The problem with ion convergence

[Solo]

I got ahold of an interesting paper by Nevins on ion thermalisation and Q in IEC machines. He discusses the BFR to some extent.

Nevins, W. M. "Can Inertial Electrostatic Confinement Work Beyond the Ion-Ion Collisional Time Scale?" 1995

I'm still trying to understand it, but he seems to say at one point that the power balance is more favorable for an IEC device that does not expend any energy trying to maintain a non-LTE ion population; ie, temperature is Maxwellian and velocity distrib. is isotropic. I'm not sure what assumptions he's making, though. Looks like a square (spherical) potential well. He comes to the same conclusion as Art does about maintaing convergence in a polywell, saying that the lumpy well shape is much worse than collisions about enhancing the angular momentum, and that ege collisions won't dampen this sufficiently.

It was shown in section 3 that the fusion rate coefficient for a nearly mono-energetic ion distribution peaks at a value not substantially greater than the peak in fusion rate coefficient for Maxwellian plasmas. Given the relatively small penalty in fusion power for allowing the ion energy distribution to thermalize, one is lead to consider an operating mode in which the ion distribution is allowed to relax to Maxwellian while the ions are removed a a rate sufficient to maintain the ion anistropy and a strong ion convergence ratio.
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A potential well depth of [3/2 the ion temperature] will be required to confine the ions, which have a mean longitudinal energy of [1/2 the ion temperature]. We can imagine pumping these ions using charge-exchange on a neutral beam with an energy of [1/2 ion temperature]....

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...the upper limit on Q due to ion pumping goes to Q<=infinity if we continue to assume that a potential well can be formed at little cost in power while abandoning the IEC concept and letting a/r_0 ->1.

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However, we always find that an optimal IEC reactor power balance occurs at the lowest allowed ion convergence ratio, a/r_0, and that the power required to maintain the ion distribution function that retains the defining characteristic of an IEC system (a/r_0~=10) is at least an order of magnitude greater than the fusion power ....

I'm sorry that I could't transcribe the equations, the pdf file won't let me copy the text for some reason and I don't feel like typing it all out.

[MSimon]

Art,

I was once a Naval Qualified Nuke Reactor Operator. I don't have a link but have studied nuke plants intensively over the past 40 years (yeah it has been a while since I was an operator).

The steam plant - boiler, turbine, condenser and aux. eqpt. accounts for 80% of the cost of the plant. I mentioned material because I did not wish to include things like environmental delays etc.

I'll see if I can dig up a link for plant costs.

BTW direct conversion costs are copper, iron, and semiconductors. i.e. a transformer and a switcher. Production is fast (relative to a steam turbine) and the transformer is a requirement for any plant (a transformer for a switcher might cost 20% more than a straight AC transformer). So you are really only looking at the cost of switching vs a steam plant. Steam turbines are large high precision pieces of machinery with 10s of thousands of parts (the blades) built to very high precision. Very expensive vs iron, copper, and semiconductors.

Note: when semi production goes to 450 mm wafers (around 2012) the cost of power semis will go down by 1/2.

Here is a link for nuke plant costs:

http://nuclearinfo.net/Nuclearpower/Web ... clearPower

The capital cost is estimated at $1 a watt. A coal fired plant is estimated in the same range. That would tend to support my contention that the BOP is the major cost of a nuke plant.

Here is another link rich url (I haven't looked at them for cost comparisons - they are looking at costs per KWh. i.e. operating costs vs capital costs)

http://www.futurepundit.com/archives/002731.html

http://www.world-nuclear.org/info/inf02.html

Part of the higher plant costs of nukes vs coal is that nuke plants are saturated steam plants that operate at about 100C lower temps than coal fired plants and without superheat. It means a larger turbine and condenser than a coal fired plant of equal power due to larger flow requirements.

[scareduck]

I got ahold of an interesting paper by Nevins on ion thermalisation and Q in IEC machines. He discusses the BFR to some extent.

