Of Line Cusps
If I understand the cusp problem as described by Art, the wiffleball will have an irregular shape and ions can get out the cusps before they fuse. They could be replaced through injection if the loss rate isn't to rapid, unless the cusps do in fact get pinched off sufficiently during the formation. That's why I was hoping electrostatic fields could build up in the cusps, help push back on the ball and smooth it out.
CHoff
I'm positive the line cusps exist and I know electrons can get out via them. What I'm still not convinced of is that all that many of the electrons are lost, or that very many ions will be lured out that way.
The electrons have no reason to go to the walls, only to the magrid. Any ions outside the magrid will be lost, but I believe the number escaping can be reduced by making a somewhat deeper potential well and producing the ions a little deeper in it. If milk is sloshing out of your bowl, use a deeper bowl!
I'd rather avoid both electrons and ions outside the magrid as they encourage Paschen discharges.
The electrons have no reason to go to the walls, only to the magrid. Any ions outside the magrid will be lost, but I believe the number escaping can be reduced by making a somewhat deeper potential well and producing the ions a little deeper in it. If milk is sloshing out of your bowl, use a deeper bowl!
I'd rather avoid both electrons and ions outside the magrid as they encourage Paschen discharges.
The larger the tank in relation to the magrid, the less chance of discharge. Assuming the ions get to the wall they could be vacuumed up, filtered out and reused. Build the tank large enough and the ions will turn around and head back to the well. Tom, do you think the well forms from the inside pushing outward or the cusps in. From everything I've heard I assume the former.
CHoff
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Art Carlson
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Art, what would stop either the electrons or the ions that sneak out from sneaking back in on the return path, and the energy lost comes back in with them. You mentioned in another thread that brems has infinite free escape paths from any mag mirror m/c. I assume they never collide with anything or interact with each other on the way out. What stops ions or electons from having the reverse, at least a few free paths to r0 without collisions in between.
CHoff
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Art Carlson
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The electric charge on the magrid. If it pushes the electrons back in, then it can only pull the ions all the way out.choff wrote:Art, what would stop either the electrons or the ions that sneak out from sneaking back in on the return path, and the energy lost comes back in with them.
Or do you still have the picture in your head of flux loops connecting one hole with another? The central flux lines of the cusps (the four faces, eight corners, and 12 edges) are purely radial by symmetry. Their neighbbors within a gyroradius don't deviate enough to turn around before slamming into the wall.
Are you suggesting that the electron distribution will form saddle points in the potential well at the cusps? If so, what prevents us from having ions with a slightly lesser energy so they can't reach those saddle points?Art Carlson wrote:@Tom: No matter how deep the bowl is, electrons will form a trail through the cusps and out beyond the magrid. What is to keep ions from sneeking along this trail under cover of the electrons' charge?
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Art Carlson
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Yes, but you must have missed the calculation where I showed that a naked electron sheet is capable of producing a potential on the order of (kT/e)*(R/lambda_D). (R/lambda_D) is around 1000. That's big. It wins over your "slightly lesser energy" every hand. The electron sheet really, really wants those ions, and it will do whatever it takes to get them.hanelyp wrote:Are you suggesting that the electron distribution will form saddle points in the potential well at the cusps? If so, what prevents us from having ions with a slightly lesser energy so they can't reach those saddle points?Art Carlson wrote:@Tom: No matter how deep the bowl is, electrons will form a trail through the cusps and out beyond the magrid. What is to keep ions from sneeking along this trail under cover of the electrons' charge?
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Jeff Mauldin
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Alternate geometries
Pardon my naivete and ignorance here.
One comment Art Carlson made on a post was that one issue of going about things the way they are being done is that we don't have a good theoretical or simulation basis to look at multiple geometries and decide what might work best before we have the actual hardware.
Experimental results trump theory, of course (if they disagree), and we'll presumably know some results from the configuration Dr. Nebel and company have constructed at this point. That should be very useful information.
However, taking this criticism to heart, how well have other geometries been considered? I know there's been discussion of different polyhedral arrangements.
