels, so it belongs (primarily) under nuclear fusion and/or aneutronic fusion. Art Carlson 2005 July 7 07:05 (UTC)

As to the other articles, I'm all for removing the content from it entirely. It certainly has nothing to do with fusion rockets, and I can't imagine why anyone would care to read about it in a cold fusion article. In fact, I think I'll go edit them now.

I cleaned up a bit, too. Art Carlson 2005 July 7 07:05 (UTC)

Maury 6 July 2005 12:00 (UTC)

## Actually...

The mention at the end of cold fusion may be out of place, I suppose, but it doesn't seem to read that way. I don't see the mention in fusion rocket any more.

Maury 6 July 2005 12:47 (UTC)

## Maximum practical electric field

I'm still worried about the realistic limit on the electric field strength at the surface of the electrodes. In the article I assumed the 230 MV/m needed to compare with a tokamak was out of the question and that 1 MV/m was already "generous". But several sources (e.g. [1]) mention a field of 25 GV/m on the tungsten electrode in pyroelectric fusion. Am I being to hard on IEC? On the other hand, we always tried to avoid voltages above 100 V when using Langmuir probes because otherwise we would get arcs. 100 V/mm is only 0.1 MV/m. Art Carlson 12:42, 2005 July 22 (UTC)

What is your source for this calculation? Is this your own work? btw: "If we assume very generously that, say, 1 MV/m could be maintained at the surface of an electrode in a fusion environment". Doesn't this miss the point? Earnshaw's Theorem states that there can be no minimum in the potential provided by the electrodes alone, the point is that the electric field is caused by the virtual electrode space charge region set up. Remember, Div B=0 and Div E=0 in both vacuum cases. What matters are the dynamic effects (or tokamaks wouldn't confine either!).Rpf 11:26, 18 April 2006 (UTC)
Well you certainly shouldn't be putting your own calculations into articles... Taking facts from "Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium" should be sufficient, shouldn't it? If I understand correctly, it's a "conclusive proof" that IEC will never work. — Omegatron 11:59, 18 April 2006 (UTC)
It's a little POV saying "IEC will never work" without mentioning cash spent by the D.o.E in recent years researching it as well as pretty reputable places like Los Alimos and Wisconsin working quite hard on it.Rpf 14:09, 18 April 2006 (UTC)
Then again, Earnshaw's theorem conclusively proved that levitation by magnets was impossible, and we levitate things all the time by violating the assumptions of his theorem...  :-) — Omegatron 12:00, 18 April 2006 (UTC)
My point exactly :) I can buy a toy for 10 bucks that does it. Anyway, not a good idea to be dismissive of an entire field of peer reviewed and published work.Rpf 14:09, 18 April 2006 (UTC)
Hey, I want IEC to work as much as the next guy. But I'm not going to let my desires get in the way of rational thought like the free energy or antigravity crowd.
I'm just an engineer, and my understanding of fusion is limited, but I've flipped through Rider's very long paper, and it seems to cover all the variations quite thoroughly. (And apparently isn't available online anymore. How lame.) If something definitely can't work, and we accept that it can't work, we can redirect our effort to something that will.
Anyway, these articles should only contain information from those peer-reviewed papers, both from the Rider "IEC can never work" papers and the DoE and Bussard's research that says it can. It shouldn't contain calculations or speculations by wikipedians, no matter how qualified, as per Wikipedia:No original research. — Omegatron 14:54, 18 April 2006 (UTC)
Agreed on the speculation. Rational thought? Remember reputable *plasma physicists* other than Todd Rider work in this field. Flip through *their* papers before comparing it to antigravity...you can buy some pretty neat neutron sources which operate on this principle and yes they do work Rpf 15:55, 18 April 2006 (UTC)
He never says that you can't make neutron sources out of them; you obviously can. He says that using it for power production would require "recirculating a prohibitive amount of power compared to the fusion power produced". I'm not really sure what that means, but it's apparently Bad. — Omegatron 05:42, 23 November 2006 (UTC)

