Why is polywell supposed to be better than cusp confinement?

Discuss how polywell fusion works; share theoretical questions and answers.

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jmc
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Re: Why is polywell supposed to be better than cusp confinem

Post by jmc »

Art Carlson wrote:One more thing, then I'm let you go. Rick Nebel says that the gradient scale length of the field must be smaller than the (electron?!) gyroradius. I hope he doesn't really mean than. Even assuming resistivity/diffusion is classical, what is the timescale for broadening of a millimeter scale current sheath?
If you can imagine a region of zero field surrounded by a membrane containing a magnetic field, each electron will only spend a fraction of its time in the field containing region, all collissions in the field free region are unimportant in relation to crossfield diffusion. The larger the device the smaller the fraction of its time the electron spends in the field free region.
When I took the classical diffussion model, I found that crossfield transport of energy was tolerable even when the scalelength was 5 elecrtron larmor orbits. If the transport is turbulent on the other hand, all bets are of...

TallDave
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Post by TallDave »

After all, Rick Nebel has said that Wiffelball confinement scaling (~B^2) has "clearly" been observed. Could somebody point me to the published data, please?
I haven't seen this either. I don't know that the data was ever published; it might just be sitting over at EMC2.

If it has been published or could be shared, I'd sure love to see it.

jmc
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Re: Why is polywell supposed to be better than cusp confinem

Post by jmc »

Art Carlson wrote: It seems to be the prevailing view that line cusps will leak like a slit with the width of a few gyroradius. I'm still haven't got a good picture of how cusps confinement works, but this result seems plausible. (It also has the nice property that the losses will be naturally close to ambipolar: The ions see a bigger hole, but they move through it more slowly.)
I have visualized the gyroradius issue, the best way to think about it is what goes in, must come out, in a cusp field there is one fieldline that goes into the region of zero field, the electron gyro-orbits ore like hula hoops and if the electrons orbits overlap this fieldline then they will enter into the cusp region and forget their moments, if they don't, then instead they will remain in the adiabatic region, without entering the cusp zone.

The cusp fieldline intersect solid surfaces, let us call these surfaces the limiter plates. These limiter plates do not need to be at the same potential as the rest of the vessel. If you place a gridded screen within a few electron larmor radii of the limiter plate and place this at a potential greater than that of the limiter plates and the plasma, although it will attract the electrons they will not be able to touch it as the magnetic field insulates them from it. The ions are not insulated from the plates by the magnetic field as they are within an ion lamor radius of them, however, if the potential difference of the gridded screen and the plasma is somewhat greater than the ion temperature, the ions will not have the energy to reach the gridded screen and will get turned back, electrostatically, back into the plasma. That way the effective loss area for the ions, aswell as the electrons can be made a few electron larmor radii.

P.S. Do you have any reason to believe cusp machines containing line cusps have been proven that they could never possible work? Bussard did make such a statement, but I have no reason to believe his words should be taken as gospel. He also stated that they conclusively proved that a closed box device could never work yet the second last machine he built was a closed box device. I find it hard to believe that a machine that only ran 4 times over a period of less than a millisecond in total clocking up a total of nine neutrons could have provided such a conclusive revelation.

93143
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Post by 93143 »

I think the line cusp issue has been adequately addressed, at least considering that there is currently an experiment running.

The Valencia paper, page 8 (which I believe was quoted on cosmiclog), mentions the existence of line cusps, and gives some criteria for mitigation in order to keep the trapping factor high. Remember that cusp losses in an open magrid design are not actually losses, since the electrons are attracted back in by the positive magrid and prevented from hitting it by the magnetic field. The goal is simply to maintain a high interior-to-exterior density ratio.

Also, Dr. Nebel says that wiffleball mode has been demonstrated experimentally, which I would tend to believe at face value until some good reason for doubting his word comes up. (I don't have the resources to replicate the experiments myself...)

hanelyp
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Re: Why is polywell supposed to be better than cusp confinem

Post by hanelyp »

Art Carlson wrote:Why is the polywell supposed to be better?
Since Dr. Carlson isn't yet satisfied with the answers given...

1. The wiffleball effect of the electron cloud pushing back on the magnetic field is supposed to make the cusps less leaky. More like a pinhole and less like a funnel.

