Cusp Ion Plug

[TallDave]

(btw - re 'RECIRCULATE' - shouldnt we mention 'possibility'/opportunity of recirulation between cusps, outside the magrid, supposing suitably configured container -

Please review and comment on the definition here: http://www.ohiovr.com/polywell-faq/inde ... =Main_Page

Thanks, good to know.

[D Tibbets]

The shape is clearly going to be a ball with spikes, what seems to have been a point of argument is that the spikes have a fundamentally different structure. Maybe they would be just the same - a spike with a central core of higher negative charge, just like the sphere.

Yes, that seems like it would work. That would plug the cusps for electrons, and ion losses would be minimal because few upscatter far enough to be pulled out.

Nonsense. You can't plug a hose with water. And where there are enough electrons to make a negative potential, the ions don't need to upscatter to go there.

Water wouldn't plug a hose entirely (unless it was frozen). But it can partially plug the hose due to wall friction/ drag/ viscosity.
I wonder if this is a contributer to the limitation of the potential well being ~ 80-85% of the potential of the injected electrons- the 'viscosity' of the narrow cusp slows them that much. How would this effect the realitive motions of the ions and escaping electrons (and subsequent effects of the recirculating electrons on the ions)? In another thread I speculated that this 15% retardation of electron energy through the cusps sets an effective elevated energy level for upscattered electrons to reach before they can escape recirculation.

Dan Tibbets

[Art Carlson]

Are you referring to this post? I didn't respond to it at the time because I couldn't identify any content. Things you mention that you seem to think qualify as "flaws in the calculation" are
cusp plugging oscillations,
WB field geometry, and
the force driving the non-ambipolar losses in a Polywell.
If there is some physics content behind these phrases that you would like me to understand, you will have to elaborate.

If they don't qualify as flaws maybe you can tell me why

Cute. You throw out some words that don't make sense, and then they "qualify as flaws" until I explain why they don't. What you write farther down in this post makes just as little sense. If somebody out there understands you, maybe they can explain to me what you're talking about. (Hint: In case of doubt, equation are always helpful.) You don't seem capable of doing that, and it's not worth any more of my time to try to figure it out for myself.

[TallDave]

Ha, just because you don't understand it doesn't mean it doesn't make sense.

I also remember you being baffled by Rick's absence of ion pressure in the ITER comparison, and you may be a bit muddled as to where the top of the well is for electrons. Maybe you should try a little harder to understand.

I don't work with physics terms all day, so throwing together equations is a lot of effort, and I certainly don't have a free year to develop a detailed simulation, which I still feel is the only way to even approach doing the system justice. I've outlined a physical scenario that appears to poke a giant hole in your equation, if admittedly only from a handwaving perspective (sorry, I don't have an equation for how often ions at the edge will get pushed away from the negative potential in the cusp by the magnetic field, but I suspect it's a big proportion if the alphas make 1000 transits. I also don't know the distribution well enough to say what proportion of ions see the cusp potential in their Debye sphere -- but I suspect it's small since ions are being injected inside the well and need to upscatter to get to the cusps. Nor can I claim to know how exactly the density drops across the cusp -- but if it's dropping by 10,000x as Bussard says that has some implications for whether the negative potential in a cusp can suck out ions.). If those forces and distributions are irrelevant or unphysical or nonsensical you should be able to explain why. If you can't do better than "Cute" in response, then you can't really complain about my contribution.

Of course, I'm pretty confident you're wrong anyway from the few tidbits Rick has shared (hotspots not on walls, losses not consistent with a stream of ions). So feel free to hide behind the lack of an equation and make faces, it's all a sideshow anyway.

[rcain]

gentelmen, however i find such intellectulal 'scrapping' entertaining (and please dont take that as an excuse to lay into me), surely the matters of ion/electron containment, losses and power balance, have already been well treated by Bussard himself, both theoretically and experimentally. vis:

http://www.askmar.com/Fusion_files/Form ... aining.pdf

esp:

p3)

The aim of this section is to show that the electrons are, in fact, trapped, and that their confinement time is consistent with theoretical expectations.

p11)

Future experiments on the Polywell fusion scheme should insist on higher current sources for energetic electrons, and on isolating the wall from the plasma. Nevertheless, it is encouraging that the production and maintenance of a potential well in the present system showed that CLASSICAL PROCESSES {my caps} guide the characteristics of the system in the parameter ranges we have been able to explore, and that potential well formation and maintenance is not likely to be an anomalous element of this fusion approach.

the analysis and calculations shown are more thorough than anything i have seen here (no disrespect), and there is shown strong agreement bewteen theory and actual experimental measurements (using Langmuir probe & microwave interferometry).

in addition, here:

http://www.askmar.com/Fusion_files/Some ... ations.pdf

p10)

