magrid configuration brainstorming

[D Tibbets]

Of course there are electrons trapped on magnetic field lines. In an ideal situation all of the electrons may rebound from the steep B- field gradiant at the Wiffleball border, but in reality there will always be electrons that have assumed a vector and speed (due to chaotic collisions) that allows them to be trapped. If nothing else, an electron that has just turned and is traveling back towards the center could hit an outbound electron and the first electron could be knocked back deeper into the B-field lines where the gradient allows for complete gyro orbits. Otherwise, Bussard would not have talked about cross field transport being the absolute limit on the performance of the Wiffleball trapping factor. And, the concept of containing only electrons (instead of both electrons and ions) against this loss mechanism (ExB drift) would not make any sense for claimed advantage of the Polywell. The apparent reason the ions do not suffer the same fate is the whole basis of the polywell. The negative space charge prevents the vast majority of the ions (over their expected lifetime before fusion) from experiencing this otherwise statistically unavoidable magnetic entrapment.
The speed at which newly injected (or recirculated) electrons become trapped may contribute to the the shape of the potential well. But, as A. Carlson insisted, and as I eventually discovered was also expected by Bussard, the potential well is square, until the ion dynamics start tugging some of the electrons along with them towards the core, at which point a parabolic well forms and because the plasma is not strongly coupled (but is weakly coupled?) a smaller virtual central anode may form. This implies that in the absence of ions, most of the electrons spend most of their time near the Wiffleball border- either rebounding off the border(perhaps at shallow angles), or actually traped on superficial field lines.The fact that negative space charge (mostly) decouples the ions from the magnetic field has to have an effect of increasing the coupling of the electrons to the magnetic fields. The same charge and vast inertia differences between the ions and electrons is what allows this tradeoff to be useful. * The smaller inertia of the electrons is what allows them to have smaller gyroradii and thus longer transport times through the magnetic fields.

Concerning the small square openings, I still believe they are essentially folded line cusps. Where the line cusps end on the corners of the metal there is an exposed area equal to the width of the cusp. The saving grace may be that these X (?) cusps are small in length. Due to another form of magnetic transport- drift in the equatorial direction instead of just N-S or up and down) the long cusps between corners in a WB6 type geometry acts as a collection area towards the nub. So a statistical probability exists that an electron transiting the cusp may find it. Whth the shorted length represented by the small X cusp, the collection area is smaller, so the losses would be proportionately smaller (?). The limit to how small you could make this x cusp is governed by the same considerations that Bussard used for WB6. There has to be enough separation between even well shielded surfaces so that the ExB drift does not allow the electrons to reach the metal (~ 3-5 gyro radii instead of 1.000001 gyro radii), which is based on the time they are in the cusps and the frequency of electron electron collisions in that area.


* This is also the basis of my disagreement with A. Calson about cusp flows being ambipolar. Because the electrons are always maintained in excess, the negative space charge inside prevents the ions from being dragged by the electrons exiting the cusps. There may be some weak coupling between the electron flows and the ion flows but this is is exceeded by the space charge effects . The reasons experience some significant tugging towards the center, but the ions do not experience significant tugging into the cusps is is due to the inertia difference and the time/ dynamic relationships between their relative speeds. A single ion can "capture " a single electron and match it's speed and vector to itself much easier than the reverse (within the brief time frame that the two particles are close enough together that this coupling can dominate over the space charge).

Dan Tibbets

[KitemanSA]

Of course there are electrons trapped on magnetic field lines. In an ideal situation all of the electrons may rebound from the steep B- field gradiant at the Wiffleball border, but in reality there will always be electrons that have assumed a vector and speed (due to chaotic collisions) that allows them to be trapped. If nothing else, an electron that has just turned and is traveling back towards the center could hit an outbound electron and the first electron could be knocked back deeper into the B-field lines where the gradient allows for complete gyro orbits.