2. Since the magnetic field is used to confine electrons but not ions, an electric field outside the magrid can recirculate electrons, greatly reducing losses.

3. Since we're using the magnetic field to confine electrons, particle with a much higher charge to mass ratio than ions, a weaker field can confine the electron to a smaller radius than if standard magnetic confinement was used.

kcdodd
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Post by kcdodd »

I hope I don't offend you too much with this post Dr. Carlson, or eat too much of my foot haha. My opinion is that it really just comes down to experiment of a specific design. I mean, you could have asked why the wright brothers plane was any better then every other plane ever built that didn't work. It's still just a couple wings held together by sticks just like the others that failed; so surely it will fail too. But it wasn't just the wing, it was flight control and a myriad of other small things that their specific design allowed them to fly where others crashed and killed themselves. Or ask why is ITER any better then any other tokamak. It is just a big magnet donut and all the other big magnet donuts failed too, right. If you can point to this specific designed being tested and failed then maybe we can gain something, but just a broad statement that anything that has cusps will fail just because other cusp machines failed is a fallacy. And we are at a disadvantage because to answer your question we would have to know why every single other cusp design failed in the first place. I will honestly say I am defiantly not qualified to begin to answer that one. And "textbook" explanations of things are notorious for not fitting reality. If we had only the theory "textbook" explanation of flight in the beginning before a plane was actually built someone would have proved it impossible to work with math. Maybe polywell will work and maybe it won't work. Maybe some people are wasting their time, but I think other people have wasted more time doing things of much less value.
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Mike Holmes
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Post by Mike Holmes »

In fact one of the Wright brothers was quoted early on in his work on flight as saying that he felt that, from what they knew, powered flight would never be achieved.

But Carlson isn't making spurious attacks, there has been credible work saying that cusps are problems. Hanelyp has given some examples of how the Polywell addresses these problems. I eagerly await Carlson's replies.

With regard to 93143's point (if that is your real number!), is Carlson saying that the experimental data to date doesn't confirm the wiffleball mode? Or just that the wiffleball mode doesn't garuntee excess power when scaled up? This is, of course, actually a question for Carlson to answer.

For we laymen trying to keep up...

I sense one of those science propositions coming up... what would it take, Dr. Carlson, in terms of data from the WB-7 tests coming up (in Aug?), for you to be a believer in the potential to scale it up to producing excess power in WB-8?

And what could we bet? Anybody got some spare cycles on a supercomputer to wager?

Has this been proposed elsewhere?

Mike

Art Carlson
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Post by Art Carlson »

I'm sorry I don't have time to respond immediately to all the responses. In particular I would like to talk in numbers concerning the consequences of a super thin current layer. But I'll make a couple quick comments right away. Since Mike Holmes thinks hanelyp raised some interesting points, I will start there.
hanelyp wrote:1. The wiffleball effect of the electron cloud pushing back on the magnetic field is supposed to make the cusps less leaky. More like a pinhole and less like a funnel.
As I understand it, the plasma pressure is what closes the slit down to the size of a gyroradius, and otherwise it would be much worse. I am not calling that effect into question. What I doubt is that the hole is a point and not a slit.
hanelyp wrote:2. Since the magnetic field is used to confine electrons but not ions, an electric field outside the magrid can recirculate electrons, greatly reducing losses.
I think there may be some misconceptions lurking behind these statements, but I have not yet addressed the issue of recirculation. I would like to first settle the question of how big the holes are before we discuss whether it is possible to plug them.
hanelyp wrote:3. Since we're using the magnetic field to confine electrons, particle with a much higher charge to mass ratio than ions, a weaker field can confine the electron to a smaller radius than if standard magnetic confinement was used.
This corresponds to the use of the gyroradius for the slit width, since it is much smaller for electrons than for ions. Or are you trying to say something else?

None of the comments of hanelyp even touch on my central point, indeed my only point so far, that the cusps are lines and not points, so I don't understand what Mike Holmes finds so interesting about them.

Moving on to 93143 (I hope you don't mind if I dispense with the title and last name and just call you 31.),
93143 wrote:I think the line cusp issue has been adequately addressed, at least considering that there is currently an experiment running.