Nevins, W. M. "Can Inertial Electrostatic Confinement Work Beyond the Ion-Ion Collisional Time Scale?" 1995

Yes, we've been over this a number of times. The standard reply is the Chacon, Miley, et al. paper "Energy gain calculations in Penning fusion systems using a bounce-averaged Fokker-Planck model" (Phys. Plasmas, v. 7, issue 11, p. 4547), in which the authors show that there are regimes under which a Penning device could be made to operate with Q>100 for certain configurations, in particular, using parabolic wells instead of square ones.

Art's calculation shows it will be difficult if not impossible to achieve ion convergence (assuming I read what he wrote correctly). I personally don't find Rick's response very compelling.

[TallDave]

New designs might reduce that cost, at least in fission plants:

http://en.wikipedia.org/wiki/Economic_S ... er_Reactor

The probability of radioactivity release to the atmosphere is several orders of magnitude lower than conventional nuclear power plants, and the building cost is 60-70% of other light water reactors.

It's not just the steam plant cost, though. It's also the efficiency of direct conversion vs a thermal cycle, which should save money over the life of a reactor, and the lack of neutrons obviously makes life easier for numerous reasons both physical and political (I doubt the Greens will ever take kindly to a highly radioactive D-D reactor).

[Art Carlson]

I was once a Naval Qualified Nuke Reactor Operator. I don't have a link but have studied nuke plants intensively over the past 40 years (yeah it has been a while since I was an operator).

The steam plant - boiler, turbine, condenser and aux. eqpt. accounts for 80% of the cost of the plant. I mentioned material because I did not wish to include things like environmental delays etc.

I'll see if I can dig up a link for plant costs.

It's always a pleasure to deal with qualified people. Especially since you are coming at the same business from a completely different side, you have a better chance of finding my blind spots. I didn't think it could be so hard to find some good numbers on-line, but I haven't been able to yet. I hope somebody can find a good reference. I'd really like to know the answer.

BTW direct conversion costs are copper, iron, and semiconductors. i.e. a transformer and a switcher. Production is fast (relative to a steam turbine) and the transformer is a requirement for any plant (a transformer for a switcher might cost 20% more than a straight AC transformer). So you are really only looking at the cost of switching vs a steam plant. Steam turbines are large high precision pieces of machinery with 10s of thousands of parts (the blades) built to very high precision. Very expensive vs iron, copper, and semiconductors.

The designs I have in mind were probably designed for mirror machines. I think they have a very large volume of vacuum and magnetic field (both expensive) in order to collimate the ions, but I'm not sure. I never looked too closely at the problem, and that was a long time ago, so there may be better ideas out there.

In my view, a confinement concept will either work or not. Direct conversion may be a great way of doubling the electrical output from a fusion plant (upping the efficiency from 40% to 80%), and it presumably won't make more than a factor of two difference in the captial costs at the outside. But if you're relying on direct conversion to make your concept work, you are shaving things too thin.

[drmike]

The cross section for p-B is about .1 barns for V ~ 100 kV. If we take the core of radius r_c, the probability of fusion is ~ i*n_0*sigma*r_c with various geometric factors ignored. i is the flux of ions flowing radially into the center.

you're using prob(fus) =i*n_0*sigma*r_c; geometry independent. Implies the central 10% of the device (0.1 m?) is an undifferentiated, isotropic thermal distribution. sigma is geometry independent, per Art's equation above.

No, I was assuming all the ions have 1-D motion and they will only interact within the
radius r_c (the core) and not do anything outside that core.

I'm just confused about what you're calculating. Are you trying to show that if you have an isotropic, low density, thermal plasma in the machine that you don't get much fusion? I thought we already knew that.

No, it was to show what the number of collisions would be with crude assumptions of mono-energetic ions. Exactly the opposite of a thermal low density plasma!

Farther up, I'm trying to figure out, if the "lumpiness" of the field, that is the imperfect geometry, is really a potential problem, then how the equation for sigma can be geometry independent.

Can't have it both ways for collisionality-- geometry dependent where it hurts, not where it matters? Or am i confused on how you're calculating sigma?

The cross section that Art computed is for coulomb interactions. I just double checked it and got the same answer, but I think the meaning has nothing to do with fusion power. Fusion cross section is a lot smaller (even for D-T) so the probability of fusion is really small.

