Hello,
I am looking for some basic, simple, direct definitions of some Polywell Terms. Maybe some of you can assist here.
1. How would you define the following words: Cusps, Mirror Ratio, Brillouin Limit and Weibel Instability?
2. Are there cusp planes? If yes, then should there be 6 cusp planes in the polywell? They would be shaped like volcanos: cones with flat tops and pits in the center. There would be 6 of these “volcanos” pointing into the center. Or are the cusps just lines? 14 lines – one for each corner and each side of the device.
3. How would you define mirror ratio? There is an equation for this - but I have it as a slightly different answer from the two sources I've checked.
4. Would you agree with the following definition for cusps? Cusps – These are lines of no magnetic field. They form when magnetic poles are placed opposite to one another or at an angle to one another. Inside the Polywell they represent holes in containment where particles can leak out from. There are 14 of them: one pointing at each corner and one pointing at each side of the containment field.
5. Can someone please provide me with a good definition of the Brillouin limit? As far as I can discern – this is a fundamental limit of a vacuum. You cannot pack anymore charged plasma into a given volume, past the Brillouin limit. Is that correct?
6. Can someone tell me what the Weibel Instability is? It forms when plasma has charge unequally spread-out. It is caused by electrostatic instability..... A similar instability is the counter streaming instability. That is where two charged beams pass close enough to one another to interact, and instability is formed. The interaction distance is the Debye screening length.
Questions
The primary argument on cusps has been between lines, points and "funny". The root of it all is where the opposing fields come together, they do no tmerge due to polarity, and thus a <most accurate word> "seam" occurs. The nature of the has been much debated. However, the easy answer is yes, there are corner cusps where three fields come together in a three way seam, and there are edge cusps where two fields come together. As polywell geometry is varied to other more polyhedral configurations, the cusp geometry would change as well in regard to how many fileds come together at the seam. Like any seam, it is not perfectly "water proof". Thus the loses as some electrons navigate their way to a critical point and gyrate to the "outside" field curvature and escape.2. Are there cusp planes? If yes, then should there be 6 cusp planes in the polywell? They would be shaped like volcanos: cones with flat tops and pits in the center. There would be 6 of these “volcanos” pointing into the center. Or are the cusps just lines? 14 lines – one for each corner and each side of the device.
Polywell is strictly persay a "mirror machine". It is mirror like, and thus as I understand does not fit standing mirror definitions. This has also been well debated without a clear resolution that I recall.3. How would you define mirror ratio? There is an equation for this - but I have it as a slightly different answer from the two sources I've checked.
No, see above. They are not holes as much as un-melded seams. The idea of wiffleball is a compression effect of these seams to significantly limit the opportunity for electrons to gyrate out.4. Would you agree with the following definition for cusps? Cusps – These are lines of no magnetic field. They form when magnetic poles are placed opposite to one another or at an angle to one another. Inside the Polywell they represent holes in containment where particles can leak out from. There are 14 of them: one pointing at each corner and one pointing at each side of the containment field.
Two points:
1. I thought the "Whifle ball" analogy meant that the containment still had holes. Probably 14 of them. One for each cusp. 6 for each side, 8 for each corner.
2. My definition of Weibel Instability - This happens in plasmas made of charged particles. It happens when one part of the plasma all moves in one direction. Typically this is the electrons, because they are smaller and move faster. When all the electrons move in one direction, it creates electrostatic waves in the plasma. These waves fight the tendency of the electrons to move in that direction. In Polywells, electrons supposedly recirculate along field lines generally pointed in one direction. It is unclear how this effect would play out, in a working polywell.
1. I thought the "Whifle ball" analogy meant that the containment still had holes. Probably 14 of them. One for each cusp. 6 for each side, 8 for each corner.
2. My definition of Weibel Instability - This happens in plasmas made of charged particles. It happens when one part of the plasma all moves in one direction. Typically this is the electrons, because they are smaller and move faster. When all the electrons move in one direction, it creates electrostatic waves in the plasma. These waves fight the tendency of the electrons to move in that direction. In Polywells, electrons supposedly recirculate along field lines generally pointed in one direction. It is unclear how this effect would play out, in a working polywell.
AND THE ARGUMENT RESUMES...ladajo wrote: However, the easy answer is yes, there are corner cusps where three fields come together in a three way seam, and there are edge cusps where two fields come together.
