The problem with ion convergence

Discuss how polywell fusion works; share theoretical questions and answers.

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Art Carlson
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Post by Art Carlson »

Tom Ligon wrote:I hear you ... all we've seen from the earlier work is a wiff of fusion. I'm content, at the moment, to await peer-reviewed results to see if the scent is now stronger, and if the dogs know which way to track.
Be my guest. I got a bit riled, but I didn't need to. The money is spent and the data are coming no matter what we do, and we all are eager to see what it is. I particularly defer to you and Rick since you both have had a close look at the data and worked with the machines. You can still be dead wrong, but your instincts have more input to work with than mine do.
Tom Ligon wrote:The point has already been answered that a magrid charged to attract electrons will not attract the sort of ions we expect to form. I allow the possibility of negative ions, but doubt they're much of a factor in such a high-energy environment. Driving ions to the outer wall is certainly a possibility, although in that case I would expect reactions during the big discharges that terminated the WB6 runs, rather than immediately preceeding the discharge and while the well was deep. What reactions would you get in stainless steel at 10 keV? Would the energy of the neutrons be distinguishable from DD fusion? I've recommended methods other than electronic thermalized neutron counters be employed. Bicron 720 comes to mind (fast-neutron specific, and with some neutron energy resolution capability), with a backup of bubble dosimeters (require fast neutrons to make bubbles).
Sorry for the sign error. Of course I meant for my (positive) ion to be formed outside but near the magrid and accelerated to the wall. I was thinking of DD fusion with adsorbed deuterium, not any spallation reaction with the stainless steel. I believe the voltage will not be high enough to get much going beyond Z=1/Z=1 reactions. There can well be evidence that speaks against this mechanism, but it seems the data is lacking to conclusively rule it out. The actual source of the neutrons could be something completely different, but still not thermonuclear fusion. It's speculation either way.
Tom Ligon wrote:In my test runs, I deliberately tried to saturate the machines with deuterium, but the RGA said I was not having much success ... the gas that blows off in the bright glows remains mostly hydrogen, although you do start to see some HD peaks with continued use. But we've noticed the present EMC2 website photo shows a helium plasma ... I have to wonder if they're deliberately trying to avoid deuterium loading.
I know hydrogen is hard to get rid of, even if all you let in is deuterium. On the other hand, I don't know but that a few percent deuterium might be enough.
Tom Ligon wrote:I would add that the extensive runs of WB-4, essentially WB-6 with a bad geometry, should have made the same apparent high fusion results if the effect were ions going to the walls. The reports say it produced fusion, but at a rate about three orders of magnitude down from WB-6. The evidence for either is relatively thin, but it does suggest WB-6 was doing something unique and worth looking in to.
How do you measure 0.002 fusion neutrons per shot?
Tom Ligon wrote:I set up the counters to not trigger on electric arcs (I shielded the entire setup strongly and super-filtered the power lines). The result was a background count rate of something like 3 counts per minute. They would not respond to a 20 kV cap-discharge arc right beside the counter. I understand they've now taken this a step or two further. I do understand any concerns about the possibility of false counts due to this cause ... Farnsworth reportedly faked results for one early demonstration before Dr. Hirsch showed an easier way to build fusors that actually worked like a charm.
I'm sure I could not have done any better under the circumstances. Of course, there are many other tests you would like to do, like comparing pure hydrogen to pure deuterium, but when your fifth shot under the relevant conditions destroys the machine, that kind of puts a cramp on your experimental protocols.

Tom Ligon
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Post by Tom Ligon »

I'm not clear on where that 1000x better ratio came from between the reaction rates of WB4 and WB6. I will say WB4 was intended to run quasi-continuously, and was operated that way for a while. I was under the impression its better fusion results came from essentially the same capacitor bank as was used with WB6. It may be that the machine did not build gas levels to a Paschen discharge as fast because it could not achieve the electron density WB6 achieved. Maybe someday Rick can enlighten us.

If those results are based on spreading the fusion runs out to a second instead of a fraction of a millisecond, that would mean a few counts per second. If spread out over a minute, that would put the count rate into the background. I suspect what really happened was an occasional count or two in some of a large number of tests. I'm sure that was very disappointing, as Dr. Bussard would have been hoping for a comparatively long and vigorous burst.