Here's an idea which occurred to me based on a comment somebody made (I think Art Carlson as well) about toroidal fields being an anathema here. I understand (hopefully correctly) that (1) tokamaks have problems partly because it's really hard to magnetically confine the positive ions which are massive and we have to get to a really high average temperature for some fusion to occur, (2) the polywell has the advantage of trying to magnetically confine much less massive electrons rather than positive ions (and the electrons hopefully induce the motion necessary on the part of the ions to result in fusion at or near the center of confinement, and high average temperature is not necessary), (3) the polywell has issues with losses of electrons (and quite possibly ions) through cusps in the magnetic confinement field (and thus wouldn't stick around sufficiently long to have fusion which results in greater energy out than in), (4) and there is a question of whether the ions would behave nicely and cycle back and forth through the middle or whether they take on some angular momentum which doesn't get removed, and thus they don't collide with each other often enough at the center to make the fusion work (I envision the ions orbiting the center rather than oscillating back and forth through the center). Obviously there are other issues, but these are the ones I was thinking about.
Here's one idea for an alternate geometry. Confine electrons using a toroidal magnetic field (maybe a large-in-size field) which does not (hopefully) have cusps for electrons to escape. Allow or inject ions into the region of electron confinement. If the behavior is polywell-like, the idea would be that the positive ions would oscillate about a line running through the center of the torus. They would, of course, have some velocity along the axis of the torus, but the relevant part of their motion would be back and forth from the inner edge of the torus to the outter edge of the torus. The big deficiency I see is that the ion convergence is distributed all around the line through the center of the torus, while in the polywell the ion convergence would hopefully be at a single point. But if the electron confinement could be made nearly lossless by having no magnetic field cusps, we might be able to let the ions oscillate a lot longer, waiting for the collisions to happen which result in fusion. (Also, I have no idea how hard it would be to create a truly toroidal magnetic field with no cusps.) Some of the angular momentum issues definitely still apply, but my naive hope would be these could be ameliorated by careful injection of the ions and also that the ion motion would tend to naturally give up some of the angular momentum (e.g. perhaps ion to ion collisions in the periphery might tend to reduce angular momentum more often than adding to it). You wouldn't have to raise the plasma to a high average temperature (hopefully) because the velocity of the ions necessary for the fusion would be produced by their oscillation about the center of the negative potential produced by the electrons, and you would be confining less massive electrons rather than more massive positive ions with the magnetic field.
Just kind of a wild idea I had. Is it worth even considering? Is it simply like something else already out there? Are there other viable geometries?
One comment Art Carlson made on a post was that one issue of going about things the way they are being done is that we don't have a good theoretical or simulation basis to look at multiple geometries and decide what might work best before we have the actual hardware.
Experimental results trump theory, of course (if they disagree), and we'll presumably know some results from the configuration Dr. Nebel and company have constructed at this point. That should be very useful information.
However, taking this criticism to heart, how well have other geometries been considered? I know there's been discussion of different polyhedral arrangements.
Here's an idea which occurred to me based on a comment somebody made (I think Art Carlson as well) about toroidal fields being an anathema here. I understand (hopefully correctly) that (1) tokamaks have problems partly because it's really hard to magnetically confine the positive ions which are massive and we have to get to a really high average temperature for some fusion to occur, (2) the polywell has the advantage of trying to magnetically confine much less massive electrons rather than positive ions (and the electrons hopefully induce the motion necessary on the part of the ions to result in fusion at or near the center of confinement, and high average temperature is not necessary), (3) the polywell has issues with losses of electrons (and quite possibly ions) through cusps in the magnetic confinement field (and thus wouldn't stick around sufficiently long to have fusion which results in greater energy out than in), (4) and there is a question of whether the ions would behave nicely and cycle back and forth through the middle or whether they take on some angular momentum which doesn't get removed, and thus they don't collide with each other often enough at the center to make the fusion work (I envision the ions orbiting the center rather than oscillating back and forth through the center). Obviously there are other issues, but these are the ones I was thinking about.
Here's one idea for an alternate geometry. Confine electrons using a toroidal magnetic field (maybe a large-in-size field) which does not (hopefully) have cusps for electrons to escape. Allow or inject ions into the region of electron confinement. If the behavior is polywell-like, the idea would be that the positive ions would oscillate about a line running through the center of the torus. They would, of course, have some velocity along the axis of the torus, but the relevant part of their motion would be back and forth from the inner edge of the torus to the outter edge of the torus. The big deficiency I see is that the ion convergence is distributed all around the line through the center of the torus, while in the polywell the ion convergence would hopefully be at a single point. But if the electron confinement could be made nearly lossless by having no magnetic field cusps, we might be able to let the ions oscillate a lot longer, waiting for the collisions to happen which result in fusion. (Also, I have no idea how hard it would be to create a truly toroidal magnetic field with no cusps.) Some of the angular momentum issues definitely still apply, but my naive hope would be these could be ameliorated by careful injection of the ions and also that the ion motion would tend to naturally give up some of the angular momentum (e.g. perhaps ion to ion collisions in the periphery might tend to reduce angular momentum more often than adding to it). You wouldn't have to raise the plasma to a high average temperature (hopefully) because the velocity of the ions necessary for the fusion would be produced by their oscillation about the center of the negative potential produced by the electrons, and you would be confining less massive electrons rather than more massive positive ions with the magnetic field.
