What is the basis for the B^4 portion of the power gain?

[TallDave]

Why does the strength of the B field scale the fusion so dramatically? Bussard mentions this scaling in both the video and the Valencia paper, but I'm not sure what he's basing this on. Was that from his experimental results?

This is a major point I see skepticism on.

[bcglorf]

Why does the strength of the B field scale the fusion so dramatically? Bussard mentions this scaling in both the video and the Valencia paper, but I'm not sure what he's basing this on. Was that from his experimental results?

This is a major point I see skepticism on.

My take from the Valencia report was that B field scaling was based off of experimental results. It was so dramatic because of how much it increased electron trapping factors and thus electron densities. Most of their experimental data was in regards to electron trapping and related densities.

[TallDave]

Hmm. I wonder if that's going to reliably scale to 100MW.

Only one way to find out for sure I guess.

[MSimon]

Why does the strength of the B field scale the fusion so dramatically? Bussard mentions this scaling in both the video and the Valencia paper, but I'm not sure what he's basing this on. Was that from his experimental results?

This is a major point I see skepticism on.

My take from the Valencia report was that B field scaling was based off of experimental results. It was so dramatic because of how much it increased electron trapping factors and thus electron densities. Most of their experimental data was in regards to electron trapping and related densities.

Actually it was based on theoretical considerations. So it will likely scale. I'll see if I can find the relevant info and post it.

Simon

[Stefan]

I'll have a try:

Power is proportional to the ion density squared.
Now a polywell confines the ions using an electron cloud, which has nearly the same charge density as the ions (the deviation procudes the ion confining E-field).
So the fusion power (=P_fusion) is proportional to the electron density (=n) squared:

P_fusion ~ n^2

The B-field is used to confine the electrons, but the electrons produce a B-field too, which works against the external B-field. At some point those fields cancel each other. This happens when the kinetic energy density of the electrons (=n*e*V, V: acceleration/grid voltage) is equal to the energy density of the external B-field (this is called beta=1 condition).

(In a polywell this is intended to happen inside of the grids: with increasing density the B-field gets 'forced' further outside, were the external field is stronger.
At some point however the external field gets weaker again. The density to cancel the field there is the maximal density possible, at this density the well will 'blow out'.)

So magnetic field energy density (proportional B^2) is equal to n*e*V, thus:
n ~ B^2 => P_fusion ~ B^4

Still, this is just the power not the power gain.

The scaling bases on the assumption that the major losses are electrons hitting unshielded surfaces.
Since there should only be unshielded surfaces outside of the wiffleball the losses are proportional to the outside electron density, which is the inside density divided by a trapping factor.

According to the valencia paper this trapping factor scales with B^2, so:

P_loss ~ n / B^2 ~ B^2 / B^2 = 1

so the losses are constant regarding the B-field and gain too scales with B^4.

My understanding is, that there are only small areas around the cusp axis through which the electrons can escape. The radius of these 'holes' is propotional to the gyro radius of the electrons, which again is proportional to B. Thus the area through which the electrons can escape is ~ B^2.

For anybody who doesn't like this 'explanation' of the trapping factor, the B^2 scaling might be relatively easy to test via simulation and I'm sure that would be appreciated around here

[MSimon]

Thanks for jogging my memory.

Let me simplify.

To escape the B field requires a velocity proportional to B. The energy of the electron is therefore proportional to B^2. The rest follows as above.

The electron can only escape at the edge of the B field. The escape probability declines with increasing R. Another way of saying that is gain goes up as R.

http://iecfusiontech.blogspot.com/2007/ ... r-out.html

Hope that helps.

[Keegan]

I concur Stephan

couldn't of said it better myself

[TallDave]

Thanks guys, that helps a lot.

[Solo]

Ok, I have a question about the cusps and the losses. The new pdf on the WB-6 final run states:

"From this work, the data showed that the MaGrid transport coefficient (in the simplistic oneterm
MG equation) was found to be about 10-20x less than from previous experiments on earlier
machines. This is a logical result of the fact that the MG transport really involves two terms, one
being the simple direct transport term and one being that due to unavoidable losses through seamlike
line-cusp areas at the inter coil joint spaces, where the trapping factor may be very much less
than that for the direct WB coil container surface regions."

I'm confused. I thought the cusps were only a factor for electron containment in the polywell, not in loss by impacting the coils. Shouldn't the recirculation effect make the escape through the cusps irrelevant? It seems to me like the only thing that should effect the electron transport losses was a lack of shielding on some parts of the machine, like the legs or connections between coils.

