I recall thinking that Joel had misinterpreted Bussard's scaling. Bussard specifically said that power output scales with the cube of the linear dimension. It also scales with the fourth power of the B field. Assume B scales with R and add in loss scaling and you get roughly a power of 5 for the gain.
Linear scaling with volume is entirely expected. It should also be noted that the effective B-field drops with size if you don't strengthen the magnets, so you have to strengthen the magnets quite a bit to get B~R equivalency in the scaling.
Maybe I misread the paper... and I can't find a working download...
WB-8 article
The pictures seem to be missing but it looks like you've got all the text if you click on 'quick view' when searching with google.
Evaluation of Net Power Polywell. Designs
Evaluation of Net Power Polywell. Designs Same title but the URL has a 2 at the end of the pdf filename.
Don't have time to thoroughly compare the two, they might be duplicates. Either way this looks like the paper you're looking for.
It's not found on archive.org database
Evaluation of Net Power Polywell. Designs
Evaluation of Net Power Polywell. Designs Same title but the URL has a 2 at the end of the pdf filename.
Don't have time to thoroughly compare the two, they might be duplicates. Either way this looks like the paper you're looking for.
It's not found on archive.org database
I havn't reduced J. Rogers simulation in detail, though I did find some curious variances from the claimed properties. That the ion losses dominate in his simulation is different. And that the the ratio of electrons to ions is 2 is completely different from the claimed conditions.
The question about magnet strength vs magnet size is an issue which has confused me. Certainly, in order to maintain the same strength in the center of the face point cusps would seem to imply that the magnetic strength would need to increase proportionately faster than the machine size.
If the pertinate field strength is that at the border between the magnets, then this would not apply as that distance would not change*. This would allow magnet strength to scale machine size- in terms of diameter, not nessisarily in terms of area.
This seems possible to me , merely because Bussard, with his engineering background would have appreciated this, and would not have referred to 10 Tesla in a 3 meter machine, with scaling proportionate to the diameter ^2, not the diameter ^3. As the diameter doubles, the space inside the magrid casing quadruples, allowing this squared scaling.
Another way of looking at it MAY be that the cusp hole sizes do increase at a Squared rate with linear dimensions, but the volume increases as the cube of the linear dimensions. Thus the cusp hole sizes/ volume, is still decreasing. How this would fit into the scaling laws is unknown. A large consideration is where thelosses dominate. Is it the 'funny' cusps, corner cusps, face centered point cusps?
Certainly the 'funny' cusp losses would decrease as the magnetic strength increases (at the same linear dimensions. The electron gyroradii would decrease and so the magnets could be placed closer together while maintaining the ~ 2-5 gryroradii needed for recirculation.
There are several things at play here, that is beyond my ability to analyze.
Dan Tibbets
The question about magnet strength vs magnet size is an issue which has confused me. Certainly, in order to maintain the same strength in the center of the face point cusps would seem to imply that the magnetic strength would need to increase proportionately faster than the machine size.
If the pertinate field strength is that at the border between the magnets, then this would not apply as that distance would not change*. This would allow magnet strength to scale machine size- in terms of diameter, not nessisarily in terms of area.
This seems possible to me , merely because Bussard, with his engineering background would have appreciated this, and would not have referred to 10 Tesla in a 3 meter machine, with scaling proportionate to the diameter ^2, not the diameter ^3. As the diameter doubles, the space inside the magrid casing quadruples, allowing this squared scaling.
Another way of looking at it MAY be that the cusp hole sizes do increase at a Squared rate with linear dimensions, but the volume increases as the cube of the linear dimensions. Thus the cusp hole sizes/ volume, is still decreasing. How this would fit into the scaling laws is unknown. A large consideration is where thelosses dominate. Is it the 'funny' cusps, corner cusps, face centered point cusps?
Certainly the 'funny' cusp losses would decrease as the magnetic strength increases (at the same linear dimensions. The electron gyroradii would decrease and so the magnets could be placed closer together while maintaining the ~ 2-5 gryroradii needed for recirculation.
There are several things at play here, that is beyond my ability to analyze.
Dan Tibbets
To error is human... and I'm very human.
Yes, I recall some head scratching when I read it as well. I am going to read it again and mull it over.
I also do not agree on recollection how he handled the loss mechanisms.
But in the end he was clear in his findings, albiet based on his assumptions going in.
I REALLY would like to see the WB7 & 7.1 package.
I also do not agree on recollection how he handled the loss mechanisms.
But in the end he was clear in his findings, albiet based on his assumptions going in.
I REALLY would like to see the WB7 & 7.1 package.
After ruminating some, I think the last paragraph of the preceding post is the pertinent point. Let me try to elaborate more clearly (hopefully).