I've been beating my head on an interesting physics problem, and it turns out it is related to "sonofusion". What if you ionized a bubblle of DTO (extra heavy water) inside a bunch of DTO water? It would be ideal - you'd have shielding, you could breed fuel with the neutrons and you could process the heat from the water easily.

The problem is that the fusion cross section is so small that the total power out is about 10^-5 of the power in to create the plasma! I won't bore people with the math - it's too thick. (It was fun for me though!) The fundamentals really boil down to the fact that you need to get the ions to go past each other 10^4 to 10^6 times to ensure fusion happens. As long as the particles are just bouncing inside a potential well (like the center of the sun) the probability that fusion happens with no energy loss is pretty good.

I think the fundamental question for polywell is confinement time or "number of tries on goal". If every D or T gets near the core 10^5 times on average, net power out is possible. For p-B it will have to be 10^7 times, the cross section is just that much smaller.

All fusion systems have the same problem, so it is not like polywell is unique. There is a good reason why stars work, and it may well be we just can't get there from here. But it will be fun to try!

I'm still digging my way thru Rick's previous papers, so I've got more questions than answers for the moment.

[MSimon]

Art,

Thanks for making the point about the increased reactor size for direct conversion. I know that and neglected to mention it.

I believe it will add 1 to 2 m to the diameter depending on the Paschen arc curve at the operating pressure and how much safety margin is required.

If we have to go with a D-D machine and a thermal plant, the costs should be around what you get from a fission plant with the advantage of no fission products and an unlimited fuel supply. It might also be possible to do superheat with some clever design tricks. If that is possible, retrofitting coal plants could give an immediate way to practical fusion plants using D-D. Since the BOP is already there the economics would be very favorable and the logistics would not be a problem. In addition with superheat the plant efficiency goes up to the 40 to 50% range. Not bad.

Direct conversion has a huge effect on plant construction time and cost of materials. If pB11 is possible I can see, with 20 years of development, costs going to the range of 10 cents to 20 cents a watt vs 50 cents a watt for a gas turbine (the lowest capital cost plant currently).

[Solo]

@scareduck: thanks, sorry I beat a dead horse. I sure wish I could get my hands on the Chacon paper, or the rest of those references Dr. Nebel posted.

[zbarlici]

A little birdie told me that there is news forthcoming and we will get it soon. The definition of soon is undetermined.

If i had the know-how i would start putting together a a webpage titled "The Dawn of Nuclear Fusion". Make sure that this community gets a jump on it. Get some web design guys and pair them up with the polywell know-how guys and put together a real nice website and have it ready for launch as soon as possible. It would be the news of the century...

[scareduck]

@scareduck: thanks, sorry I beat a dead horse.

Not at all. I only wish there were a more comprehensive bibliography available. I started working on one and collecting the necessary papers.

I sure wish I could get my hands on the Chacon paper, or the rest of those references Dr. Nebel posted.

You might try a well-stocked local university library. This paper is available electronically.

[TallDave]

@scareduck: thanks, sorry I beat a dead horse. I sure wish I could get my hands on the Chacon paper, or the rest of those references Dr. Nebel posted.

Ask, and ye shall receive.

http://scitation.aip.org/getabs/servlet ... s&gifs=yes

And as long as we're on the topic of ion convergence, some guy called Nebel co-authored this paper:

http://adsabs.harvard.edu/abs/2004APS..DPPNI2005P

Furthermore, dynamic control of the virtual cathode lifetime using the POPS concept has been demonstrated by controlling the amplitude of the external rf modulation at the POPS resonance. In addition, recent theoretical works using 1D particle simulation show a high degree of plasma compression during POPS, leading to an ion density enhancement of up to 10^4 at the core

That sounds helpful.

[cuddihy]

you're using prob(fus) =i*n_0*sigma*r_c; geometry independent. Implies the central 10% of the device (0.1 m?) is an undifferentiated, isotropic thermal distribution. sigma is geometry independent, per Art's equation above.

