The problem with ion convergence

[rnebel]

Let me summarize my views on this thread.

1. Art’s objections are centered on the assumption that flux surfaces are equipotential surfaces. That’s where the defocusing aberrations come from. That’s a valid assumption for l.t.e. plasmas like
Tokamaks, but not IECs. Electron inertia allows gradients along field lines. It’s not clear that there will be any aberrations.
2. Art claims that these aberrations accumulate with several passes. Bussard and Krall’s calculations indicated that every electron scattered in the edge with every pass and thus there was no accumulated effect.
3. This has all been discussed previously in the literature. As near as I can tell, there is nothing new in this thread. 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. I suggest that people who are concerned about this look at the original references.

Finally, one comment on costing. Back when I was Nuc E student the rule of thumb for costing a plant was 10% in the power core, 90% in the balance of plant (similar to Simon's numbers). This is what drove commercial reactors to large sizes (~ 1GWe) in order to be competitive.

[drmike]

Thanks Rick. Keeping the electrons non-thermal will be an interesting problem, and hopefully I'll get a chance to dig into more papers one of these days.

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.

Yes, it's a BOE guess which is order of magnitude close enough. In that vein, the time in the core can be guessed by the diameter/velocity, or you can get fancy and call it 1/2*a*t^2 = r_c. Guessing acceleration is another game though. The cross section for fusion for p-B is about is about 0.1 barns (1e-25 cm^2). The average distance you need to go before fusion is roughly 1/(n*sigma) where n is the # of protons and boron ions per unit volume and sigma is the cross section. Take that number divided by r_c to get an estimate of how many times an ion has to traverse the core before fusion takes place. Multiply that by the time spent bouncing between MaGrid and center, and you get a crude estimate of how much time you need for confinement.

That's BOE. Reality is a lot more complicated.

[choff]

It occured to me today that Dr. Bussard, his consultants and his critics spend 17 years going over potential show stoppers, doing calculations and then recalculations. This helped to reinforce his view that the process would work.

If Arts objections are correct, then how could it be in all that time both Dr. Bussard and his critics failed to discern the electron sheet/cusp problem as the fatal flaw.

I recall one newcomer to talk-polywell some time before who had a similar arguement to the electron sheet problem, and the answer was high potential voltage/low kinetic energy in the core, reverse at the edge. But I don't believe that was missed this time.

[scareduck]

The real problem, I think we can all agree, is the paucity of actual published data and theoretical considerations.

[choff]

Agreed. But if he abandoned the Riggatron once he decided it was impratical, why would he continue to flog the dead polywell horse if thats what it was show to be.

[scareduck]

It occured to me today that Dr. Bussard, his consultants and his critics spend 17 years going over potential show stoppers, doing calculations and then recalculations. This helped to reinforce his view that the process would work.

Kind of interesting in that I realized that the thread on what is or isn't science also applies here. From the Wikipedia page on "scientific method":

1. Use your experience: Consider the problem and try to make sense of it. Look for previous explanations. If this is a new problem to you, then move to step 2.
2. Form a conjecture: When nothing else is yet known, try to state an explanation, to someone else, or to your notebook.
3. Deduce a prediction from that explanation: If you assume 2 is true, what consequences follow?
4. Test : Look for the opposite of each consequence in order to disprove 2. It is a logical error to seek 3 directly as proof of 2. This error is called affirming the consequent.

The problem here is part 4; you have to constantly be looking for places where you might be wrong. Without peer review, myopia can set in.

[tonybarry]

Hello scareduck,
The thread on what is or isn't science always applies. **especially** applies here, where the onus of proof is on us and we have not got a lot of answers. While we may move forward, awaiting experimental results, we have to recognise that neither blind faith nor bluster will do us any good. Only the truth works.

Regards,
Tony Barry

[drmike]

The interesting aspect of the sheet charge is that it points to the "wiffle-ball" current. If a transverse field builds up in the cusps, it starts a circular current across the planes. One of my major concerns was how that current could start, and this is a reasonable theory. How it could be a net current I still don't get, but I'm willing to build an experiment and go look!

[Art Carlson]

Let me summarize my views on this thread.

1. Art’s objections are centered on the assumption that flux surfaces are equipotential surfaces. That’s where the defocusing aberrations come from. That’s a valid assumption for l.t.e. plasmas like
Tokamaks, but not IECs. Electron inertia allows gradients along field lines. It’s not clear that there will be any aberrations.

It is true that I am assuming that the flux surfaces are (more or less) equipotential surfaces, and that electron inertia can modify this. By now you should know that I am a friend of quantitative estimates. Let's try to see how much difference electron inertia can make. Ohm's law is essentially force balance on the electrons. Using the convective derivative for dv/dt rather than collisions to balance the electric force, we have:
m*(v dot nabla)v = e grad phi
This is perhaps more intuitive in the integrated form:
m*v^2/2 = e*(Delta Phi)
To significantly change an electric potential, we need to let a significant fraction of the electrons run downhill and then throw them away. If we let them reflect, then the mean velocity is zero. I don't think you really want to do this, Rick. That would mean that the electrons have no confinement. Even if you substitute "10%" for each time I used the word "significant", you are likely to wind up with a figure for the energy loss which is deleterious. Remember that we have a discrepancy of 8 orders of magnitude on the table. (Which may not be right. I haven't double checked my calculation, and I don't think anybody else has either.) Even a little bit of non-sphericity is likely to mess up convergence in short order. While it may not be "clear" to you that there are any aberrations, everything points in that direction. If I made a mistake, it's up to you to point it out or offer an alternative estimate.