The basic observation remains, WB4 evidently did not make the neutron bursts WB6 did, which suggests the WB6 results were not due to deuterons blasting the walls. To which you will reply there was not much data one way or another, and I would have to agree. Hopefully, it now exists, and, after a long and responsible look by some people with good credentials, we'll get to see it.

Thin as the WB6 results were, I have to believe they're being shown warts and all. If they were faked, they would be a lot better-looking.

D Tibbets
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Post by D Tibbets »

[quote="Art Carlson"]You guys are amazing. The theory of this machine is really weak, but the experimental data is non-existent. The only positive data you have is a number of neutrons that I can count on my fingers. A reactor will have to produce around 10^30 neutrons.


I can't resist. At the risk of exposing my ignorance I believe your number of 10^30 neutrons per second for a useful reacter is off by at least a facter of a billion.

Using the calculater from : http://www.beejewel.com.au/research/fus ... ulator.htm
a production of ~ 10^20 neutrons per second produces about 100,000,000 Watt/s of power. By that calculation a reacter that produced 10^30 neutrons per second would be producing about 1,000,000 trillion Watt/s of power.

Or, to illistrate the scale by using moles: a mole of duterium fusing/s would produce ~ 3 x 10^23 neutrons (one half of Avagadro's number). So, 10 ^30 neutrons per second would be consuming over 1,000,000 moles of duterium per second.Each mole of duterium weighs 2 grams so 10^ 30 neutrons /s would be equivalent to fusing over 2 kilograms of deuterium per second. Assuming a power output of ~ 1,000,000 times that of coal, an equivalent coal fired plant would be burning coal at a rate of 2,000,000 Kilograms per second. That plant would go through a trainload of coal (100 cars at 50 KT/car) every 2-3 seconds!

And a few DETECTED neutrons is relitive. Assuming the counts are real, The claimed production is actually close to 10^9 neutrons per second .

And finally, stating that 'the experimental data is non-existent', should be 'the experimental data is non-existent or unaviable'.
To error is human... and I'm very human.

Art Carlson
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Post by Art Carlson »

rnebel wrote:Let me see if I can summarize this. The basic claim is that the electric potentials will take on the shape of the magnetic field structure. This will give electrostatic potentials that are defocusing for the ions and they add angular momentum to the ions with each pass (i.e. we have an ion optics problem). Is that a fair characterization?
Yes.
rnebel wrote:If this is a problem, I’m suggesting the following mitigation strategies:
rnebel wrote:1. Look at higher order, more spherical systems like dodecahedrons which will move the aberrations to the edge. Regularity requires that aberrations go like r**m where m is related to the order of the polywell (it’s 3 for a truncated cube, and higher for other systems). This may not cure the problem, but it should help.
rnebel wrote:3. Introduce the ions you want to focus at a radius that’s a little inside the nonspherical region. Pellets are one possibility. This will require you to apply a higher potential to the coils to get the same ion energy, but it should improve the focusing.
The surfaces can be made be more nearly spherical by increasing the order of the polyhedron or by moving farther inside. The combination of these two measures would likely be even more effective than their simple sum. Both measures will also cost you elsewhere. Increasing the order of the polyhedron increases losses by increasing the length of the line cusps, and moving farther inside costs fusion volume and also hurts the power balance by forcing you to larger voltages. Even if you don't consider these additional costs, I don't see how these measures can help more than a factor of a few, where what you need is a few orders of magnitude.
rnebel wrote:2. Ion collisionality will mitigate some of the accumulation of angular momentum. Ions spend most of their time near their turning points and this is where they are the slowest and the most collisional. These collisions will take angular momentum out of the ions. This should help too
I may be missing something, but I would not expect that collisions would be able to narrow the spread in azimuthal velocity.
rnebel wrote:4. As I pointed out in another thread, the notion that flux surfaces will become equipotential surfaces is incorrect for inertial electrostatic confinement. That only happens if you allow the plasma to thermalize, which we don’t intend to do. These are driven systems and the finite electron inertia will allow you to impose potential gradients along field lines.
rnebel wrote:Now let’s suppose that mitigation factors 1-3 don’t sufficiently improve the focusing. How do you take advantage of number 4? The answer is probably in the electron optics. Although this hasn’t been explored in Polywells (at least to my knowledge) there is an analogous problem that crops up in gridded systems. Grid wires tend to add angular momentum to ions or electrons which also leads to defocusing. We had this problem when we were doing the POPS studies (see previous references). We were trying to make harmonic oscillator potentials and we kept getting potential wells with the electrons clustered near the edge. What we learned was that we could reduce the angular momentum and improve the focusing by using a two-grid system where the inner grid had a retarded potential compared to the outer grid. Ron Moses had studied this effect 10 years earlier (Ron did his thesis work on electron optics) and had demonstrated that a properly aligned two grid system with a retarded inner grid could produce stable electron orbits and vastly improve the effective grid transparency. I believe that the MIT people are using similar techniques for their ion-based IECs. While this technique was used to modify radial profiles, similar things could be used to reduce aberrations in the virtual cathode.
First, I am amayzed that you talk about non-thermal electrons as though they were an asset instead of a serious liability. Is there a detailed description somewhere of how that is supposed to work? It's about the same story with the idea of adding electrodes to fix the lumpy surfaces. Electrodes are generally part of the problem, not part of the solution. At any rate, I can't imagine any way to make that work. Until you sketch a solution, please permit me to remain highly skeptical that it can be done.