I agree that electrons can BECOME trapped on a mag-field line. I just don't think it can STAY trapped for long. To be trapped, the curvature of the line must be much gentler than the gyro curvature. And between cusps, this might be the case. But AT the cusps, where all field lines lead, there is a VERY sharp corner and most of the electrons must surely leave the line; no?

Otherwise, Bussard would not have talked about cross field transport being the absolute limit on the performance of the Wiffleball trapping factor.

I was under the impression that the cross field transport he referenced was that which happened while exiting a cusp, the only place that electrons follow field lines thru great changes in dynamic regieme. I could be wrong here.

[D Tibbets]

Speaking of bowed sides. I have been considering the idea of bowing the magrid until the ends of the grids meet at the top and the bottom. Start with a WB6 truncated cube. Discard the top and bottom grids. Lengthen the side grids till they are ~ 2 times as tall as wide.* Then bow them inward until they almost meet at the top and bottom. You end up with a 4 sided near sphere shape. The advantages is that you only have 4 magnets instead of 6. It is more spherical. And, there are fewer cusps. There are 4 point cusps instead of 6. These point cusps may be larger, but I don't think they would exceed the area of the original 6 point cusps. There would be two corner cusps instead of 8. The resultant individual corner cusp area may be modestly larger (or not). But the number advantage would be significant. The side 'funny' cusps would be longer individually, but the total would (I think) be the same. So, I think you would have a ~ 4 X advantage in corner cusp losses, while the other cusp losses would be unchanged. I Think this might result is and ~ 4 x advantage in the cusp confinement dominated Wiffleball trapping facter ( the corner cusps are the most significant for losses) and this would result in a ~ 4X increase. This would translate into a 4X density advantage and a 16X fusion rate advantage. Multiply that by the 3-5X advantage Bussard expected from a more spherical shape and the net gain might be ~ 45- 75X.

You would need perhaps two connecting nubs on each side of the magnets- one perhaps neat each end of the grid, but the total nubs in this case would be 8, compared to 12 in WB6. This represents a 1.5X gain in the exposed metal considerations, With separate stand off supports, the number of legs might be 16, instead of the 24 in a WB6 truncated cube design- the same gain.

With the two (top and bottom) corner cusps dominating the cusp losses (IE: the alpha escape routes), there may be advantage in designing a conversion system for a P-B11 reactor.


* I say ~ 2X the height for the pre bent grids, because as the ends approach each other on the top and bottom, the opposing fields may dispace each other to a degree. In order to get a near spherical shape to the internal B-field edge, the physical magrid shap may need to be elongated somewhat ( or perhaps even shortend a bit, depending on how close together they approach each other and the angles) . Perhaps as much as 1.5 times as tall as wide for the bowed physical grids would be required.

This closure angle and overall (vs width) height may be adjusted somewhat to maximize alpha collection advantages (make the end cusps more leaky) . This would compromise containment advantages somewhat, but if my estimates are real, you are starting with an ~ 4X advantage, so there is some wiggle room. If your priority is to maximize alpha (or other charged fusion ion) flows through the ends of the device (like in a rocket engine- use one side for direct conversion, and the other end for thrust) you could trade off size for this polar flow advantage. Even for stationary reactors this might give enough direct conversion engineering advantages that it is worth the larger size (espepecially as that would also ease other engineering concerns).

[EDIT] I don't think bowing the sides would result in concave towards the center magnetic fields. Though this concern might require the the pre bowed length be be a little longer to prevent the deformations of the opposing fields on the ends resulting in this problem . Or instead of increased length, a shallower closure angle (say each side bowed inward ~ 88 degrees instead of 90 degrees); or a combination of both might be used.

Dan Tibbets

[D Tibbets]

Of course there...

I agree that electrons can BECOME trapped on a mag-field line. I just don't think it can STAY trapped for long. To be trapped, the curvature of the line must be much gentler than the gyro curvature. And between cusps, this might be the case. But AT the cusps, where all field lines lead, there is a VERY sharp corner and most of the electrons must surely leave the line; no?