Just kind of a wild idea I had. Is it worth even considering? Is it simply like something else already out there? Are there other viable geometries?
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ravingdave
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I have mentioned previously that the corner cusps resemble a reflex klystron, albeit with a magnetic field and without a cavity resonator.
A reflex klystron has a hot cathode,(source of electrons) a positively charged accelerator\ring grid, and a negatively charged repeller plate.
http://www.tpub.com/neets/book11/45d.htm
A polywell has a wiffleball (source of electrons) a positively charged magrid with a squarish shaped hole in the corner, and a negatively charged repeller grid. ( the grid outside the magrid which keeps electrons from seeing the +1-4 Megavolt charged collector.
Electrons attracted towards the positively charged hole in the cusps, will travel down the opening in the magnetic field, accelerating until they reach the midpoint, then deaccelerate all the way to the repeller grid, until they are finally attracted back to the positively charged hole.
As i've mentioned before, it seems to me they will either oscillate with a period equal to the electron transit speed, or they will bunch up and form a stationary cloud. Either way, it seems like the hole is going to get pluged by a "virtual electrode."
That's my take on it anyway.
David
A reflex klystron has a hot cathode,(source of electrons) a positively charged accelerator\ring grid, and a negatively charged repeller plate.
http://www.tpub.com/neets/book11/45d.htm
A polywell has a wiffleball (source of electrons) a positively charged magrid with a squarish shaped hole in the corner, and a negatively charged repeller grid. ( the grid outside the magrid which keeps electrons from seeing the +1-4 Megavolt charged collector.
Electrons attracted towards the positively charged hole in the cusps, will travel down the opening in the magnetic field, accelerating until they reach the midpoint, then deaccelerate all the way to the repeller grid, until they are finally attracted back to the positively charged hole.
As i've mentioned before, it seems to me they will either oscillate with a period equal to the electron transit speed, or they will bunch up and form a stationary cloud. Either way, it seems like the hole is going to get pluged by a "virtual electrode."
That's my take on it anyway.
David
There are some some geometrical requirements due to how the magnetic fields meet that only a few polygons fulfill; basically, only a truncube and a dodec are reasonable.However, taking this criticism to heart, how well have other geometries been considered? I know there's been discussion of different polyhedral arrangements.
I think there's a thread on toroidal Polywell here somewhere, if you're interested in why they're probably non-optimal.
The charge on the Magrid is positive. It doesn't pull on ions, but if an ion gets out, it's gone.The electric charge on the magrid. If it pushes the electrons back in, then it can only pull the ions all the way out.
Of course, if the Magrid is a Faraday cage then ions can't see the electrons outside it anyway and there's nothing to pull them out. But since the Faraday effect works by rearranging charges on the cage itself, they should still see the large positive charge on the cage itself and ions will be pushed in by it.
Art,
If I recall, Dr. Bussard estimated one in about three thousand passes across the interior volume of the magrid, an electron will sneak out a cusp. Evidently he expected most of those to make it back in. They carry full energy passing the magrid, but give up that energy moving away from the magrid. They're only going to waste significant energy if they give it up to the magrid. If the ion population is too high and the energies get down where recombination is likely, you could lose some that way, and ions with them.
The ions, as soon as they pass the magrid, are lost, and lost at full energy, accelerated by the electric field between the magrid and the walls. The electron population out there should be low enough that they can only abate the effect somewhat. I don't expect the electrons will "drag" ions out there ... the lumpy well boundaries will allow them to come somewhat further out from the center at the cusps than elsewhere, but if they are born sufficiently far away from the well, they should not leave unless they pick up substantial energy by collisions. Some will.
I'm presuming the electrons will form beams on all the faces and corners, and to some degree the line cusps, which will more or less mimic the incoming e-beams from the emitters, which would be space-charge limited by Poission's equation. If they have sufficient room, they may arch between cusps, but they could just as happily go out near the walls, turn around, and go back inside.
For proof, I defer to the particles themselves. Let's wait and see the results.