The device thus functions as a “momentum transformer” in which the ion dynamic pressure in the central core region is much greater than the electron dynamic pressure at the surface due to electron reflection by the polyhedral magnetic fields

p17)

Since one term (cusp losses for electrons) varies inversely and the other (ohmic coil losses) directly with the square of the B field amplitude, it is evident that an optimum B field value must exist that will minimize the total power loss.

p18)

Cusp losses are a surface to volume effect and larger (machine) sizes lead to proportionately lesser losses

just to focus the argument, are there any equations/assumptions (germane to our current discourse - eg. eqn 35 on p17 of the second link, for Power loss through cusps) in either of these papers that are disputed? or can we just agree that the Polywell system, insofar as it has been described and studied, basically works?

ps. @chrismb - do you have a link to the patent examiners notes you mention reading?

[TallDave]

Actually, that is pretty much what is being disputed. Absent data, you can either believe Bussard or attempt to poke holes in his claims (and have holes poked in your claims in turn).

Or we could do something more productive like argue over the optimum operating conditions.

One issue involving the cusp confinement aspect of the
HEPS experiment is whether electrons injected into a
point cusp will be confined at all; will injected electrons
simply find their way out of a point cusp on an opposite
face in a single transit.7

Heh, I wondered about that once. I hadn't realized they actually looked into that.

Nice picture of a collector shell too.

[rcain]

... yes, well, i dont see that it 'is' disputable. given the significant evidence available.

as to data, i can SEE data, eg. in all the graphs of confinement times and density, etc on the secend link esp. now if anyone is suggesting that Bussard and his team, made them up, or that they cant draw a graph properly - well that is a different 'accusation', and i'm sure that Rick Nebel and the US Navy would be interested in knowing how they've been led a dance all this while.

i dont think so.

other 'nuances' of operation and the challenge of Q (not to mention energy take-off/extraction), are, for me at least, the nub at this point. the rest is of academic interest (albeit substantial).

re. (mean, varience, probability of) electron transits before exit - all the visualisations (Indrek's PIC animations, et al) to date, inuitively at least, demonstrate why this is not a problem (a 'little' orderd chaos appears to helps us), and Bussards calculations show numerically how we can ensure we remain 'in-envelope'.

personally, i have always tried to think of Polywell as a sort of (4++D) resonant cavity device/filter, so criticalities of injection current, injection timing and direction have featured as critical in my thoughts. born out perhaps by the latest EMC2 contract requirement for 'sexy' ion injectors.

[Art Carlson]

gentelmen, however i find such intellectulal 'scrapping' entertaining (and please dont take that as an excuse to lay into me), surely the matters of ion/electron containment, losses and power balance, have already been well treated by Bussard himself, both theoretically and experimentally. vis:

http://www.askmar.com/Fusion_files/Form ... aining.pdf

esp:

p3)

The aim of this section is to show that the electrons are, in fact, trapped, and that their confinement time is consistent with theoretical expectations.

p11)

Future experiments on the Polywell fusion scheme should insist on higher current sources for energetic electrons, and on isolating the wall from the plasma. Nevertheless, it is encouraging that the production and maintenance of a potential well in the present system showed that CLASSICAL PROCESSES {my caps} guide the characteristics of the system in the parameter ranges we have been able to explore, and that potential well formation and maintenance is not likely to be an anomalous element of this fusion approach.

the analysis and calculations shown are more thorough than anything i have seen here (no disrespect), and there is shown strong agreement between theory and actual experimental measurements (using Langmuir probe & microwave interferometry).

Thank you very much. This may be the only published measurement of confinement time in a polywell. It is a single point, that is, there is no experimental indication of the scaling with magnetic field, energy, density, or anything else. The experimental value is "about 1-2 μs", compared to a theoretical estimate "in the range 0.5-2.5 μs". (Whether this can be accurately described as "strong agreement" I will leave each to decide for himself.)

The "implications of these experiments for the Polywell fusion scheme" discussed in Section V are remarkably sketchy, basically this:

Nevertheless, it is encouraging that the production and maintenance of a potential well in the present system showed that classical processes guide the characteristics of the system in the parameter ranges we have been able to explore, and that potential well formation and main tenance is not likely to be an anomalous element of this fusion approach.

Note that no effort is made to extrapolate the confinement time to reactor conditions. This may be because the model is based on mirror confinement, which Bussard later admitted will not be good enough for fusion. The enhancement of confinement time in the mirror model is something like (R/rho)^3/4. Using Bussard's idea of point cusps with beam diameter of a few times rho, the enhancement would be (R/rho)^2. Using my model, i.e. either point cusps with conservation of magnetic flux in the sheath or line cusps, the enhancement is (R/rho), not much better than mirror confinement. To have a chance of making net power, you need Bussard's scaling, for which there is no evidence presented in this paper.

For these reasons I do strongly dispute that this paper represents the last or even the most thorough word on polywell confinement.