Otherwise, Bussard would not have talked about cross field transport being the absolute limit on the performance of the Wiffleball trapping factor.

I was under the impression that the cross field transport he referenced was that which happened while exiting a cusp, the only place that electrons follow field lines thru great changes in dynamic regime. I could be wrong here.

Both of your point sound reasonable, at least when talking about single particles. I suspect the picture is much more complex when talking about the dynamic chaos within the Polywell. I don't know what the curvature of the B-field at a cusp throat might be. Presumably fairly acute, but the electron gyroradii is also very short. And if the electrons escapes much past the very beginning of the cusp throat, it will fly to the opposite side of the cusp, where it will be captured again or escape from again, and fly to the opposites side of the cusp, where... In effects, the behavior might be ~ the same as it would be if you considered the electron captured on only one side of the cusp.

If the cusp escape path represents only ~ 1/ 10,000th of the surface area of the Wiffleball, then the exposure of the electrons to collision induced ExB drift (or should I say diffusion?)in the cusps is proportionatly less, then I would expect the cusp contribution to be very small, everything else being equal. Admittedly, the cusps are three dimensional in area, while the surface exposure to the core is essentially 2 dimensional (this is what determines the loss exposure ratio I mentioned above), but, unless the density of electrons is much greater here than in the rest of the Wiffleball surface, I don't think the difference could be made up.
Remember ExB drift is not the same as bouncing/ oscillating back and forth along a field line. Any time there is a coulomb collision between a trapped electron and another electron, it can be knocked one gyroradii deeper into the magnetic field. How this is modified if the electron reaches a cusp before being knocked all the way to the magnet is surely complex. I guess that the lower speed electrons would have a greater chance of diffusing to a magnet surface before reaching the cusp, especially as these electrons would probably be more likely to reverse as they approached the acute curvatures of the magnetic fields in the cusp throats. Once in the cusps, the behavior of these deeply embedded electrons is uncertain (for me). A hint that a significant portion of the electrons , especially those deeply embedded in the magnetic fields are not completely freed from magnetic effects upon recirculation, is that even the newly injected electrons carefully aimed down a cusp throat only obtain ~ 80% (well depth) of the potential of the injected electrons.

Certainly, in the cusps, the Wiffleball border can be much closer to the physical grid, but the magnetic fields are also more compacted/ strong in these regions, so the gyro radii jumps would be proportionately smaller. I assume the 3-6 gyro radii separation Bussard chose was a compromise. Increased widening would decrease the diffusion losses in the cusps per electron transit, but the total number of electrons transiting the cusps would also increase. This compromise distance is presumably a minimum between these competing conditions. And, this is irrelevant to the same processes in other areas of the Wiffleball ( other areas are contributing much less to losses)- until such time as cusp losses and compensating recirculation results in confinement efficiency approaching that of the ExB drift mediated confinment efficiency of of the rest of the Wiffleball. At that point you have reached the maximum efficiency obtainable, even if you had a cuspless magnetic confinement system for electrons.

PS: to clarify, I am not saying that cusp losses match diffusion losses in a WB4 type machines. The collisions on unprotected surfaces (grids, nubs, walls, etc) dominate. In WB 4. In WB6 these direct collision losses were improved to the extent that with recirculation, the losses were improved ~ 10X. Based of comments in the 2008 patent, I'm guessing that this was still 10_100 times worse than the total diffusion losses over the rest of the Wiffleball. But these were still losses. They are ignored though as they contribut little to the total. As the collisional losses are decreased through improvements of shielding, etc. the ExB drift losses over the entire machine become the limiting factor.

Sheesh, now I'm confusing myself. Perhaps a better short answer would be :
The manipulation of the cusps serve two purposes. First, to contain the average electrons as well as possible so that the containment is as close as possible to that represented by an imaginary cuspless sphere where ExB drift is the limiting factor. But, at the same time, maintaining the very important property of allowing the bad upsecttered electrons to escape quickly, before they can heat the general population of electrons. This second consideration is very important.