"Line cusps" are where two opposing fields meet. (And even the term "opposing" is liable to be mis-understood. Here I mean where two of the same polarity fields oppose each other.) A three way field would simply end the "line cusp". This is what happens in the current WB implementations of Polywell.
The term "Corner Cusp" is so fraught with mis-understanding that I don't use it. After all, is the user speaking of the corner of the cube projected by the torii (point cusp) or the vertex of a RECTIFIED cube Polywell (funny cusp)?
If you mean "radial" for that one direction, ok. But in no way is there a uniform direction for tangential field lines.mattman wrote: In Polywells, electrons supposedly recirculate along field lines generally pointed in one direction. It is unclear how this effect would play out, in a working polywell.
Re: Questions
No. It is a hole in the CONTAINMENT but no necessarily a place of no field. All it needs is for there to be no tangential field.mattman wrote:Hello,
4. Would you agree with the following definition for cusps? Cusps – These are lines of no magnetic field. They form when magnetic poles are placed opposite to one another or at an angle to one another. Inside the Polywell they represent holes in containment where particles can leak out from. There are 14 of them: one pointing at each corner and one pointing at each side of the containment field.
Where the torii come nearest each other in the WB series units, the (assumed in pointing) fields are squeezed together very strongly while trying to exit between the torii. But, while the fields there are very strong, they are radially directed. This provides no containment. Not hole in FIELD, but a hole in containment. EXCEPT when four or more (even number) fields meet, there is actually a hole. This is called a funny cusp. It is part of the theoretical basis of the Polywell.
By the way, check out the Polywell Wiki FAQ at:
http://www.ohiovr.com/polywell-faq/inde ... =Main_Page
http://www.ohiovr.com/polywell-faq/inde ... =Main_Page
Whether a cusp is described as a seam, hole or otherwise, whether the electron motion is considered as a gyro motion a direct linear bouncing motion, the net effect is similar. T, thus Bussard's use of the "Wiffle Ball" as an analogy serves to illustrate the properties of the 'hole' to total surface area topology.
These holes could be considered as round holes, triangular holes or rectangular holes. What is important is the net dimensions of these holes as a percentage of the total surface area individually and summed. Since the corner cusps have most of their loss area near the center of the cusp, they are sometimes described as point cusp like. With the early Polywells where the coils actually touched, these corner cusps were well defined. But, with the separation introduced with WB6, these corner cusps actually communicate with all of the other corner cusps, so there is some ambiguity about where to draw the borders. with the interconnecting nubs in WB6 and 7.0 these can serve as borders. With WB7.1 (?) and WB8 where standoffs from the vacuum vessel walls are used (basically far enough away from the cusps that they are independent (almost) of the cusps ) leaves the magnet closest approach regions open and communicating with the next cusp. With more magnets these 'semi linear cusp' portions become less significant compared to the corner cusps, and the corner cusps become smaller and more numerous. Perhaps more importantly, the central true point cusps become smaller provided the B field strengths are unchanged. Whether the smaller but more numerous corner cusps, the smaller but more numerous central point cusps, the shorter but more numerous line like cusps (evolved from the funny cusps which I believe were the touching points for the early theoretical zero thickness electromagnets) improve the electron confinement by 3-5 X as claimed by Bussard is due to one or several or all of these cusp types is unknown.
Should these short line like cusp regions between magnets be considered as separate tiny cusps or just be considered as part of the edge or corner cusps?
As far as various definitions, there is a Polywell Wiki that has a list of definitions.
[EDIT] Of course when talking about the cusp hole or seam size compared to the charged particle in question, the use of gryromotion chariteristics are essential in differentiating the confinement chariteristics of electrons compared to ions.
Dan Tibbets
These holes could be considered as round holes, triangular holes or rectangular holes. What is important is the net dimensions of these holes as a percentage of the total surface area individually and summed. Since the corner cusps have most of their loss area near the center of the cusp, they are sometimes described as point cusp like. With the early Polywells where the coils actually touched, these corner cusps were well defined. But, with the separation introduced with WB6, these corner cusps actually communicate with all of the other corner cusps, so there is some ambiguity about where to draw the borders. with the interconnecting nubs in WB6 and 7.0 these can serve as borders. With WB7.1 (?) and WB8 where standoffs from the vacuum vessel walls are used (basically far enough away from the cusps that they are independent (almost) of the cusps ) leaves the magnet closest approach regions open and communicating with the next cusp. With more magnets these 'semi linear cusp' portions become less significant compared to the corner cusps, and the corner cusps become smaller and more numerous. Perhaps more importantly, the central true point cusps become smaller provided the B field strengths are unchanged. Whether the smaller but more numerous corner cusps, the smaller but more numerous central point cusps, the shorter but more numerous line like cusps (evolved from the funny cusps which I believe were the touching points for the early theoretical zero thickness electromagnets) improve the electron confinement by 3-5 X as claimed by Bussard is due to one or several or all of these cusp types is unknown.