[Art Carlson]

...
in addition, here:

http://www.askmar.com/Fusion_files/Some ... ations.pdf
...
just to focus the argument, are there any equations/assumptions (germane to our current discourse - eg. eqn 35 on p17 of the second link, for Power loss through cusps) in either of these papers that are disputed? or can we just agree that the Polywell system, insofar as it has been described and studied, basically works?

In case you haven't noticed, I dispute Bussard up and down the block. Eqn. 35 uses his notation that has never made sense to me, but I believe it takes credit for recirculation that I dispute, at least when it comes to energy, not just electrons, and it ignores both the line cusps and flux conservation in the sheath leading to the point cusps. He also uses rho_e as the characteristic sheath thickness, justifying it with the simple statement (on p.9) that

This leakage radius applies for the case, valid here, of trapped electrons in a non-neutral plasma system and not for the confinement of neutral plasma, which can escape through a leakage path width comparable to the geometric mean of the ion and electron gyro radii r_e,i in the cusp field.

This statement is probably wrong, but is at best unjustified, misleading, and sloppy (The plasma is quasi-neutral, not non-neutral.).

[chrismb]

@chrismb - do you have a link to the patent examiners notes you mention reading?

The ones in respect of Bussard's last patent?

[Art Carlson]

... yes, well, i dont see that it 'is' disputable. given the significant evidence available.

as to data, i can SEE data, eg. in all the graphs of confinement times and density, etc on the secend link esp. now if anyone is suggesting that Bussard and his team, made them up, or that they cant draw a graph properly - well that is a different 'accusation', and i'm sure that Rick Nebel and the US Navy would be interested in knowing how they've been led a dance all this while.

i dont think so.

What the? The second link?? Bussard, Fusion Technology, Volume 19, March 1991??? There are 6 figures and 2 tables in that paper, but not a single one shows experimental data on the polywell.

[TallDave]

rcain,

I'd go back and look at Rick's statements on the pre-WB-7 data if you want to know where they were at. He gives some good indications of what they trusted and where they were skeptical.

For instance, Bussard's team was measuring density using PMTs to guess where beta=1 was. Rick's team felt that was unreliable so they did density interferometry.

viewtopic.php?p=18445&highlight=pmt#18445

The big question is how WB losses scale, and no one really knows that (except maybe the guys running WB-8 as we speak?). We don't really even have a good equation for cross-field diffusion.

and i'm sure that Rick Nebel and the US Navy would be interested in knowing how they've been led a dance all this while.

Heh. I wouldn't worry too much about that.

[rcain]

...What the? The second link?? Bussard, Fusion Technology, Volume 19, March 1991???

Art, my apologies - I actually meant to say the first link, and yes they are both quite veteran papers. They do, to me at least, provide general experimental evidence (using HEPs-Polywell config) supporting basic geometry and confinement and show that these correlate 'reasonably' well with theoretical predictions. ie. no show stoppers are identified.

I agree, there is no serious attempt (in these papers at least) to extrapolate to reactor conditions. I will do some further digging.

As far as I can see, Bussard never suggested mirror confinement was adequate; I was under the impression that this has long been a known limitation and so therefore he need 'admit' nothing. (may be just a choice of words thing). He did us a mirror equation (p4 eqn 6) to estimate lower bound on containment at cusps under LOW pressure conditions.

However, he then went on to show ('admit'), how as the neutral density (identified 10degress off a cusp line) increases, so the potential (well) drops off, badly:

Because the failure of the potential to persist when the density of the neutral background far exceeds the unneutralized density that forms the potential which will also be the conditions on a reactor scenario (1,4) might be interpreted as a flaw in the concept, it was important to understand this behavior. To this end we carried out a set of studies to understand the behavior of the back ground plasma itself given in the Appendix, and then a set of studies to understand the behavior of the potential as a function of background density, electron energy, and electron current described below.

and... (p10-p11):

With no background plasma, the potential builds up to the gun energy; this potential prevents further buildup of unneutralized electrons, thus clamping the unneutralized electron density. After the background plasma has forced the potential to drop below the gun energy due to energy conservation, as discussed above, the number of unneutralized electrons is instead determined by a balance between the injected current and cusp losses.

Thereafter, the hot electron density depends on the background plasma density, only to the extent that the background might change the hot electron energy somewhat, and therefore its cusp loss rate. The fact that
the number of hot electrons does not change much with background plasma density, while the potential changes a lot, creates an apparent problem with Poisson’s equation, since del^2ϕ is proportional to the unneutralized density.

The resolution to this apparent conundrum is that as the density increases, the potential will be confined to an increasingly small sheath near the periphery, with the same excess charge producing a smaller potential.

The data shown in Figure 10a and 10b confirms this trend. The lower density run, Figure 10a, has a potential that increases fairly smoothly with radius. The higher density run, Figure 10b, has a potential that is quite flat until the sharp rise at about 65 cm. This trend is expected from the model.