Dan Tibbets

[KitemanSA]

Dan:
Re: Popping off a field line at a cusp:
I see two extremes and a somewhere in between.
IF an electron reaches a cusp that has so tight a corner that the electron pops off immediately it seems that it would continue on across the cusp mouth and be re-captured on the other side to be trapped for the next segment. At that point it is subject to the drift of which you speak.
IF an electron reaches a cusp that is gentle enough the electron will follow the line thru the cusp and be recirculated.
If an electron reaches a cusp that is somewhere in between it will make it part way around the corner, pop off, travel across the mouth at an angle and be reflected like a typical cusp containment system, resulting in an electron that is now bouncing back and forth thru the core. Only the first, (unlikely?) situation keeps the electron trapped for any significant length of time. At least that is my guess. Yes, I said guess.

My guess would also be that the rate of drift accross the ball would be somehow inversely proportional to the number of passes an electron can be expected to make without collisions, and wasn't that a fairly high number?

[D Tibbets]

The mean free path between Coulomb collisions will be ~ 0.1 to 100 mm, depending on the density

http://en.wikipedia.org/wiki/Mean_free_path

The mean free path till fusion will be much longer, probably in the range of kilometers for a Polywell.

Making some assumptions of electron speeds of 10^7 M/s (average speed along a field line), 1 meter between cusps,and 0.1 M MFP, then the electron would be bumped ~ 10 times during its spiral path betwen cusps. If all of these bumps resulted in 1 gyro raddius displacements deeper into the magnetic field, then ~ 10 gyro radii, or ~ 1 cm(?) depth would be needed to prevent s significant number of electrons from hitting the magrid. If the electrons mirrors back (reverses direction on the field line before exiting a cusp and being exposed to the recirculating potential, then the effective distance/ time it spends in the magnetic field can be much larger than the minimum of ~ 1 meter. In the case of a closed box machine like WB5, the electrons would not recirculate at all, so their lifetime would depend entirely on the Wiffleball cusp confinement time. If WB5 confinement was ~ 1000 passes, WB4 was 10,000 passes, and WB6 was 100,000 passes. The 1000 passes in WB5 would have to be either bouncing around inside the Wiffleball or mirroring back and forth on a field line . I don't know what the proportions are but for this argument, I will assume that on average an electron will rebound ~ 100 times before being trapped, and once trapped it does not escape (which is why I am using this example of a non recirculating machine as I'm guessing recirculation frees the trapped electron, or at least boosts it to a higher level in the magnetic field). With the gryo radius of ~ 1 mm used above and the 10 passes (10/1000 total passes) between cusps would result in ~ 10 cm of EXB drift. I'm uncertain how this decay would progress, but essentially 1 percent of the electrons would be lost to cross field diffusion for each 1000 passes. 1000 passes at ~ 10^7 m/s gives a diffusion limited lifetime of ~ 10 M / 10^7 M/s, or ~ 1 microsecond once the electron is trapped. As the process continues I guessing that ~ 50 % of the electrons would be lost in ~ 50 MS due to cross field diffusion alone. Of course this is a worse case scenario. The random walk process may result is a number closer to ~ 0.1 millisecond. If this sloppy analysis has any validity, it gives a baseline for the best possible confinement. Of course my numbers are guesses,. The actual gyro radius may be smaller than 1 mm, the magnetic field thickness may be more than 10 cm (in a 2 meter diameter machine like this example), etc. The diffusion lifetime may be as much as several orders of magnitude either way. And with stronger magnetic fields the diffusion lifetime may be several orders of magnitude greater. And if recirculation resets things, the net diffusion times may be an ~additional order of magnitude greater. Presumably the mentioned electron lifetimes of a few seconds in a large machine with strong magnetic fields and very good recirculation that approach the diffusion containment efficiency seems possible.