rnebel
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Post by rnebel »

Art:
2. The general rule of thumb on ion collisions is that ion collisions in the core add angular momentum to the ions (thermalization) while collisions in the edge remove angular momentum. The reasons edge collisions remove angular momentum is that as the ions reach their radial turning point, their angular velocity exceeds the radial velocity. Consequently, thermalization takes energy from the angular direction and puts it in the radial direction. The collision rate gets big because the velocities are small. The upshot of this is that if you want to look at the effect of collisions on ions, you have to do something like bounce-averaged Fokker-Planck where you take into account the collisions at all points in the ion orbit. There are two places this is discussed in the literature. The original work is:

M. ROSENBERG and N. A. KRALL, Phys. Fluids B, 4,1788 (1992)

There is also a 1993 paper by these authors (I don’t have good access to Journals here) but I think the correct one is the one above. Of course, the Chacon paper also looks at this.

4. The idea behind inertial electrostatic confinement is that you inject electrons with directed (radial) energy into the system. These electrons then form a virtual cathode by giving up their kinectic energy to potential energy in the virtual cathode (hence the importance of inertia). You don’t want thermal electrons. Eventually electrons will thermalize and slow down. When that happens they accumulate around coil cases resulting in screening and other things you don’t want. That’s why you need to either cycle electrons through the system, or find a way to add radial energy to them. This is fundamental.

As for the optics issues, we can change the optics with either magnetic or electrostatic fields. The electrostatic example was just to show you that you can modify the distribution functions with optics. Right now, we’re not at the point where studying that is a priority item with us. We’ll fix that one if and when it needs to be fixed.

Tom Ligon
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Post by Tom Ligon »

Art,

A few posts up, you say "deuterium always comes with a small fraction of tritium." Really? How small? We believe all the deuterium ever created was produced in the "big bang", and is 13 billion years old. It can't survive in stars, and even brown dwarfs can burn it. But tritium? About a 12.5 year half-life ... no original tritium still exists, so it would have to be recently made. What is the fraction of tritium in natural sources (the only data I have is trace/negligible)? It must be trivial, and would get more trivial by the minute.

I don't recall it ever showing up on the RGA, and I should have been able to detect at least 3, maybe 5 orders of magnitude down from the D2 levels.

I would have been delighted to have had some available ... I think we would have gotten some fusion out of WB3, which could make deep enough potential wells for seconds at a time to burn D-T. I think PXL-1 might have burned it as well. However, the paperwork required to handle it would have probably sunk us.

If that were a significant contributor to the fusion rate, the neutron would be distinctive, around 13 MeV if I recall correctly. It should make big whopping flashes in a scintillation material.

rnebel
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Post by rnebel »

Tom:

All deuterium contains traces of Tritium due to nuclear testing.

Art Carlson
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Post by Art Carlson »

D Tibbets wrote:I can't resist. At the risk of exposing my ignorance I believe your number of 10^30 neutrons per second for a useful reacter is off by at least a facter of a billion.
I didn't mean per second but in its lifetime. 30 years = a billion seconds, so the math works out. How relevant this comparison is, is debatable, but probably not very fruitful.