... i would agree that treatment around this point seems rather scant. But, Bussards point, i believe, is that the trend is promising enough to pursue, not least, because we seem to be able to explain it, and to a greater or lesser extent, control it.

i dont see any treatment of (diamagnetic) Wiffle-ball (WB) effects anywhere here. Nor, as you rightly point out, any constructive treament of confinement 'scaling', whatever the cause. i'm certain there is adequate treatment elsewhere however, i'll dig it out.

since everyone agrees, WB formation is fundamental to feasibility, this (precise behaviour) seems to be key, still.

regarding your assertion of (R/rho) as the 'confinement enhancement ratio(?)' cf Bussards (R/rho)^2 - please could you repoint me to your derivation - i am very interested in reading though and understanding your point of view further. (though please bare with me as my own knowledge and experience of this science is considerably infererior to your own).

For these reasons I do strongly dispute that this paper represents the last or even the most thorough word on polywell confinement.

.

fair enough, and i wouldnt disagree (they are old papers after all). though in truth, thats not what i claimed.

In case you haven't noticed, I dispute Bussard up and down the block

yep, we had noticed. and it is for that reason that your learned assessments here are so highly valued.

Eqn. 35 uses his notation that has never made sense to me, but I believe it takes credit for recirculation that I dispute, at least when it comes to energy, not just electrons, and it ignores both the line cusps and flux conservation in the sheath leading to the point cusps. He also uses rho_e as the characteristic sheath thickness, justifying it with the simple statement (on p.9) that

This leakage radius applies for the case, valid here, of trapped electrons in a non-neutral plasma system and not for the confinement of neutral plasma, which can escape through a leakage path width comparable to the geometric mean of the ion and electron gyro radii r_e,i in the cusp field.

This statement is probably wrong, but is at best unjustified, misleading, and sloppy (The plasma is quasi-neutral, not non-neutral.).

in what way does the notation of eqn 35 (http://www.askmar.com/Fusion_files/Some ... ations.pdf), not make sense?

it seems to me he (Bussard) is putting a general case, albeit he then qualifies with eg.

... where the parameters jo and Gj are related to others by various constraint equations...

- which seems slightly fudgy to me also. surely however, this is where we deem experimental discovery of parameters necessary.

your assertion of 'probably wrong' however, also seems to me begging some more definite proposal. did you have anything in mind?

@chrismb:

The ones in respect of Bussard's last patent?

- yes

@TallDave: thanks for the link - Photomultiplier Tubes - i had wondered how they used those for this app. what we really want though are a few measly graphs from more recent experiments, showing things are 'on-track' (or not), and to answer questions such as Art has just posed re. confinement enhancement. what are the chances of that do you suppose? Is Rick Nebel still looking in?

[Art Carlson]

...What the? The second link?? Bussard, Fusion Technology, Volume 19, March 1991???

Art, my apologies - I actually meant to say the first link,

OK. I've been a bit irritable lately. May have overreacted. Don't read too much into my choice of the word "admit", either.

regarding your assertion of (R/rho) as the 'confinement enhancement ratio(?)' cf Bussards (R/rho)^2 - please could you repoint me to your derivation - i am very interested in reading though and understanding your point of view further.

With no confinement, the electrons would be lost in a transit time ~R/v. With cusp confinement, they usually bounce after each transit, but occasionally hit one of the cusps, which have a total effective area of A_cusp. The average number of bounces before hitting a cusp is the enhancement factor and is simply given by the ratio of the surface area of the sphere, 4pi*R^2, to the area of the cusps, A_cusp.

Bussard considers only point cusps and assumes the radius of each one is the Larmor radius rho. (Whether the proper Larmor radius to use is that of the electrons or that of the ions or the geometric mean of the two is an open question. I accept for the sake of argument Bussard's choice of the electron Larmor radius.) Thus for Bussard, A_cusp is a smallish number times rho^2, so the enhancement factor is roughly (R/rho)^2.

I either take the line cusps or the flux conservation in the sheath into account. For details, see the thread 1977 Review by Haines. The answer turns out to be the same for both assumptions, but take the line cusps for simplicity. I assume, similar to Bussard, that they are about a Larmor radius, rho, thick. Since they are line cusps, they meander over the surface of the sphere and have a total length equal to a smallish number times the radius, R. This gives me A_cusp ~ rho*R, or an enhancement factor on the order of R^2 / (rho*R) = (R/rho).

[rcain]

Art - thank you for the explanation. Your thinking is a lot clearer to me now. I'll take it as a challenge, to either a) find an equally plausible/more plausible equation for cusp losses, or b) find some experimental data that puts either your figures, or Bussards (or both) in doubt.

(dont hold your breath, obviously, though i promise to try )