I have wondered if bouncing off the curved magnetic field surfaces, after several bounces could result in the particle traveling more towards the center ( like multiple bounces on a billiard table). But Bussard mentioned ions reaching the magnetic field and bouncing off tend to lose central focus. I assume this is because the low speed, high coulomb collision crossection in this (annealing) region dominates so that the multiple bounces off the magnetic surfaces do not have a net corrective action. I don't know if the electrons which are traveling faster in this edge region would behave differently.

Dan Tibbets

[Randy]

Speaking of bowed sides. I have been considering the idea of bowing the magrid until the ends of the grids meet at the top and the bottom. Start with a WB6 truncated cube. Discard the top and bottom grids. Lengthen the side grids till they are ~ 2 times as tall as wide.* Then bow them inward until they almost meet at the top and bottom. You end up with a 4 sided near sphere shape. The advantages is that you only have 4 magnets instead of 6. It is more spherical. And, there are fewer cusps. There are 4 point cusps instead of 6. These point cusps may be larger, but I don't think they would exceed the area of the original 6 point cusps. There would be two corner cusps instead of 8.
Dan Tibbets

I really 'LIKE' this idea. Thanks for the contribution.
~Randy

[WizWom]

Just for comparison, here is the same four coil model shown with all north poles facing toward the core:

Notice the line cusps between the individual coils.

The cusps are not the issue. Not the difference in magnetic field in the center. You don't want much magnetic field in the middle of a polywell; you want it to be as close to zero over as large a region as possible.

[MrBill]

Randy -- I have nothing to add to your idea except to bump it for further consideration. The response has been good but not to the level I think it deserves. In case any one missed it -- Randy suggested a configuration where not all the coils were of the same polarity. I've been lurking for some time with nothing to contribute, but one thing I've noticed is that all the discussion is for coils of the same polarity (north pointing in or out) and no significant discussion of the case when half the coils are of opposite polarity. This could be a bogus idea or it could be a game changer -- and I think some thoughtful consideration may be a value.

In a previous lifetime I worked on traveling wave tubes and we used a series of magnets of opposite polarity to focus the electron beam to the center of the tube. The benefit was the change in magnetic field tended to focus the beam where if the magnets were all of the same polarity the electrons were not focused periodically and would drift away from the center of the tube eventually contacting the coil. Turning something on it's head sometimes provides an insight that solves the problem.

Dan -- when I was in high school I read about fusion in Encyclopedia Britanica (remember when encyclopedias came as books on paper?). One of the concepts for magnetic confinement was the more or less spherical field produced by the same geometry you suggest, but with the east-west coils of reverse polarity to the north-south coils (two of the coils with south pointing inward and the other two with north pointing inward). The current flow around the confinement volume wasn't really in separate coils -- rather the current flowed in the same geometry as you see in the stitches on a baseball (hence the subject). In many respects similar to Randy's suggestion if you wrap all the edges of his sketch around so they meet. For the last fifty years whenever I have been reminded of it I've tried to imagine how the magnetic field would look by using the right hand rule sliding around the stitches on a baseball and end up with my fingers all in a knot. Has anyone else heard of this idea for magnetic confinement?

Randy -- perhaps you could model it? My fingers will forever thank you.

Bill

[DeltaV]

For the last fifty years whenever I have been reminded of it I've tried to imagine how the magnetic field would look by using the right hand rule sliding around the stitches on a baseball and end up with my fingers all in a knot. Has anyone else heard of this idea for magnetic confinement?

http://www.flickr.com/photos/llnl/3085193876/

[KitemanSA]

Just for comparison, here is the same four coil model shown with all north poles facing toward the core:

Notice the line cusps between the individual coils.

The cusps are not the issue. Not the difference in magnetic field in the center. You don't want much magnetic field in the middle of a polywell; you want it to be as close to zero over as large a region as possible.

The diamagnetic effect of a plasma at beta=1 push back the field for you.