Art Carlson
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Post by Art Carlson »

Tom Ligon wrote:A few posts up, you say "deuterium always comes with a small fraction of tritium." Really? How small? We believe all the deuterium ever created was produced in the "big bang", and is 13 billion years old. It can't survive in stars, and even brown dwarfs can burn it. But tritium? About a 12.5 year half-life ... no original tritium still exists, so it would have to be recently made. What is the fraction of tritium in natural sources (the only data I have is trace/negligible)? It must be trivial, and would get more trivial by the minute.
Some is made naturally by cosmic rays and spontaneous fission, but Rick is probably right that most of it now is left over from atmospheric bomb tests. I have no idea how much this is. Possibly I'm mixing something up, maybe that experimental tokamaks are contaminated with tritium due to DD fusions. DT fusion (even at the 2 count per shot level) can probably be ignored in polywell experiments.

Art Carlson
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Post by Art Carlson »

rnebel wrote:Art:
2. The general rule of thumb on ion collisions is that ion collisions in the core add angular momentum to the ions (thermalization) while collisions in the edge remove angular momentum. The reasons edge collisions remove angular momentum is that as the ions reach their radial turning point, their angular velocity exceeds the radial velocity. Consequently, thermalization takes energy from the angular direction and puts it in the radial direction. The collision rate gets big because the velocities are small. The upshot of this is that if you want to look at the effect of collisions on ions, you have to do something like bounce-averaged Fokker-Planck where you take into account the collisions at all points in the ion orbit. There are two places this is discussed in the literature. ...
OK. I get the idea. I agree that you quickly reach the point where you really need to do kinetic calculations. I have an idea of how I can make an analytic estimate of the interaction of annealing with lumpy equipotentials, but maybe it is better to try to make a connection to the published calculations. What I expect is that the angular momentum added by the lumpy surfaces will be much larger than that added by collisions in the core, so that the azimuthal velocities at the edge are correspondingly higher, and annealing collisions much less likely. I can think of two quantitative questions to ask of the spherically symmetrical simulations that could throw light on this possibility. (1) What is the probability that any given ion on any given bounce undergoes a collision at the edge? (2) What is the self-consistent ion temperature at the edge? Do you know the answer to either of these questions?

Art Carlson
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Post by Art Carlson »

rnebel wrote:4. The idea behind inertial electrostatic confinement is that you inject electrons with directed (radial) energy into the system. These electrons then form a virtual cathode by giving up their kinectic energy to potential energy in the virtual cathode (hence the importance of inertia). You don’t want thermal electrons. Eventually electrons will thermalize and slow down. When that happens they accumulate around coil cases resulting in screening and other things you don’t want. That’s why you need to either cycle electrons through the system, or find a way to add radial energy to them. This is fundamental.
Obviously you don't want total thermodynamic equilibrium perpendicular to the magnetic field. You don't ever want that in magnetic confinement. I can see there are a number of places you don't want electrons to build up a thermal distribution parallel to the field. That doesn't apply to the high beta interior, does it? You have to give the electrons enough energy to climb into the magnetic bucket, but once they are there, there should be no particular problem if they thermalize.
Is "cycling electrons" a sophisticated form of poor electron confinement? How big is the current associated with this cycling? What is the associated power?

Tom Ligon
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Post by Tom Ligon »

Art,

I think the DT contribution must be negligible unless T is a lot higher than we think.

Let's guess that its in the PPM range. The DT cross section at the sorts of reaction conditions seen in WB6 would probably be something like 30-50x higher than DD. Obviously, T has a target painted on its back, but if their population is 1e6, or even 1e3, lower than D, the cross section can't make up for it.

And with counting efficiency down to one count for 13,000 fusions, the odds of catching one in the published data must be nil.

In a one-second burst, at 1e9 fusions per second, I might not be surprised at the occasional killer neut showing up in the data.

It would be wonderful news if the DD reaction bred enough T to matter, but so far I know you will agree that's a pipe dream in the WB machines. It would be a mark of success if it were true.