(Just to be clear, is "inter coil join spaces" refering to the places where the edges of two coils are close together, or to the triangular region where three coils have 'cornerns'? The term line-like makes me think it's the first of those two. )

[cuddihy]

Ok, I have a question about the cusps and the losses. The new pdf on the WB-6 final run states:

"From this work, the data showed that the MaGrid transport coefficient (in the simplistic oneterm
MG equation) was found to be about 10-20x less than from previous experiments on earlier
machines. This is a logical result of the fact that the MG transport really involves two terms, one
being the simple direct transport term and one being that due to unavoidable losses through seamlike
line-cusp areas at the inter coil joint spaces, where the trapping factor may be very much less
than that for the direct WB coil container surface regions."

I'm confused. I thought the cusps were only a factor for electron containment in the polywell, not in loss by impacting the coils. Shouldn't the recirculation effect make the escape through the cusps irrelevant? It seems to me like the only thing that should effect the electron transport losses was a lack of shielding on some parts of the machine, like the legs or connections between coils.

(Just to be clear, is "inter coil join spaces" refering to the places where the edges of two coils are close together, or to the triangular region where three coils have 'cornerns'? The term line-like makes me think it's the first of those two. )

Yes, intercoil join spaces would be the triangular areas where by necessity the coils do not meet. I can't speak to the experimental results, but don't confuse the term "trapping factor" with cusp recirculation. Trapping factor refers to percentage of overall e- NOT lost to walls or chamber, including recirculated ones. In other words, you are correct that electrons circulating through both the point cusps (in the center of the face) and line cusps (at the triangular corners) will return inside the polywell.

I suspect the emphasis on "two transport equations" refers to their relief at discovering that conformal coils and reduced metal gave such a dramatic increase in trapping factor. Remember, WB-5 has the coils outside a box, with magnets at the cusps. They must have been suprised that just taking the metal out of the line cusps gave such a better result.

[Solo]

Terminology issues. Bah. I would have taken trapping factor to mean the ability to keep the electrons in the wiffleball as opposed to having them escape through the cusps (regardless of recirculation). I would use something like "shielding factor" ( or the transport coefficient Bussard uses) to talk about how quickly the electrons are absolutely lost by hitting the magrid. It seems to me that if the magrid is running at high positive potential and the electron emitters at ground, then you won't ever have a problem with the electrons being lost to the walls. Recirculation ought to be complete, and the only electron losses would be to the Magrid.

As to the cusps, I would have thought that there would be cusps where the coils run parallel to each other along what represents the edge joining the hexagonal faces of a truncated cube. But it looks like the "line cusps" are not *along* these edges, but protrude through the center of the triangular regions, eh? Good to figure that out.

[TallDave]

Terminology issues.

As to the cusps, I would have thought that there would be cusps where the coils run parallel to each other along what represents the edge joining the hexagonal faces of a truncated cube. But it looks like the "line cusps" are not *along* these edges, but protrude through the center of the triangular regions, eh? Good to figure that out.

Yeah, Bussard mentions earlier efforts had equatorial cusp losses, which I guess would be "plane cusps."

[cuddihy]

Terminology issues.
. . . .
As to the cusps, I would have thought that there would be cusps where the coils run parallel to each other along what represents the edge joining the hexagonal faces of a truncated cube. But it looks like the "line cusps" are not *along* these edges, but protrude through the center of the triangular regions, eh? Good to figure that out.

Didn't mean to confuse, ALL of the seam-like joints between coils, including the "sides" and "corners", should be "line" cusps, the only "point" cusps are in the center of the coil face. But you asking that made me reread the Valencia paper, and now I think we were both wrong in our assumptions.

I now think this was saying that the 10-20 times improvement in transport loss coefficient --i.e.with subsequent average electron lifetime or Mean Free Path (MFP) increase -- was due entirely to the virtual elimination of seam to metal flow. Remember, this paragraph was in regards to the difference between the WB-5 boxed coils and the WB-6 Open coils. So, although eliminating the box and allowing "full" recirculation had little effect on the face-to-metal flow, it had a game-changing effect on seam-to metal electron flow.

This is why WB-6 and WB-4 were so much superior to WB-5 and the PXLs--the seam loss dominates, evidently by a factor of 10-20 times, and both had open seam recirc.

That's probably also the "aha" factor that made calculating the necessary unshielded metal fraction an important factor.

Man, that paragraph would be a lot easier to interpret with numbers.