Due to the inverse square law the opposing magnetic field strengths in the cusps will fall off at the square of the separation- ie the linear diameter of the magnet. Keeping the field strength the same while increasing the diameter 10X would result in a 100 fold weaker field- bigger cusp area. To compensate, you would need to increase the magnet strength 100 fold. This would result in a cusp size that was unchanged. This ignores most of the curvature of the concave field geometry that leads into the cusps with increasing linear dimensions. I can see this being a benefit, or more likely a neutral effect, but not a liability, if considered.
The important point is that this maintains the cusp size, while the rest of the area covered by that magnet increases by the area of the face of that magnet. , So the 'hole' area as a percent of the face is reduced a 100 fold.
Thus, the cusp confinement would be 100 fold better, not because you shrunk the cusp size, but because you maintained the cusp size, while greatly increasing the area that is shielded. So, if my reasoning is correct, compared to WB6, a 10 Tesla magnet strength in a 3 meter diameter Polywell would have an improvement of 100 X in cusp confinement, provided the same Wiffleball effect (appropriate voltage and current of electrons (and ions)) is maintained.
So, yes, the raw magnet strength (not the magnet strength / square of the diameter) scaling at the square of the linear dimensions provides the benifits claimed.
This benefit would result in the squaring of the density. And since the fusion rate goes up as the square of the density, this accounts for the B^4 scaling claimed for the system. Otherwise it would be described as the (B/Diameter ^2)^4 scaling.
I'm still foggy on just how the input loss scaling fits into this picture. R^3/R^1, fits but I'm not clear on how to describe it in my mind.
[EDIT] Actually, it occurs to me that if the density is squared, then the leakage through a given sized hole would also be squared- Yureka, I think I've got it (at least until somebody shoots me down)!
Dan Tibbets
Due to the inverse square law the opposing magnetic field strengths in the cusps will fall off at the square of the separation- ie the linear diameter of the magnet. Keeping the field strength the same while increasing the diameter 10X would result in a 100 fold weaker field- bigger cusp area. To compensate, you would need to increase the magnet strength 100 fold. This would result in a cusp size that was unchanged. This ignores most of the curvature of the concave field geometry that leads into the cusps with increasing linear dimensions. I can see this being a benefit, or more likely a neutral effect, but not a liability, if considered.
The important point is that this maintains the cusp size, while the rest of the area covered by that magnet increases by the area of the face of that magnet. , So the 'hole' area as a percent of the face is reduced a 100 fold.
Thus, the cusp confinement would be 100 fold better, not because you shrunk the cusp size, but because you maintained the cusp size, while greatly increasing the area that is shielded. So, if my reasoning is correct, compared to WB6, a 10 Tesla magnet strength in a 3 meter diameter Polywell would have an improvement of 100 X in cusp confinement, provided the same Wiffleball effect (appropriate voltage and current of electrons (and ions)) is maintained.
So, yes, the raw magnet strength (not the magnet strength / square of the diameter) scaling at the square of the linear dimensions provides the benifits claimed.
This benefit would result in the squaring of the density. And since the fusion rate goes up as the square of the density, this accounts for the B^4 scaling claimed for the system. Otherwise it would be described as the (B/Diameter ^2)^4 scaling.
I'm still foggy on just how the input loss scaling fits into this picture. R^3/R^1, fits but I'm not clear on how to describe it in my mind.
[EDIT] Actually, it occurs to me that if the density is squared, then the leakage through a given sized hole would also be squared- Yureka, I think I've got it (at least until somebody shoots me down)!
Dan Tibbets
Last edited by D Tibbets on Tue Mar 01, 2011 2:04 am, edited 1 time in total.
To error is human... and I'm very human.
Thanks, Betruger. The first one works better.
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I have removed my analysis; I made a basic goof-up that caused the whole thing to be wrong. Joel's density scaling is consistent with B ~ R.
However, I remain dubious about the conversion of the loss power to 3D. It doesn't seem right to me. I'll think about it.
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@D Tibbets: These are effective wiffleball-edge fields and not magnet surface fields. The power and gain calculations use B in the magnetic pressure equation to get density scaling. Also, you can back it out of Bussard's B ~ R assumption: conductor cross-sectional area increases as R^2, leading to B_close ~ R^2 for a given magnet type and distance from the middle of the conductor, but since the field at the centre of a current loop is inverse with R, the effective field at the wiffleball only scales with R (roughly). You can dodge this effect somewhat by switching from copper to superconductors, which is probably why Bussard and Nebel expected reasonably-sized net power machines...
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I'm also dubious about the dominance of ion losses observed in the simulations; this may indicate suboptimality in how the simulated Polywells were run... I was under the impression that the majority of the losses in the real machines were supposed to be electron current...