Should these short line like cusp regions between magnets be considered as separate tiny cusps or just be considered as part of the edge or corner cusps?
As far as various definitions, there is a Polywell Wiki that has a list of definitions.
[EDIT] Of course when talking about the cusp hole or seam size compared to the charged particle in question, the use of gryromotion chariteristics are essential in differentiating the confinement chariteristics of electrons compared to ions.
Dan Tibbets
To error is human... and I'm very human.
This may be a good time to ask a question concerning cusp size/ width -vs- B field strength.
When the B field is doubled in strength, how does the cusp size change? When the distance between the magnets is halved, how does the cusp size change?
Does inverse square relationships apply, or is it more complicated?
If same strength magnets are moved to 1/2 of their prior separation, does the effective cusp diameter decrease to 1/4th in the one dimension. Does it decrease to 1/16th in 2 dimensions ( considering a ring magnet)?
Dan Tibbets
When the B field is doubled in strength, how does the cusp size change? When the distance between the magnets is halved, how does the cusp size change?
Does inverse square relationships apply, or is it more complicated?
If same strength magnets are moved to 1/2 of their prior separation, does the effective cusp diameter decrease to 1/4th in the one dimension. Does it decrease to 1/16th in 2 dimensions ( considering a ring magnet)?
Dan Tibbets
To error is human... and I'm very human.
Re: Questions
The "funny" cusp was so named by reviewers in 1987 because it's theoretically a hole of zero field over zero radius. But this requires zero cross-section coils, so the practical equivalent presumably have some finite radius.
Here's the patent comments on electron and ion annealing.
http://www.freepatentsonline.com/y2008/0187086.html
Given the claims of "excellent" confinement, development of high loss regimes due to electron thermalization is presumably not a problem in WB-8 (though this is still a question for larger machines where electron lifetimes are longer). Ion annealing is still something of an open question given that we don't know the WB-8 output power, but getting ion focus is not as critical.
Here's the patent comments on electron and ion annealing.
http://www.freepatentsonline.com/y2008/0187086.html
One might raise questions concerning the ability of the device to maintain its quasi-monoenergetic energy distributions among the ion and electron populations. These are, of course, driven by the dynamic injection of fast electrons, and their subsequent loss to structures. One might be concerned that if electrons live sufficiently long in the machine they could become Maxwellianized (thermalized) and develop high energy loss distributions. However, this has been found not to be the case. The same arguments have been found for the ions, as well. Detailed analyses show that Maxwellianization of the electron population will not occur, during the lifetime of the electrons within the system. This is because the collisionality of the electrons varies so greatly across the system, from edge to center. At the edge the electrons are all at high energy where the Coulomb cross-sections are small, while at the center they are at high cross-section but occupy only a small volume for a short fractional time of their transit life in the system. Analysis shows that this variation is sufficient to prevent energy spreading in the electron population before the electrons are lost by collisions with walls and structures.
Similarly, for ions, the variation of collisionality between ions across the machine, before these make fusion reactions, is so great that the fusion reaction rates dominate the tendency to energy exchange and spreading. Ions spend less than 1/1000 of their lifetime in the dense, high energy but low cross-section core region, and the ratio of Coulomb energy exchange cross-section to fusion cross-section is much less than this, thus thermalization (Maxwellianization) can not occur during a single pass of ions through the core. While some up- and down- scattering does occur in such a single pass, this is so small that edge region collisionality (where the ions are dense and “cold”) anneals this out at each pass through the system, thus avoiding buildup of energy spreading in the ion population. Both populations operate in non-LTE modes throughout their lifetime in the system. This is an inherent feature of these centrally-convergent, ion-focussing, driven, dynamic systems, and one not found (or even possible) in conventional magnetic confinement fusion devices.