## On recirculating power

80% of the fusion energy produced in a DT cycle comes out in the form of energetic (14 MeV) neutrons. Fusion power reactors stop these neutrons in a "blanket" where they both heat the blanket and are used to breed tritium (through the reaction n + Li6 -> T + alpha). Breeding tritium is necessary to close the fuel cycle because there are no other sources of tritium available to fuel your DT fusion power reactor. The thermal energy deposited in the blanket is converted to electrical energy through a conventional thermal cycle, which can be expected to have an efficiency of about 35%. It is possible in principle to "directly convert" the remaining 20% of fusion power (which emerges as 3.5 MeV alpha particles). While this technology has yet to be developed, initial exploration suggest that a conversion efficiency as high as 90% may be possible. We will also assume that any recirculated power can be converted back to electrical power through a thermal cycle at a 35% efficiency. With these assumptions you reach break-even (that is, your "power plant" produces exactly as much electrical power as it requires to maintain operation) at a fusion gain -- that is, (fusion power produced)/(recirculated power) -- of 1.41. Of course, the goal of a fusion power plant is to produce excess power which can be sold to pay for the whole enterprise. People will only willingly purchase fusion power if it can be priced competitively with alternate source of electrical power. Electrical generating equipment is expensive (this is the bulk of the capital cost for coal and gas-fired plants, while it is about 1/2 of the capital cost for nuclear plants). A competitive fusion power plant has to be able to sell most of the electrical power which it produces. At a fusion gain of 10 (and the assumptions about power conversion presented above) about 80% of the electrical power generated will be available for sale, while the remaining 20% must be recirculated in order to keep the fusion power plant operating. Nevins [W.M. Nevins, Phys. Plasmas <2> (10), 3804 (October, 1995)] showed that the IEC systems described by Bussard and others cannot achieve a fusion gain greater than 0.1 [disclaimer: I am the Nevins in question]. One concludes that IEC systems cannot form the basis for a commerial electrical power plant. I would further point out that this conclusion is not controversial within the DoE-funded fusion community. Wmnevins 19:26, 5 June 2007 (UTC)

## Merge

Not sure whether Bussard's devices should go here or in Fusor, though they might get merged anyway. Bussard says a lot, and he says it fast. I'm just an engineer, so I don't know what a lot of these terms mean, but here's my summary of notes from watching the Google lecture. We should cover a lot of this stuff:

Omegatron 09:38, 25 November 2006 (UTC)

Please contribute this to the article Polywell. I wrote a framework for it, but it's missing a lot of specifics that you've gathered.
Polywell should not be merged with Fusor; they're both inertial electrostatic confinement, but have very different engineering challenges. I also disagree that the two should be merged into IEC; I'll be damned if decade-long fusion projects with multimillion dollar research budgets and potential for scale-up don't deserve their own articles. It'd be a travesty to crush them together, being forced to omit large amounts of information from each due to space constraints. As time goes on, there will only be more IEC methods, so the problem will just get worse. Leave them separate. -- Rei 22:33, 28 November 2006 (UTC)
Do you believe that every reseach group has a completely seperate article on their version of IEC? Don't you think somebody new to the field would find it easier looking under IEC for all the different incarnations? Please keep in mind the size of the IEC community compared with other fusion communities. If fusor is kept seperate from IEC, then I guess polywell could too, but I believe quite strongly that they are all lumped under IEC. Come on, these things all give the same fusion per unit current. He may have gotten millions of bucks over the years, but can he say it would perform better than any other IEC incarnation for a given power? -- Rpf 00:28, 29 November 2006 (UTC)
Please keep in mind the size of the IEC community compared with other fusion communities. -- that doesn't change the fact that these are projects with budgets of tens of millions of dollars, decades of history, and radically different approaches to the problem.
Come on, these things all give the same fusion per unit current. He may have gotten millions of bucks over the years, but can he say it would perform better than any other IEC incarnation for a given power? Actually, he specifically did say that -- he reported 100,000 times higher neutron output for the same well depth and driving conditions as Farnsworth, and unlike the standard fusor, there are no known scaling issues with Polywell (for example, fusors have problems with inner grid overheating when they scale up). -- Rei 19:20, 29 November 2006 (UTC)
As said elsewhere, his numbers conflict with other numbers I've heard. Others seem to get comparable rates, so it's no "world record".
I agree with the non-merge, so I'll take down the tags, but this article should become a summary and general article, with links to the specific incarnations. Any content specific to a certain device should be moved to that device's article.
I'll move my summary of notes to Talk:Polywell, which I didn't know existed at the time. — Omegatron 20:32, 29 November 2006 (UTC)
I agree; specific info should be moved out of this article. As for the fusion rate, what were the well depth and driving conditions used to create the other numbers that you saw? Bussard made a very specific statement: about 100,000 times the rate of Farnsworth at the same well depth and driving conditions. Of course if someone builds a bigger device and/or puts more current into it, they'll get a higher fusion rate. That doesn't mean that the larger device is scalable. -- Rei 22:50, 29 November 2006 (UTC)

## Maximum Pressure Calculations

Have these been peer reviewed? I see no references, and this concerns me. I am not qualified to offer a rebuttal, but it seems to be assuming a relatively simplified situation, ignoring the fact that most fusion in IEC devices occurs in microchannels of low field strength (i.e., in between the wires)[[2]]. This seems completely against the assumptions of this section.