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I have removed my analysis; I made a basic goof-up that caused the whole thing to be wrong. Joel's density scaling is consistent with B ~ R.
However, I remain dubious about the conversion of the loss power to 3D. It doesn't seem right to me. I'll think about it.
...
@D Tibbets: These are effective wiffleball-edge fields and not magnet surface fields. The power and gain calculations use B in the magnetic pressure equation to get density scaling. Also, you can back it out of Bussard's B ~ R assumption: conductor cross-sectional area increases as R^2, leading to B_close ~ R^2 for a given magnet type and distance from the middle of the conductor, but since the field at the centre of a current loop is inverse with R, the effective field at the wiffleball only scales with R (roughly). You can dodge this effect somewhat by switching from copper to superconductors, which is probably why Bussard and Nebel expected reasonably-sized net power machines...
...
I'm also dubious about the dominance of ion losses observed in the simulations; this may indicate suboptimality in how the simulated Polywells were run... I was under the impression that the majority of the losses in the real machines were supposed to be electron current...
Last edited by 93143 on Tue Mar 01, 2011 3:12 am, edited 4 times in total.
I think what 93143 said is similar to what I was describing, though he used a little different and percise language to do so.
I agree that Joel Rogers simulation did not assume or provide for Wiffleball pinching to decrease electron losses. And perhaps more importantly, there was no provision for annealing to retard upscattered ion losses. This may account for the relatively high ion losses. It seems vaguely like what A. Carlson claimed in some of his arguments.
I now recall that I was disappointed with his size estimates, though I found it interesting that he felt breakeven could still be reached if the machine was scaled big enough, despite the lack of a Wiffleball effect and no annealing(?), and modest B field strengths.
Dan Tibbets
I agree that Joel Rogers simulation did not assume or provide for Wiffleball pinching to decrease electron losses. And perhaps more importantly, there was no provision for annealing to retard upscattered ion losses. This may account for the relatively high ion losses. It seems vaguely like what A. Carlson claimed in some of his arguments.
I now recall that I was disappointed with his size estimates, though I found it interesting that he felt breakeven could still be reached if the machine was scaled big enough, despite the lack of a Wiffleball effect and no annealing(?), and modest B field strengths.
Dan Tibbets
To error is human... and I'm very human.
I didn't say that. What I meant was that it's possible that the way the simulations were run (physical parameter choice and possibly startup procedure or even numerical parameters), the cusps didn't fully close. I didn't say his methodology excluded the possibility.D Tibbets wrote:I agree that Joel Rogers simulation did not assume or provide for Wiffleball pinching to decrease electron losses.
If collisions were allowed for (necessary to produce upscattering), then there should have been annealing, assuming the physical and numerical conditions were appropriately chosen. If they weren't, all bets are off...And perhaps more importantly, there was no provision for annealing to retard upscattered ion losses.
That 2:1 electron-to-ion ratio does look dubious, especially at nearly a tesla...
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I did the analysis wrong due to a scaling error right at the beginning, and have accordingly removed it. Joel's density ratio is, in fact, consistent with B ~ R, so if his answer is incorrect, the error is elsewhere. Unfortunately I have no more time to spend on this right now... sorry for pulling the rug out from under you...
"If collisions were allowed for (necessary to produce upscattering), then there should have been annealing..."
Perhaps. It depends on how he set up the equations. If he used one reaction space or zone for the entire analysis, then I don't think it would work. The spherical geometry needs to be taken into account, along with the different collisional crossections in the ion populations at different radii within the machine. As the speed increases with the the ions falling down the potential well, the Coulomb crossection needs to be adjusted. An integration would presumably do this, though it is probably complicated, depending on the starting parameters. Also, in addition to the collisionality adjustments, you have to account for the ion dwell time within each zone, and the thermalized energy spread as a function of the average ion energy in each zone . Finally you have to determine the density in each zone within this spherical geometry.
Several papers described this in a simplified manner where three zones were considered- the core, mantle and edge. This illustrated the relationships, though many more zones would be needed to accurately describe this dynamic action.
The starting (or cycle starting) conditions would ideally be an ion on the edge of the Wiffleball with a small energy spread and lateral movements that are defined by the thermalized distribution of the ions at this low energy zone. As they drop down the well they will speed up, and become more dense (depending on how good the confluence is on that single pass). These two competing processes determine the Coulomb scattering rate in each zone.
The question then becomes how may collisions (and the contributory significance of each collision) are needed to thermalize past some tolerable energy spread deep within the machine before the ion returns to the edge region. IE: does a high energy thermalization spread occur in one pass, as opposed to the hopeless question of whether this occurs over the lifetime of the ion before escape or fusion. Note that I said a high energy thermalization spread, not the low energy thermalization spread that is claimed to dominate to such an extent on the edge that indeed full thermalization around a low value does occur in this location on each pass of the ion.