Given the claims of "excellent" confinement, development of high loss regimes due to electron thermalization is presumably not a problem in WB-8 (though this is still a question for larger machines where electron lifetimes are longer). Ion annealing is still something of an open question given that we don't know the WB-8 output power, but getting ion focus is not as critical.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
And, as previously discussed, the question remains (for us at least), does the improvement in confinement increase the issue?At the edge the electrons are all at high energy where the Coulomb cross-sections are small, while at the center they are at high cross-section but occupy only a small volume for a short fractional time of their transit life in the system. Analysis shows that this variation is sufficient to prevent energy spreading in the electron population before the electrons are lost by collisions with walls and structures.
Do you mean the confinement improvement from WB-6/7 to WB-8? Or just generally with increased B?
From that excerpt I get the impression confinement is itself in some respects an inverse function of the electron thermalization, so that would seem to be a self-limiting problem, though I suppose it's possible they reach an equilibrium at unacceptable losses. I guess the other issue there is the electron optics, which could decrease ion focus and therefore power output unacceptably.
That makes me wonder though: did Bussard really extrapolate confinement from WB-6, or was his loss calculation from theory? IIRC when you calculate the losses from WB-6 and extrapolate them to 100MW output, you get more than the 10MW that's been suggested as input power (I remember being mildly disturbed by this). I suspect (one or both):
1) he assumed he could do better than WB-6
2) his confinement scaling law was optimistic
A lot of people have certainly argued #2. Bussard of course thought he was getting B**.25*r**2. And Rick said of the WB-7 design that confinement was only "okay" and they wanted it to get to "good" (and we hope the reported "excellent" is a value on the same scale). The most likely scenario to me is that loss scaling isn't quite as good as Bussard hoped, but WB-8 is better than WB-6 because of the design change.
(edited for missing words)
From that excerpt I get the impression confinement is itself in some respects an inverse function of the electron thermalization, so that would seem to be a self-limiting problem, though I suppose it's possible they reach an equilibrium at unacceptable losses. I guess the other issue there is the electron optics, which could decrease ion focus and therefore power output unacceptably.
That makes me wonder though: did Bussard really extrapolate confinement from WB-6, or was his loss calculation from theory? IIRC when you calculate the losses from WB-6 and extrapolate them to 100MW output, you get more than the 10MW that's been suggested as input power (I remember being mildly disturbed by this). I suspect (one or both):
1) he assumed he could do better than WB-6
2) his confinement scaling law was optimistic
A lot of people have certainly argued #2. Bussard of course thought he was getting B**.25*r**2. And Rick said of the WB-7 design that confinement was only "okay" and they wanted it to get to "good" (and we hope the reported "excellent" is a value on the same scale). The most likely scenario to me is that loss scaling isn't quite as good as Bussard hoped, but WB-8 is better than WB-6 because of the design change.
(edited for missing words)
Last edited by TallDave on Mon Oct 03, 2011 6:03 pm, edited 1 time in total.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
When the word confinement is used concerning electrons, I think we might need to think a little differently. Electrons are not necessarily confined in the classical since. They are allowed to circulate. By "allowing" them to circulate outside the magrid, their lifetimes are increased. So, you could say their "confinement" is extended by allowing circulation. It was this supporting circulation that was Bussard's ah ha moment (specifically, forming the elements of the magrid to reduce the intersection of magnetic lines of force with any metal, thus increasing lifetime, allowing more circulation, and therefore "more confinement".) So, a 1987 patent that talks about lost by collisions with walls and structures does not include the idea of circulation.
So, my thinking is the "excellent confinement" comment is about ions and Bussard knew what he was talking about. No assuming, no being overly optimistic.
So, my thinking is the "excellent confinement" comment is about ions and Bussard knew what he was talking about. No assuming, no being overly optimistic.
Famous last words, "Hey, watch this!"
This is the lines of my thinking. I agree with gbrown that the patent is from pre-Ah-ha!, but in that, since ah-ha, we have not seen a good public revisit to scaling. The re-circ (or oscillating as our majority seems to think) is obviously important. But as we increase e- population and drive levels, it does beg the question. But, I remain faithful that excellent confinement means exactly what it says.I suppose it's possible they reach an equilibrium at unacceptable losses
As for Ions, and ion to e- interactions, and the whole equilibrium discussion, as well as annealing, it remains to be seen in the public realm what they are seeing. I am thinking that they will eventually need to re-write some of the standing papers, and may have already started.
In any event, I remain skeptically optimistic. They are doing good science IMO, just not sharing it so much.