Can someone please comment on this? -- Rei 17:13, 30 November 2006 (UTC)

Scrolling up, I see that this was original work by User:Art Carlson. Seing as it's already been contested, in addition to the issues that I just noted, I'm going to move it to the talk page. Once we can get some peer review on it, I'd be willing to move it back. Please don't take this personally, Art -- I just am uncomfortable with non-peer-reviewed information being presented as scientific fact. "Person X claims..." statements are fine, but "This is the case..." statements in a scientific article which have not undergone scrutiny is pushing it. You basically wrote a whole non-reviewed paper and put it in the article. Given that you don't even know what sort of charge potentials are used... -- Rei 17:18, 30 November 2006 (UTC)
This hardly counts as a paper; it's more of a back-of-the-envelope calculation. We could cite Template:Hide in printTemplate:Only in print, which is a more complicated treatment that arrives at similar conclusions. - mako 07:34, 1 December 2006 (UTC)
I'm trying not to take it personally, but you are making so many changes that I find questionable that I fear it might take a lot of work to undo the damage. It's likely the article will come out better in the end, but it makes it hard to juggle my priorities between Wikipedia and my daytime job. Where do we stand:
• References: It would undoubtably be better if we could refer to peer-reviewed publications. I don't have any, but mak has made a first suggestion. IEC, though no one is calling it pseudoscience, is such a small field that not every topic we need to mention has been specifically published. Furthermore, most papers will be written by those with a high emotional and financial stake in the field; an objective observer who looks at the concept and decides, possibly with excellent reasons, that it is not promising, will not necessarily be motivated to publish his considerations. So, let's try to get references, but don't expect them to be perfect.
• Nature of the calculations: Are the calculations I had put in the article original research or "back-of-the-envelope"? I admit they are closer to original research than I would like, but looking through them, every step is explained and is based on uncontroversial physics. I think what I wrote is verifiable on that basis and is generally useful for the reader. mak seems to agree. Where exactly do you think I step over the line? Can we have a fourth opinion?
• Improvements: There are a few arguably POV words in there: "very generously", "unthinkable". I could formulate the math in 3-d, if you would like to have it more general, but it would probably be harder for non-scientists to follow without providing any new insights. The selection of a "feasible" field at the electrodes is very shaky.
• Non-neutrality (of the plasma, not the POV): You seem to think that IEC devices necessarily use pure ion plasmas. I have seen nothing that would suggest this is the case. Can you back that up? The bremsstrahlung calculations of Rider at least rule out IEC reactors with a substantial electron component. Why shouldn't we report that? And my calculation, which is just a fancier form of Gauss's Law, does not make any assumption about the electrons one way or the other, neither concerning their density (zero or not) nor concerning their geometry (microchannels or not). If there has been a misunderstanding, then that is a good reason to try to make the section clearer, not to eliminate it.
--Art Carlson 09:02, 1 December 2006 (UTC)
I have reason to believe that your "back of the envelope" calculations do not describe what's going on. You don't even know what sort of electric potentials are used, for one. When you're talking about meters of vaccuum for a full sized fusor, that is a *lot* of dielectric to break down. Also, your calculations do nothing to suggest the formation of microchannels, which is where the plurality of the high energy ions exist (something I've been providing references for). This is why IEC devices often operate in what is described as "star mode", in which there are numerous rays that penetrate the core. An ion in a microchannel has a very low chance of leaving that channel without a collision, making its odds for fusing notably greater. Your calculations are giving a single density figure, but we know for a fact that IEC devices have varying density dependent on where you are in the core. Most of the core has less density than in your calculations, but the microchannels have notably more density. Not only that, but how long an ion remains confined is of utmost importance in determining how much fusion will occur (and thus whether it has hope of scaling to operating as a power plant), whether you're talking about the migration of ions toward the walls of a tokamak or how readily ions enter an IEC microchannel and leave one. You don't discuss this at all.
In short, your calculations seem greatly oversimplified from everything else that I've seen, which is why I'm very wary of seing them in here without peer review on them. Even if they didn't, it would be completely improper to have this here without peer review. I hope you can understand my and Omegatron's concerns on this.
Rider's paper is only on quasineutral plasmas. I don't see how anyone can describe this as a quasineutral plasma. Sure, there will be *some* electrons. The system will never be perfect; you can't get an ideal fusor. But by it's fundamental nature, it is *not* quasineutral. If it were quasineutral, there would be no electrostatic confinement. Trying to shoehorn a non-neutral plasma into calculations done on quasineutral plasmas seems to be junk science. Rider's calculations assume an amount of electrons to similar to the charge of the ions. In IEC, we're fundamentally guaranteed that this is not the case. -- Rei 16:32, 1 December 2006 (UTC)
Update: as per talk on the Fusor page, apparently Rider has another paper, and this one is applicable to IEC fusion: A general critique of inertial-electrostatic confinement fusion systems. I won't contest, by any stretch of the imagination, the addition of this paper. It seems perfectly applicable. -- Rei 16:59, 1 December 2006 (UTC)
I thought that was The Rider paper that everyone refers to. Should have been more clear... — Omegatron 21:57, 1 December 2006 (UTC)