No, I was assuming all the ions have 1-D motion and they will only interact within the
radius r_c (the core) and not do anything outside that core.

please bear with me, as you can probably tell, I'm not a physicist & my understanding of particle physics, like simon's, was learned at a navy nuke school years ago. They only teach us enough to be less dangerous than otherwise So I'm trying to understand how well what you're calculating above applies for a real polywell.
From what I remember,
"little" sigma is a probability of interaction usually expressed as inverse area
n_0 is a particle population/unit volume
r_c is the radius of the area you're considering in length
i is a flux-unit area/unit time

In a polywell, n_0 and i, from r=0 to r=r_c ,should be roughly inversely related. Where n_0 is big i is little, where i is big, n_0 is little. And little sigma is changing througout. To me this says that this is a poor equation even for roughly modeling interaction rate unless you assume that there is roughly no focusing within r_c. Using this approximation, you'd get the same answer at r=0, r=0.5*r_c or r=r_c?

But I think focus matters in this case.

Say you made an experimental determination of microscopic cross section in the traditional way: if you theoretically check your experiment for the expected cross section, do you take as the reaction space the area where the beam and target interact(case 1), or do you take as the reaction space the target+the rest of the volume of the beam (case 2)?

In one case, you're dealing with interaction of a known flux at a fixed target volume and population. in the second, you're dealing with a much larger population and volume, but the same assumed flux and same resulting reaction rate. You'd get drastically different answers for cross section. The second case is calculated with no focusing on the target.

The same thing applies in reverse. Unless you have a clue how good the focusing is, you have no idea what the reaction rate is, and assuming a perfectly out of focus core indeed gives you a low reaction rate. So somehow how well the polywell or the core exhibits focus is going to drastically effect your reaction rate. It has to go in somewhere. you can't derive it from coulomb rate dependant on a sigma that also depends on the focus.

So where have I veered off here?

[MSimon]

please bear with me, as you can probably tell, I'm not a physicist & my understanding of particle physics, like simon's, was learned at a navy nuke school years ago. They only teach us enough to be less dangerous than otherwise

Loved that. So true. Which is why I don't have too much to say about theory. Design of course is a different story.

BTW the fact that you are a nuke makes us shipmates.

[drmike]

"sigma" is used as unit area in this case, not inverse area.

The target volume is 4/3*pi*r_c^3 where r_c is some estimate of a reasonable size using a fudge factor of "that looks about right!" Near the MaGrid, ion velocity is slow, so no fusions take place. As the ions fall into the core, they will cross some point where the fusion cross section is possible. Some where past that you pick r_c.

So if the system were linear, and you had 100kV grids, you'd get 80 kV ions about with r_c ~ 0.2 R or 20% of the MaGrid radius. At 160keV there is a peak in the p-B fusion cross section, so "that looks about right".

Nothing is linear in a plasma, and especially not in a fusion plasma. So it's a lot of hand waving. But for BOE calculations, it will give you order of magnitude and tell you if there's even a hope.

Sonofusion has no hope. Stopping distance of 10^4 eV ions is 2 nm in water, but you need a radius of .3 m to get fusion power out. If we can find something similar for Polywell, then it will be easy to shoot it down. If we can't find anything wrong, then we need real data to point the way.

Let's stay tuned!

[Aero]

Hi drmike,
I have been posting to a design thread (direct conversion) where we really need a value for the radius of an area within the Polywell that I have dubbed the "fusion core." I define the fusion core as that area where conditions exist for p-B11 fusion and from where alpha particles may be expected to originate. Is that the same as what you are calling r_c? Am I correct when I interpret your estimate of the value of the radius of the fusion core to be about 0.3 meters for a 100 Megawatt BFR? This would give the volume of the fusion core of 0.11 cubic meters.
I don't have the math and physics to attack the problem head first as you, Art and others have, but since this is not a military exercise, I thought there might be something to be discovered by backing into the problem. I calculated 2.5886 E+23 fusion events per hour (seems low) required to generate a gross 100 Megawatt-hours. But that's hours. If I could guess the ion density of the fusion core and the time constant for ion fusion (how long will an ion be expected to reside within the Polywell before it fuses) then perhaps I could estimate how much volume is required within the fusion core. Obviously that had better come out to be something less than the volume of the Polywell, about 14 cubic meters, and really should be close to your estimate above.
Any help you or anyone can provide will be appreciated.