Some questions answered, some introduced

[Aero]

The 30 page patent linked below, prepared and filed after WB-6 was completed, brings together much if not all of Dr. Bussard's final thoughts on Polywell fusion. It may be that on publication, he already knew that the contract was to be extended and the lid would be clamped down on the information flow. There is a lot of interesting information there-in, including:

Another physics feature of importance in system operation is that the fusion products will, in general, not deposit their energy in the plasma region (as in the case in “conventional” concepts for fusion), but will escape from this region to the structures and surfaces bounding the polyhedral magnetic/plasma system. In this escape, these particles will leave as positively charged ions, thus increasing the net negative potential of the plasma region. Each fusion event will cause an increase in the well depth which is confining the reacting ions, hence will cause an increase in the particle density and resulting inter-particle reaction rate which will, in turn, cause a further increase in the negative potential, the well depth, etc., etc. The onset of fusion reactions in a negative potential well of the type contemplated herein will thus initiate a self-generating process to increase the well depth and thus to increase the fusion rate. Under certain special conditions (of total recirculating ion current) it is possible, but not certain, that-once started-a reacting assemblage of this type could become self-sustaining without any further excess external electron injection, beyond that needed for balance with the ion injection rate itself. In any case, this self-generating-well effect might allow the reduction of electron injection for well sustenance, and thus could result in a reduction in the externally-supplied power required to drive the electron injection system.

The power to maintain the well is the significant loss mechanism, so the above is saying that the reactor automatically replaces its own losses, to a more or less extent.
http://www.freepatentsonline.com/y2008/0187086.html

[chrismb]

I suggest it would be highly doubtable that this would've ever cleared the patent examiners, had the application been continued and not abandoned (as is the case). It would require clear evidence of a rate of fusion that could perpetuate this, and there is none.

[Aero]

I suggest it would be highly doubtable that this would've ever cleared the patent examiners, had the application been continued and not abandoned (as is the case). It would require clear evidence of a rate of fusion that could perpetuate this, and there is none.

Forget the patent examiners. Based on what we know, or think we know, what does our best judgment tell us? Does each fusion abandon electrons within the well? Are they cold electrons to sit in the bottom of the well or hot electrons to climb right out of the machine? And how do they number compared to the million or so required to maintain the quasi-neutral plasma?

[D Tibbets]

Impressive find. It looks like there is a lot of information here (~30 pages). I will need to read it several times to digest it, but it looks like it will easily trump the Velencia paper as a source of consolidated information.

Concerning left behind electrons. Some presumptive calculations.
1)Assume the machine uses neutral gas injection, so the generated ion input = generated free electron input, adjusted for the small 1 PPM excess electrons provided by the electron guns.
2)Assume 100 MW fusion output. That comes from the fusion of ~ 10^20 deuterium ions per second.
3)Assume electron lifetimes are ~ 2 milliseconds with recirculation.
4)Assume fuel ion loss rates are small enough to be ignored.
5)Assume the density within the Wiffleball is 10^22 particles /M3 and the Wiffleball diameter is ~ 1 meter so that the volume is 1 M^3 so there are ~ 10 ^22 ions and 10^22 electrons (I wont worry weather I should actually be using total population of 2* 10^22 particles (ions + electrons) as this is a small possible error compared to my ball park figures.
6) If all of the electrons are lost and need to be replaced every 2 milliseconds, that would mean ~ an electron current (from ionization and the guns of ~ 10^24/s or !~ 100,000 Amps.
7) the gas-ion current would have to be at least 10^22/ s

So, the electron current would exceed fusion ion current by a factor of ~ 500. This would not effect the balance much.

But, I'm obviously missing something here as this direct translation from WB6 data would result in electron losses far in excess of the presumed scaling laws. Electron losses in WB6 were ~ 40 Amps, that scaled up to ~ 1 meter diameter should result in ~ 10X increase (~r^2 loss scaling) or ~ 400 Amps (~10^22 electrons per second). I'm guessing that as the containment efficiency increases with stronger B fields, the electron lifetimes must also increase, though I'm not sure that makes sense. Also, fuel ion mean time to fusion is supposed to be ~ 20 ms (I think I remember reading this somewhere), not 1 second like would be in the example above. Using the 20 ms for the fuel ion lifetime before being lost to fusion would imply that the ion current would be ~ 10% of the electron current if the electron lifetimes are kept at 2 ms.
This would imply that the fuel neutrals that are first converted to fuel ions and free electrons and then to fusion ions that escape (and according to Nebel they would not contribute significantly to heating) could effectively resupply ~ 10% of the needed electrons. So if the reactor needed 10MW of electron power , that would be reduced to ~ 9 MW. A small but significant advantage.