2. Art claims that these aberrations accumulate with several passes. Bussard and Krall’s calculations indicated that every electron scattered in the edge with every pass and thus there was no accumulated effect.

I believe the previous calculations assume perfect spherical symmetry and conclude that annealing works. My estimates indicate that it is the lumpy surface which kills annealing.

3. This has all been discussed previously in the literature. As near as I can tell, there is nothing new in this thread. 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. I suggest that people who are concerned about this look at the original references.

I'll visit the library tomorrow. Or are these available on-line?

Finally, one comment on costing. Back when I was Nuc E student the rule of thumb for costing a plant was 10% in the power core, 90% in the balance of plant (similar to Simon's numbers). This is what drove commercial reactors to large sizes (~ 1GWe) in order to be competitive.

I acknowledge that, but still find it hard to believe. If I could build a nuclear plant for 10% more than a gas turbine power plant, why wouldn't I do that all the time so that I would never see another fuel bill? I suspect we may be having some confusion over what to book as "balance of plant" besides the steam turbines. I'd really appreciate some literature.

[TallDave]

If I could build a nuclear plant for 10% more than a gas turbine power plant, why wouldn't I do that all the time so that I would never see another fuel bill?

Some countries do (see France). For the others, the reasons are mostly political.

Of course, for a long time fuel was pretty cheap.

[MSimon]

Finally, one comment on costing. Back when I was Nuc E student the rule of thumb for costing a plant was 10% in the power core, 90% in the balance of plant (similar to Simon's numbers). This is what drove commercial reactors to large sizes (~ 1GWe) in order to be competitive.

I acknowledge that, but still find it hard to believe. If I could build a nuclear plant for 10% more than a gas turbine power plant, why wouldn't I do that all the time so that I would never see another fuel bill? I suspect we may be having some confusion over what to book as "balance of plant" besides the steam turbines. I'd really appreciate some literature.

Art,

You are comparing apples to oranges. i.e. steam plants vs gas turbines.

1. Steam plants require hours to get up production. Gas turbines take minutes.

2. There is a lot more material in a steam plant vs a gas turbine: Steam turbines are heavier, you need a condenser, you need a boiler. Also there are extensive auxiliaries in a steam plant they include: feed water pumps, coolant pumps, and in some cases cooling towers.

3. The BOP ratios are economic rules of thumb. It is not strictly a technological problem.

4. Maintenance is much higher for a steam plant. It is one of the reasons you want to spread that cost over more KWhs.

One very good reason for going to direct conversion is that it makes the plant more dispatchable. Turn it on and collect the juice vs having to warm up the plant to operating temperatures - for mechanical reasons this must be done slowly in a steam plant. This is especially true for stem turbines.

[Art Carlson]

You are comparing apples to oranges. i.e. steam plants vs gas turbines.

Oops. Yes, that must be at least part of the problem. You can tell I'm just a physicist.

[rnebel]

Art:

Having those electrons reflect is exactly what you want them to do. During part of their orbit they exchange kinetic energy for potential energy, and during another part of their orbit they exchange potential energy for kinetic energy. To them the potential well (virtual cathode) looks like a potential hill. As they slow down going up the hill their kinetic energy becomes potential energy (i.e. it adds to the potential hill). After they turn around the potential energy turns back into kinetic energy. I think that the easiest way to see this is to realize that the equations of motion for an electron parallel to the magnetic field are identical to the equations of motion in a system that has no magnetic field. The equivalent system is a gridded system where we accelerate electrons in the mantle, they move through the grid, and then they for a virtual cathode in the interior. We know that this system works (see previous references). Does that make sense?

I don’t think that the fusion technology papers can be found online. You’ll probably have to look at the journals.

The problem with building nukes to replace gas plants is that you need units ~ 1000 Mwe in order to get the 10%-90% split. If you make them smaller than that the costs of things like the containment (which is the same cost regardless of the unit size) will make the nukes much more expensive. The financial risk involved in building a 1000 Mwe unit is huge. In good times it took ~ 7 years to build one, which meant that if you couldn’t accurately project your demand 7 years down the road, you were setting yourself up to take a financial bath. That’s what really killed nuclear power in the US. Demand turned out to have a lot more elasticity than anyone projected. John Ahearne wrote an excellent article on this in the late 80s, but I don’t have the reference.

On the other hand, gas-fired plants are typically in the 100-200 Mwe range. They can be built cheaply and in a big hurry. The principle cost for gas-fired is for the fuel. Consequently, the financial risk for building these units is relatively small.

These facts have huge implications for fusion power, particularly for large systems like ITER. However, people in the fusion community largely ignore them.

[MSimon]

Art, Rick,

Vincent Page of GE did a talk about plant costs with respect to Fusion. I did a blog post on it here

http://powerandcontrol.blogspot.com/200 ... -good.html

which summarizes the issues. It has a link to his presentation which I think you will find helpful.

I believe the Japanese are proposing to build a 1,700 MWe fission plant which is well above the typical 1,000 MWe size that is more normal.

[scareduck]

I'll visit the library tomorrow. Or are these available on-line?

Fusion Technology (now Fusion Science and Technology) is a publication of the American Nuclear Society. Their online archive only goes back as far as 1997; I had to go to UCLA to get a hard copy of all the early papers, though I found out later that some of them were available on the askmar.com website (not the Aug. 1993 and March 1994 papers, though).