You can estimate the effect by putting an internal "diamagnet" in your model such that the radial field components cancel at a specific radial position and the tangential add. Check old posts by a guy titled Indrek. He has done this before and describes how he did it. I think his profile also shows a web-site where he placed many analyses.

Have fun!

[KitemanSA]

Randy -- I have nothing to add to your idea except to bump it for further consideration. The response has been good but not to the level I think it deserves. In case any one missed it -- Randy suggested a configuration where not all the coils were of the same polarity. I've been lurking for some time with nothing to contribute, but one thing I've noticed is that all the discussion is for coils of the same polarity (north pointing in or out) and no significant discussion of the case when half the coils are of opposite polarity. This could be a bogus idea or it could be a game changer -- and I think some thoughtful consideration may be a value.

MrBill,
ALL Polywells have about half of the "coils" being opposite polarity. The distinction is simply whether the coils are "real" or "virtual". In WB6 there were 6 real coils (call them "in") and 8 virtual coils that would be "out". Randy showed an octagon with 8 real coils of alternating polarity. He could get essentially the same effect by having 4 real coils of one polarity and 4 virtual coils of the other. Only the details of the funny cusps would be different.

[D Tibbets]

I believe the 'Baseball stitching" Magnet array was an attempt to improve on a variety of Penning Trap. According to the EMC2 2008 patent application background information, this approach was tried and failed.

Dan Tibbets

[WizWom]

ALL Polywells have about half of the "coils" being opposite polarity. The distinction is simply whether the coils are "real" or "virtual".

Or, rather, whether they are actual loops, or the opposite pole areas between coils.

If all your coils point North in, all the space between them will be South.

If you make the engineered magnets to have a large area and a certain magnetic field going in, the outgoing fields will, of necessity, be higher, as they must concentrate. This is good, because that means that electrons and ions will have a smaller gyro radius as they approach the cusp, and more of a change to hit another ion and scatter.

If you engineer some poles in and some poles out, you will get significant lines of null field. That would be BAD. That has been PROVEN bad.

There are no "VIRTUAL COILS" because those rings are not complete. The "cusps" are merely places where the outgoing magnetic field lines concentrate, because of the geometry of the coils.

Physics-212 stuff, guys. Chapter 28 of my first year physics text (Giancoli, 2008). I'm sure you are only getting confused because it's a 3-dimensional structure.

[KitemanSA]

[/quote]

ALL Polywells have about half of the "coils" being opposite polarity. The distinction is simply whether the coils are "real" or "virtual".

Or, rather, whether they are actual loops, or the opposite pole areas between coils.

If all your coils point North in, all the space between them will be South.

Which will either be cusp, or virtual coil. More coil, less cusp is good. This is a function of SHAPE not size.

If you make the engineered magnets to have a large area and a certain magnetic field going in, the outgoing fields will, of necessity, be higher, as they must concentrate. This is good, because that means that electrons and ions will have a smaller gyro radius as they approach the cusp, and more of a change to hit another ion and scatter.

It is not so much the size of the "out, but the shape. The WB6 shape has a smallish "out" area, but a poor shape factor wrt that area so there are more line-like cusp and less point & funny cusp. If I read Dr. B's Valencia paper correctly, he prefers point and funny cusp. He demonstrates this by wanting to check out a "square plan form "real" magnet resulting in larger but more triangular virtual "out" magnet.

If you engineer some poles in and some poles out, you will get significant lines of null field. That would be BAD. That has been PROVEN bad.

Reference?

There are no "VIRTUAL COILS" because those rings are not complete. The "cusps" are merely places where the outgoing magnetic field lines concentrate, because of the geometry of the coils.

Not my phrase, Dr. B's I think. And he wanted to make them more coil like by changing the shape of the virtual out from convex triangular to pure triangular. In other words, he wanted to make the virtual out coils BIGGER but better shaped. I'll take his opinion until I see a reason to doubt them.