Also, this argument can be applied to the electrons. Their low energy thermalization would dominate in the core, rather than the edge, and the dynamics would be different. I wonder how that would work out.
Then throw in considerations of the electrons being dragged along to a modest extent by the ions, the effects of resultant complex potential wells with virtual central anode formation, etc, and the dynamics become increasing complicated to model.
Dan Tibbets
Perhaps. It depends on how he set up the equations. If he used one reaction space or zone for the entire analysis, then I don't think it would work. The spherical geometry needs to be taken into account, along with the different collisional crossections in the ion populations at different radii within the machine. As the speed increases with the the ions falling down the potential well, the Coulomb crossection needs to be adjusted. An integration would presumably do this, though it is probably complicated, depending on the starting parameters. Also, in addition to the collisionality adjustments, you have to account for the ion dwell time within each zone, and the thermalized energy spread as a function of the average ion energy in each zone . Finally you have to determine the density in each zone within this spherical geometry.
Several papers described this in a simplified manner where three zones were considered- the core, mantle and edge. This illustrated the relationships, though many more zones would be needed to accurately describe this dynamic action.
The starting (or cycle starting) conditions would ideally be an ion on the edge of the Wiffleball with a small energy spread and lateral movements that are defined by the thermalized distribution of the ions at this low energy zone. As they drop down the well they will speed up, and become more dense (depending on how good the confluence is on that single pass). These two competing processes determine the Coulomb scattering rate in each zone.
The question then becomes how may collisions (and the contributory significance of each collision) are needed to thermalize past some tolerable energy spread deep within the machine before the ion returns to the edge region. IE: does a high energy thermalization spread occur in one pass, as opposed to the hopeless question of whether this occurs over the lifetime of the ion before escape or fusion. Note that I said a high energy thermalization spread, not the low energy thermalization spread that is claimed to dominate to such an extent on the edge that indeed full thermalization around a low value does occur in this location on each pass of the ion.
Also, this argument can be applied to the electrons. Their low energy thermalization would dominate in the core, rather than the edge, and the dynamics would be different. I wonder how that would work out.
Then throw in considerations of the electrons being dragged along to a modest extent by the ions, the effects of resultant complex potential wells with virtual central anode formation, etc, and the dynamics become increasing complicated to model.
Dan Tibbets
To error is human... and I'm very human.
The simulations were done with a particle-in-cell code. This is not a simple three-zone model or anything like that; it's a full 2D simulation (quasi-3D of a thin slice, as I understand it). Collisions happen where they happen, and cross section is (should be!) correctly modeled as a function of relative velocity.
If you represent the physics sufficiently well, you shouldn't need to "model" specific features. Of course, in this case the physics are rather difficult to represent adequately... Last time anyone heard from them, EMC2 seemed to have a lot more confidence in their scaling than Joel does, and they've done PIC simulations too...
If you represent the physics sufficiently well, you shouldn't need to "model" specific features. Of course, in this case the physics are rather difficult to represent adequately... Last time anyone heard from them, EMC2 seemed to have a lot more confidence in their scaling than Joel does, and they've done PIC simulations too...
Rick on simulation challenges:
http://blogs.knoxnews.com/munger/2011/0 ... ops-c.html
Maybe he can borrow this one. Then he could model those 3D shear flows for the cross-field diffusion.rnebel wrote:3-D Particle-in-cell is extremely expensive. Resolution goes like (N)**.5 where N is the number of particles. You have multiple timescales and multiple spatial scales to resolve. This means supercomputers.
http://blogs.knoxnews.com/munger/2011/0 ... ops-c.html
As I recall though, he dd eventually find some cold electron cusp-plugging. Are you guys on his mass email?DTibbets wrote:I agree that Joel Rogers simulation did not assume or provide for Wiffleball pinching to decrease electron losses.
I wonder how WB-8 is fitting their WB-7 models.rnebel wrote:we plan to be doing a lot more simulations over the next 2 years.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
his name doesnt appear as the company officer anymore... I mean they did finish making the WB8, if everything is still on track, then about less then 5 years until we really know for sure. All this NDA stuff and whatnot... it's all rather confusing. I wish they would just release it, if more people worked on the problem, then the problem should be solved quicker, i dont understand the reason to keep everything on lock down.Skipjack wrote:AFAIK, he is still with EMC2.
If he is not, then it is a sure sign that the polywell is going nowhere...
But the last information I had was that he is still with EMC2.
Throwing my life away for this whole Fusion mess.