Detecting hot ions at mass 3, Q of 1 and 2, would make a nice optional method to detecting neutrons from DD, I would think. They should have an unambiguous signature to the right detector.

rnebel
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Post by rnebel »

OK. I get the idea. I agree that you quickly reach the point where you really need to do kinetic calculations. I have an idea of how I can make an analytic estimate of the interaction of annealing with lumpy equipotentials, but maybe it is better to try to make a connection to the published calculations. What I expect is that the angular momentum added by the lumpy surfaces will be much larger than that added by collisions in the core, so that the azimuthal velocities at the edge are correspondingly higher, and annealing collisions much less likely. I can think of two quantitative questions to ask of the spherically symmetrical simulations that could throw light on this possibility. (1) What is the probability that any given ion on any given bounce undergoes a collision at the edge? (2) What is the self-consistent ion temperature at the edge? Do you know the answer to either of these questions?

Art:
Go ahead and give it a try analytically, but there are some real pitfalls here. Let me give you one example. Suppose you start with a bunch of mono-energetic ions with no angular momentum. All of those ions will have the same turning point near the edge. At that turning point the ion density will be HUGE! So will the collision rate. Is that physical? Probably not. A little thermalization will spread out the density and dramatically drop the collision rate. How much spread is reasonable? I don’t know. This is the reason Luis Chacon did the full bounce averaged calculations. The scary thing about his results were that little changes (like changing to potential well from a square well to a harmonic oscillator) made big changes in the answers.
I don’t know the answer to either of your questions. I hadn’t seen the Polywell for 10 years before I got involved with EMC2 so I’m on a learning curve just like everybody else is. Luis might have a better idea about it, and you might want to contact him. If you want to do that, I can get you an e-mail address. He’s a very low key person, but he’s also very smart.

rnebel
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Post by rnebel »

[quote="Art Carlson"][quote="rnebel"]4. The idea behind inertial electrostatic confinement is that you inject electrons with directed (radial) energy into the system. These electrons then form a virtual cathode by giving up their kinectic energy to potential energy in the virtual cathode (hence the importance of inertia). You don’t want thermal electrons. Eventually electrons will thermalize and slow down. When that happens they accumulate around coil cases resulting in screening and other things you don’t want. That’s why you need to either cycle electrons through the system, or find a way to add radial energy to them. This is fundamental. [/quote]
Obviously you don't want total thermodynamic equilibrium perpendicular to the magnetic field. You don't ever want that in magnetic confinement. I can see there are a number of places you don't want electrons to build up a thermal distribution parallel to the field. That doesn't apply to the high beta interior, does it? You have to give the electrons enough energy to climb into the magnetic bucket, but once they are there, there should be no particular problem if they thermalize.
Is "cycling electrons" a sophisticated form of poor electron confinement? How big is the current associated with this cycling? What is the associated power?[/quote]

Art:
The electron collision time in the interior is long compared to the electron transit time so collisions for electrons is also a global process. One of the results of this is that if electrons are in l.t.e. at one radius in the interior, they won’t be in l.t.e. anywhere else in radius. The only solutions that have the property that they can maintain l.t.e. everywhere in the radius are the POPS solutions that Dan Barnes and I worked out. John Finn and I showed that these solutions are unique in that property. They only work in a harmonic oscillator potential, which we won’t have for electrons.

Thus, the approximation that we usually use in magnetic confinement of local thermalization with global gradients doesn’t work here. Calculations for the interior are generally done with either 1-D PIC (1-D profiles with finite angular momentum) or a 1-D (2-D velocity space) Vlasov-Poisson equilibrium solver. Bussard’s people did a lot of studies with the 1-D Vlasov-Poisson solvers in the early to mid 90s. I don’t think that work is published, but I know that a lot of the internal EMC2 reports were released and are available on the web. Loren Jameson did most of this work. They used these models to do all of their reactor extrapolations.
Right now the electron confinement times are shorter than the electron collision times so electron thermalization shouldn’t be a huge issue. As we extrapolate to reactors and confinement improves, these times become more comparable and down-scattered electrons accumulating near the grid may become more of an issue.
As for the power associated with this, it’s just VI (applied voltage times current at the coil casings). For reactor extrapolations these numbers generally come out to about 10 MW. Currents are in the 100 Amp range.

rnebel
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Post by rnebel »

Art:

I just happened to stumble across the Dolan/Bussard/Krall exchange on defocusing. Dolan's original comments appear in the August 1993 edition of Fusion Technology. Bussard and Krall's response is in the March 1994 edition of Fusion Technology. The discussion should look familiar.

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