My reasoning is uncertain. I need some help and/or serous head scratching.
Also, I'm not sure what the conditions were for the ion mean time to fusion number I quoted. If it represent a working reactor near maximum efficiency the 20 ms lifetime may be in the ball park. If it represents the conditions in a breakeven machine, then in a working high Q reactor (increased density?), the fuel ion mean time to fusion may more closely approach the electron lifetimes. Or not, depending on what the mean time to fusion actually is.


Dan Tibbets

[Aero]

Item 5 - isn't there another factor of 2 in there somewhere? Dia is 1 meter so volume ~ 1/2 M^3
Hey thanks! I found this which is new to me.

For most practical uses, the volume of a sphere can be approximated as 52.4% of the volume of an inscribing cube, since \pi/6 \approx 0.5236. For example, since a cube with edge length 1 m has a volume of 1 m3, a sphere with diameter 1 m has a volume of about 0.524 m3.

And yes, a lot of information. I gotta go now.

[ladajo]

But, I'm obviously missing something here as this direct translation from WB6 data would result in electron losses far in excess of the presumed scaling laws. Electron losses in WB6 were ~ 40 Amps, that scaled up to ~ 1 meter diameter should result in ~ 10X increase (~r^2 loss scaling) or ~ 400 Amps (~10^22 electrons per second). I'm guessing that as the containment efficiency increases with stronger B fields, the electron lifetimes must also increase, though I'm not sure that makes sense. Also, fuel ion mean time to fusion is supposed to be ~ 20 ms (I think I remember reading this somewhere), not 1 second like would be in the example above. Using the 20 ms for the fuel ion lifetime before being lost to fusion would imply that the ion current would be ~ 10% of the electron current if the electron lifetimes are kept at 2 ms.

These numbers are also discussed in Krall's 1992 Paper on Polywell.
Partial Available on Joe's page at:

http://www.strout.net/info/science/poly ... -1992.html

The full paper says that the 2ms electron lifetime is for the test article not the full size. I think it was more like 120ms for full size. (2m device/1m core).

Read the below in two columns.
Left column is the full size, right is the concept test device.
Device radius, R (m) 2 1
Ion source radius (m) 1 0.5
Magnetic field, Bo (T) 1 0.2
Electron gun energy, E, (keV) 50 20
Ion source energy, Eo (eV) 5 5
Bulk density, no (m-3 ) 2 x 10^20 10^16
Core density, n, (m3-) 2 x 10^24 4 x 10^9
Core radius, r, (m) 10^-2 0.8 x 10^-2
Electron confinement time, T, (Ms) 120 2
Electron injection current 5 kA 5 A
Fusion power (MW) 800 ---
Electron loss (MW) 40 ---
Radiation loss (MW) 4 ---
Efusion = 15 MeV
Gain = fusion power/electron loss 20 ---

Corrected the full scale e- lifetime to 120ms, based on the data provided vice the 200ms from my head.

Also want to make note of the estimated core sizes...much smaller than we have talked about...

[D Tibbets]

I guess it makes sense that the electron lifetime increases as it is directly linked to the ion density which goes up with B field increases.

Lets see. If losses scale mostly as r^2 and electron losses make up most of this, then at 1 meter radius and 10 T, the ion /electron density would have increased ~ 10,000 X. The electron losses would be 40A * (100 cm/ 15 cm) ^2= ~ 6.6 ^2 = ~40X or 1600 A . That is a gain of ~ 10,000X/40X = 250 X.
I think that would translate into an electron lifetime of 250/2 = ~125 milliseconds electron life times (assuming the same recirculation contribution. If recirculation is improved as discussed below, then the effective containment is even higher. Rember though that (I think) recirculated electrons are essentially reset for energy and radial vector.

Interesting that in the patent application Bussarrd(?) claime that with good recirculation the electron losses are dominated (almost?) by cross field transport. He goes on to say that the nubs and other non shielded surfaces near the magrid could decrease the recirculation by a factor of 10-100X.

This added to what Nebel said about the nubs being a hot spot in WB7, and suggests that if the nubs, etc can be moved to less vunerable areas, shielded or converted to standoffs for each seperate magnet grid, then electron losses might be greatly reduced. If I assume WB6 represented the 100X vunerable surface condition, if this could reduced to the 10X vunerable surface condition the required current to maintain the Wiffleball could be reduced ~ 10 fold or ~ 4-5 Amps in a WB6 type of machine. That would make it considerably easier for the secondary electrons from neutral gas puffers to maintain the potential well as the positive fusion ions leave. It's even possible that some of the fuel might have to be supplied by ion guns (not just neutral gas puffers)to prevent runaway accumulation of electrons.

Apparently the recirculation of the electrons is much better than I conceived, potentially very close to 100%. This has several implications. In this case the electron losses would be dominated by trans field transport. Electrons would ground on the magnet cases and there would be very few electrons outside the immediate vicinity of the magrid. Also, there would be no electrons contributing to escaped ions hanging around outside the magrid. They would have a greater tendency to go straight to the vacuum vessel (or conversion grid) surfaces. This might ease arcing concerns some (thus allowing greater internal densities.
A question would be that since upscattered electrons are not confined by the positive charge on the magrid, so that once they leave the magrid they would tend to follow the ions to the walls. In this case if the electron losses are dominated as above, the number of upscattered electrons must be a small percentage of the total. Concidering the energy these upscattered electrons give up to the electron potential well (Pos. magrid) the numbers could be significantly more, but the energy loss would still be small.