References: It would undoubtably be better if we could refer to peer-reviewed publications.

No. It's necessary to refer to external publications (though not necessarily peer-reviewed), especially if disputed.
This is what No original research is all about. If it's not published elsewhere, we aren't publishing it, either, regardless of whether it's true or not. The threshold is verifiability, not truth.
There is a sort of "undocumented exception" for things that can easily be seen to be true, or trivial derivations from well-known facts, but these calculations aren't trivial, as demonstrated by this discussion. As soon as something's disputed, the exception no longer applies, and references are required.
I'm sure there are papers on the subject that could be cited, especially if this is as common knowledge as you claim. I'm surprised you can't cite Rider's paper on these subjects. Doesn't he cover all of this stuff?
By the way, there's nothing personal here at all. You are orders of magnitude more qualified to talk about nuclear fusion than me, but our policies exist for a reason. (Besides, Hirsch and Bussard are also drastically more qualified than me, and they've worked on this concept for years. What's a layman to do?)
Also, I think it would be acceptable for you to publish this elsewhere and let someone else reference it in this article, saying "Art Carlson says..." — Omegatron 16:11, 1 December 2006 (UTC)
I suspect that this calculation is too trivial to publish it anywhere (except perhaps embedded in a larger work). You apparently think it's not trivial, but there is a chance that says more about you or my expository skills than about the calculation itself. As near as I can figure out, your biggest reason to object to the calculation (or to be "wary" of it) is that you don't see how it accounts for complex geometry. Would you be satisfied if I can present a 3-d version of the derivation? --Art Carlson 21:05, 1 December 2006 (UTC)

The rule is no original research. When I said "trivial derivations from well-known facts", I was talking about something that is against the rules, but often overlooked and not removed by other editors because of its triviality. As soon as there's a dispute or it's removed by other editors, that obviously no longer applies, and you need to cite references.

I can put "2+2=4" in an article without a reference, and it will probably survive forever. But as soon as someone says it equals 5, it's disputed and I need to add a reference. That's just the nature of the project.

My lack of knowledge or qualification about the subject (which I freely admit) is irrelevant.

And when I say "publish elsewhere", I mean anywhere. Not necessarily a peer-reviewed paper.

This policy does not prohibit editors with specialist knowledge from adding their knowledge to Wikipedia, but it does prohibit them from drawing on their personal knowledge without citing their sources. If an editor has published the results of his or her research in a reliable publication, then s/he may cite that source while writing in the third person and complying with our NPOV policy.

But really, this isn't covered, even in passing, in any peer-reviewed papers?? I'm sure that it is.

Sorry if you're frustrated with us uneducated folk who can't understand your "trivial" derivation (I know basic electromagnetics and vector calc and it's non-trivial to me), but this sort of expert-layman dispute comes up a lot here, and our policies are the tiebreaker, for better or worse. See Wikipedia:Expert retention and Wikipedia:Expert editors, for instance. (I think I added you to the "Users who are content" list a few months ago based on something you had in your user page? I hope that's still accurate, but feel free to put yourself in a different group.) — Omegatron 21:57, 1 December 2006 (UTC)

Moved from article:

### Maximum pressure achievable

{{Unreferenced}} {{Original research}} Although portable neutron sources based on the IEC concept are commercially available, most experts are skeptical that the IEC concept can ever be used for power production. Most discussions of IEC consider the behavior of a small number of ions in potential structures imposed by electrodes. A potential well for ions, however, is a potential hill for electrons, so it is not possible to contain a neutral plasma with any set of electrodes. There must be at least some regions where the charge density of one species or the other dominates. As the density in these regions is raised, at some point the net charge density will destroy the potential well.