If I recall, Dr. Bussard estimated one in about three thousand passes across the interior volume of the magrid, an electron will sneak out a cusp. Evidently he expected most of those to make it back in. They carry full energy passing the magrid, but give up that energy moving away from the magrid. They're only going to waste significant energy if they give it up to the magrid. If the ion population is too high and the energies get down where recombination is likely, you could lose some that way, and ions with them.
The ions, as soon as they pass the magrid, are lost, and lost at full energy, accelerated by the electric field between the magrid and the walls. The electron population out there should be low enough that they can only abate the effect somewhat. I don't expect the electrons will "drag" ions out there ... the lumpy well boundaries will allow them to come somewhat further out from the center at the cusps than elsewhere, but if they are born sufficiently far away from the well, they should not leave unless they pick up substantial energy by collisions. Some will.
I'm presuming the electrons will form beams on all the faces and corners, and to some degree the line cusps, which will more or less mimic the incoming e-beams from the emitters, which would be space-charge limited by Poission's equation. If they have sufficient room, they may arch between cusps, but they could just as happily go out near the walls, turn around, and go back inside.
For proof, I defer to the particles themselves. Let's wait and see the results.
To my way of thinking, the center well will have a much higher negative potential than any field or electron sheet close to the magrid, the negative pull on the ions will always be stronger inward.
For electrons to escape the cusps they will have to hit them on a dead center straight path from r0, or a convergent path. Since our cusp problem is caused by a non convergent lumpy well the electrons will have off center curved paths with less energy than than a convergent well, harder to escape without getting caught on a field line.
The distance from r0 is less than r to any face and at least 1.414r to the corners. With a non convergent well the distance to the faces is even shorter but the length to the corners has to remain the same to keep an escape path, so the non convergent well would have to end up with an escape path twice as long as a face path.
Maybe an upscatter collision could get the electrons or ions up this escape path, its like a bullet hitting a bullet causes a dead center bulls eye. Maybe Annie Oakley could make the shot. As for a converged well, the well will be circular, farther away from the corners that our non converged well, with very tiny cusps. Even harder to escape.
For electrons to escape the cusps they will have to hit them on a dead center straight path from r0, or a convergent path. Since our cusp problem is caused by a non convergent lumpy well the electrons will have off center curved paths with less energy than than a convergent well, harder to escape without getting caught on a field line.
The distance from r0 is less than r to any face and at least 1.414r to the corners. With a non convergent well the distance to the faces is even shorter but the length to the corners has to remain the same to keep an escape path, so the non convergent well would have to end up with an escape path twice as long as a face path.
Maybe an upscatter collision could get the electrons or ions up this escape path, its like a bullet hitting a bullet causes a dead center bulls eye. Maybe Annie Oakley could make the shot. As for a converged well, the well will be circular, farther away from the corners that our non converged well, with very tiny cusps. Even harder to escape.
CHoff
Choff,
Pretty much. The density of electrons inside should be so much higher than those outside, I doubt the ions will be tempted much to go out.
As for the odds of ions colliding, even Annie would have a hard time hitting that target. The catch is, with something like 1e12 poor shots per cubic centimeter, somebody is bound to get lucky. And the odds of a fusion collision are even smaller, so if the fusion collisions don't happen, the whole idea is doomed.
The odds that bug me are background neutrals. There is nothing good to say about them. They're big, fat targets, and offer several ways to sap energy from the reactor. Charge exchange (fast ion and slow neutral produce slow ion and fast neutral) is one such route, and neither the magnetic nor electric fields can fix it. Neutrals don't care about cusps, line cusps, wiffleballs, beta ... they just drift in and cause trouble.
The lot of us together, including Rick and Art, are not clever enough to model this thing. We can't even agree on many of the basics. Only the particles can figure this out. Back to the lab!
Pretty much. The density of electrons inside should be so much higher than those outside, I doubt the ions will be tempted much to go out.
As for the odds of ions colliding, even Annie would have a hard time hitting that target. The catch is, with something like 1e12 poor shots per cubic centimeter, somebody is bound to get lucky. And the odds of a fusion collision are even smaller, so if the fusion collisions don't happen, the whole idea is doomed.
The odds that bug me are background neutrals. There is nothing good to say about them. They're big, fat targets, and offer several ways to sap energy from the reactor. Charge exchange (fast ion and slow neutral produce slow ion and fast neutral) is one such route, and neither the magnetic nor electric fields can fix it. Neutrals don't care about cusps, line cusps, wiffleballs, beta ... they just drift in and cause trouble.
The lot of us together, including Rick and Art, are not clever enough to model this thing. We can't even agree on many of the basics. Only the particles can figure this out. Back to the lab!