Also, with greater lifetimes, how are electron thermalization issues handled? Some don't beleive the electrons can avoid thermalization over 1 ms, let alone 125 ms, and in an enviornment that is 10,000 times more dense.

Dan Tibbets

[ladajo]

Also want to make note of the estimated core sizes...much smaller than we have talked about...
Machine radius (m) 2 1
Core radius, r, (m) 10^-2 0.8 x 10^-2

[icarus]

Also want to make note of the estimated core sizes...much smaller than we have talked about...

Any elucidation on how 'core' is defined in this instance?

Might have to include a rigorous definition for WB radius, and hence explain the field--plasma interface/layer/boundary physics.

[ladajo]

See page 45 of Fusion Power vol 22, 1992 Section III B, of Krall's article that talks about ion spherical convergence and the dense core as they understood it then.
It is suppossed to be a function of machine radius (magrid), ion birth energy, well depth which in turn drives the angular turn rate at the edges, which in turn determines the central core density and size.

Interestingly, Joel's paper holds core r=.16m (.32 m diameter) as observed.

The idea is there are three regions, the edge, in between, and the "dense core".

[TallDave]

The 30 page patent linked below, prepared and filed after WB-6 was completed, brings together much if not all of Dr. Bussard's final thoughts on Polywell fusion. It may be that on publication, he already knew that the contract was to be extended and the lid would be clamped down on the information flow. There is a lot of interesting information there-in, including:

Another physics feature of importance in system operation is that the fusion products will, in general, not deposit their energy in the plasma region (as in the case in “conventional” concepts for fusion), but will escape from this region to the structures and surfaces bounding the polyhedral magnetic/plasma system. In this escape, these particles will leave as positively charged ions, thus increasing the net negative potential of the plasma region. Each fusion event will cause an increase in the well depth which is confining the reacting ions, hence will cause an increase in the particle density and resulting inter-particle reaction rate which will, in turn, cause a further increase in the negative potential, the well depth, etc., etc. The onset of fusion reactions in a negative potential well of the type contemplated herein will thus initiate a self-generating process to increase the well depth and thus to increase the fusion rate. Under certain special conditions (of total recirculating ion current) it is possible, but not certain, that-once started-a reacting assemblage of this type could become self-sustaining without any further excess external electron injection, beyond that needed for balance with the ion injection rate itself. In any case, this self-generating-well effect might allow the reduction of electron injection for well sustenance, and thus could result in a reduction in the externally-supplied power required to drive the electron injection system.

The power to maintain the well is the significant loss mechanism, so the above is saying that the reactor automatically replaces its own losses, to a more or less extent.
http://www.freepatentsonline.com/y2008/0187086.html

That's certainly an interesting idea. Thanks for sharing.

I don't believe there's much chance this means it could be run without an e-drive -- the electrons need to be fed in at a certain minimum rate to overcome maxwellianization. I suppose it depends on where that minimum maxwellianization-replacement value lies.

One thing I'm not sure about, though -- if electrons are in a 60KV well, and the ions that fall in at 60V are leaving at MeV, does this affect the well depth? Presumably they only use the same energy climbing out of the well as they gained falling in, and I don't think the temp of the fusion product ions makes any difference to the temp of the well-forming electrons. I think he must just be referring to the fact the ions are leaving.

[TallDave]

Also want to make note of the estimated core sizes...much smaller than we have talked about...
Machine radius (m) 2 1
Core radius, r, (m) 10^-2 0.8 x 10^-2

Have we talked about core sizes much? Maybe I missed that. I've been assuming (on no good basis, just a guesstimate from the pictures) the WB radius is half that of the machine, but I haven't tried to estimate core size. Maybe someone else has.

Of course, for the ITER comparison it didn't matter much because we assumed no core convergence, or calcuated for a point in the core rather than a core volume -- but it certainly would be helpful to know the ratio of WB:core if we wanted to calculate overall power, so thanks for sharing that.

OTOH as 93143 mentioned the other day, there's some confusion about the PW geometry. There was a view floating around for awhile that the ions orbited the WB. Maybe there's some confusion about WB volume vs core volume.

This added to what Nebel said about the nubs being a hot spot in WB7, and suggests that if the nubs, etc can be moved to less vunerable areas, shielded or converted to standoffs for each seperate magnet grid, then electron losses might be greatly reduced.

Yep, that's another reason why WB-8 scaling is so, so important to know. One could even make a case that the machine might not run at all without nubs, if one were pessimistically inclined.