In pure IEC, the pressure gradient will be balanced by the electric force on the net charge density. In one dimension this is

${\displaystyle -p'+\rho E=0\,}$,

where p is plasma pressure and ρ is charge density. Gauss's law relates ρ to E as

${\displaystyle \epsilon _{0}E'=\rho \,}$.

Together these give

${\displaystyle -p'+\epsilon _{0}E'E=0\,}$ or ${\displaystyle (p-p_{0})=(1/2)\epsilon _{0}E^{2}\,}$,

where p0 is a constant of integration, equal to zero if the electric field vanishes when the density does (which minimizes the electric fields and potential drops for a given density).[1] Note the similarity to the concept of magnetic pressure, B²/2μ0, from magnetic confinement fusion. This arises from the symmetry of the Maxwell stress tensor with respect to E and B, with the change of sign being due to the fact that the gradients are parallel to E but perpendicular to B. For comparison, a D-T tokamak reactor would operate at about n = 1020 m−3 and T = 10 keV, which gives an ion pressure of p = (3/2)nkT = 0.24 MPa. Reaching the same pressure in an IEC reactor would require an electric field at the electrode of

${\displaystyle E=(2p/\epsilon _{0})^{1/2}=230\,\mathrm {MV/m} }$

If we assume very generously that, say, 1 MV/m could be maintained at the surface of an electrode in a fusion environment, then an IEC reactor would be a factor of 230² worse than a tokamak in terms of both power density and Lawson criterion.

To find the spatial dependence of the pressure outside the electrode we need to relate the pressure to the charge density. The simplest case is to take a single species (ions or electrons) at a uniform temperature, ρ = nq = pq/kT, and to take p0 = 0. The result is p(x) ≈ x−2.

Aside from the achievable electric field strength another factor limiting the density in an IEC device will be the fact that the ions must pass through holes in the electrode, and these holes must be smaller than the Debye length. Otherwise, the potential of the electrode will be dropped in the Debye sheath around the hole and will not be available to confine the ions. If the scale of the holes is δ, then we have

${\displaystyle \delta \leq \lambda _{D}={\sqrt {\frac {\epsilon _{0}kT}{nq^{2}}}}}$.
${\displaystyle p=nkT\leq \epsilon _{0}(kT/q)^{2}/\delta ^{2}}$.

The result has the same form as the previous result, but with the electric field at the electrode replaced by (kT/q)/δ. To achieve 1 MV/m with T = 100 keV would require δ no larger than 10 cm. To achieve confinement comparable to a tokamak would require a value 230 times smaller, namely 0.4 mm. Survival of a material grid in contact with a fusion plasma would be a tremendous problem anyway but is unthinkable if it must be structured on a sub-millimeter scale.

### Notes

1. L.P. Block, "Potential Double Layers in the Ionosphere", Cosmic Electrodynamics 3, 349 (1972)

### Rostoker vs. Rider

I have reverted a recent edit which removed a statement of Rider's argument and replaced it with a blanket dismissal based on a paper by Rostoker. As far as I can tell, Rostoker is not criticizing the "escape over the top of the electrostatic well" argument, but the "recirculating power with a non-Maxwellian distribution" argument. (Rider was all over the block.) The first is relevant to IEC, the second to Rostoker's CBFR, so this criticism is invalid here. --Art Carlson 09:03, 7 March 2007 (UTC)

Nice catch Art! Maury 13:12, 7 March 2007 (UTC)

I have reverted these edits. They seem to apply, like the other edit mentioned in this section, to the CBFR, not to any form of IEC. If you disagree, please explain why here. --Art Carlson (talk) 09:45, 11 January 2008 (UTC)

The CBFR utilizes a positive charge on the plasma to electrostatically confine electrons.
From the design: "Confinement of the energy of electrons... the plasma has a positive charge, so that electrons are electrostatically confined."
Also, the linked discussion specifically cites the Rider thesis "A general critique of inertial-electrostatic confinement fusion systems," and Nevins contributes as well, and the link discusses non-thermal schemes generally. 76.16.44.246 (talk) 23:05, 1 March 2008 (UTC)
There is a big difference between confining the electrons by some means and using their charge to confine the ions (the IEC approach) and confining the ions by some means and using their charge to confine the electrons (CBFR). It is true that Rostoker refers to "electrostatically confined" electrons, but he never calls his scheme IEC, and I have never seen anyone in the peer-reviewed literature call it that, either. Neither in the reference you propose nor in the original article in Science does Rostoker specifically discuss Rider's critique. It is also good to remember that Rider made a lot of arguments, so it would be important to verify that any argument being contended is the one under discussion in the Wikipedia article. Finally, as a question of form, Wiki articles try to avoid back-and-forth criticisms of criticisms. For all of these reasons, I find you edit out of place. --Art Carlson (talk) 10:26, 2 March 2008 (UTC)
OK, fair points. How about we change the wording in the edit to "nonthermal" rather than IEC? I think we can agree that much of the objections to IEC and CBFR are similar in that respect 76.16.44.246 (talk) 18:02, 2 March 2008 (UTC)

## External link not to free content

The external link in the critique section is not to free content. Is this OK?

"According to Todd Rider in A general critique of inertial-electrostatic confinement fusion systems, net energy production is not viab" 125.238.50.90 22:13, 23 May 2007 (UTC)

Why wouldn't that be ok? — Omegatron 14:08, 24 May 2007 (UTC)

## Fuel?

"... a small amount of fusion fuel is introduced" -- Could we please link-to or otherwise define what fuel is used in this, as this is an important characteristic of fusion systems. (vs. fission, for example). See for example Nuclear fuel. Thanks. -- 201.19.15.178 15:01, 2 September 2007 (UTC)

Actually, it's hard to say what fuel would be used, though I agree elucidation would be helpful. Perhaps a link to http://en.wikipedia.org/wiki/Nuclear_fuel#Fusion_fuels.76.16.44.246 (talk) 23:41, 1 March 2008 (UTC)

## handling Todd Rider reference

Currently, Rider's work is cited inline in the first sentence of the Critique section:

According to Todd Rider in A general critique of inertial-electrostatic confinement fusion systems, net energy production ...

Todd Rider's 1994 Masters Thesis: A General Critique of Inertial-Electrostatic Confinement Fusion Systems

The second instance is more useful because it is a PDF file, but it lacks the full bibliographical information. I would be inclined to remove the External link, and change the mention in Critique from an external link to a normal reference, including bibliographical info and a link to the PDF. Other suggestions?

On a related note, in the first line of the second paragraph of the Critique section, there is a reference to Nevin in non-standard format.

This is a plea to somebody else to do the work. Even if that doesn't happen, I thought it a good idea to make a note of the potential improvement here for later reference.

--Art Carlson (talk) 09:17, 4 February 2009 (UTC)

Is it just me or is the name "Todd Rider" being thrown around a lot in Wikipedia articles concerning Fusion (and especially related to Bussards work)? I have no expert knowledge on the history of fusion research, but a quick Google on Todd Rider doesn't seem to indicate that this is an especially notable scientist (which is not meant as criticism at all). And if that is the case then in my opinion his name shouldn't be dropped in wiki-articles as carelessly as seems to be the case. If that was justifiable then the guy should probably have a wiki-article about himself, no? And anyway, in the "Critique" section there is a lot of namedropping, with surnames like Nevin, Rostoker, Monkhorst, etc introduced without further ado. That doesn't look elegant, and it gives the impression that these are names which should be familiar to the reader (which wouldn't be the case if you're just starting to learn about the concept of IEC). Hence, in my opinion these names should be relegated to the "References" section as far as possible, and less "personal" language used in refering to these critiques.
--Lars —Preceding unsigned comment added by 193.157.137.241 (talk) 20:33, 4 February 2010 (UTC)
Rider himself is not particularly notable. (I believe he is no longer working on fusion.) But his peer-reviewed work on this topic is unique and often cited - even outside Wikipedia. (In my expert opinion, his work is also excellent, but my opinion doesn't matter here.) This topic is not fringe, but it is not directly mainstream either, so there aren't that many players. I think a non-personalized formulation ("some say", "most think") would be wishy-washy and misleading. The section needs some clean-up, but I would leave the names in, making sure that there is always a reference to the article where their opinion has been published. --Art Carlson (talk) 08:44, 5 February 2010 (UTC)