The Valencia paper, page 8 (which I believe was quoted on cosmiclog), mentions the existence of line cusps, and gives some criteria for mitigation in order to keep the trapping factor high. Remember that cusp losses in an open magrid design are not actually losses, since the electrons are attracted back in by the positive magrid and prevented from hitting it by the magnetic field. The goal is simply to maintain a high interior-to-exterior density ratio.
If anyone actually understands what Bussard was trying to say, maybe they can translate it into English (or at least Physics) for me. (What are "line cusp corner spacing flow factors"?) It sounds to me like he is back peddling because he realized it is not possible to obtain point cusps so he is now relying on even better recirculation, but like I said, I don't really know what he is saying.
93143 wrote:Also, Dr. Nebel says that wiffleball mode has been demonstrated experimentally, which I would tend to believe at face value until some good reason for doubting his word comes up. (I don't have the resources to replicate the experiments myself...)
I haven't called into doubt anything that Nebel said, I just asked for more details. If this is supposed to resemble a scientific discourse, then appealing to "pumpkin papers" isn't going to get us anywhere.

As for believing in a scale up to a power reactor, ITER is predicted to produce 30 times as much fusion power as JET, and I am pretty sure they will land within a factor of 2 of that. If WB-7 works as predicted, what is the scale factor to a power reactor? A million? That's a long row to hoe. Purely empirical extrapolation over more than a factor of 3 or 4 is very iffy. That is one of the reasons I am pressing to understand the basic physics of the concept. Even if the toy experiments work in accordance to somebody's model, the model could still be wrong and/or physical understanding can identify show-stoppers waiting in the wings.

kcdodd
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Post by kcdodd »

I did this plot several months back of individual electron trajectories. As you can see the line cusps receive nearly zero flux. Only one path actually penetrated the line cusp from all the trials, it myst hit the cusp directly or the internal structure of the magnetic field funnels any electrons headed toward the line cusp to a corresponding corner intersection of three of the faces. So these corners seem to receive flux nearly identically to the point cusps of the faces. Bussard knew they were structurally completely different than the point cusps of the faces, but yet they acted almost identically almost as if they were point cusps. I think he called them funny cusps or something. The face point cusps and corner funny cusps were the only gates into or out of the core.

Now, in high beta operation I think he assumed they would have similar relative properties and treated the funny cusp pretty much as the point cusp, knowing they are not the same thing. Now, you can of course argue that at high beta the magnetic structure is not the same so perhaps they do not cause these funny cusps at all. But assuming it did for a second, and assuming the wiffle ball effect at high beta had closed down the gates through the corners and faces, so to speak, you have attained high confinement.

Image
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seedload
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Re: Why is polywell supposed to be better than cusp confinem

Post by seedload »

Art Carlson wrote:Bussard, by the way, is very clear about the fact that you can forget about any configuration with line cusps.
Bussard wrote "In any realistic device, the effective overall trapping factor is reduced from the pure WB mode by circulation through the semi-line-cusps at the spaced corners, which allow much greater throughflow per unit area than through the point cusps of the polyhedral faces."

From that it is pretty clear that he accepts line cusps exist in a practical implementation of his invention.
Art Carlson wrote:Of course, compared to a cusp machine, the polywell may also get some credit for density peaking and recirculation (although I will question both of these effects), but it seems certain that line cusps will be a killer, and it seems pretty sure to me that line cusps are unavoidable."
To me, from a purely 3D mental visualization perspective, I don't see why the WB would be any less effective at narrowing line cusps as opposed to closing the point cusps. And that is probably the answer to the question in the topic line of this thread.

Although I think your points on scaling are where you really want to go with this conversation. I am trying to come to grips with your points. Are you saying that because there are slits and not just points that someone messed up the scaling numbers?

Art Carlson
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Re: Why is polywell supposed to be better than cusp confinem

Post by Art Carlson »

seedload wrote:
Art Carlson wrote:Of course, compared to a cusp machine, the polywell may also get some credit for density peaking and recirculation (although I will question both of these effects), but it seems certain that line cusps will be a killer, and it seems pretty sure to me that line cusps are unavoidable."
To me, from a purely 3D mental visualization perspective, I don't see why the WB would be any less effective at narrowing line cusps as opposed to closing the point cusps. And that is probably the answer to the question in the topic line of this thread.

Although I think your points on scaling are where you really want to go with this conversation. I am trying to come to grips with your points. Are you saying that because there are slits and not just points that someone messed up the scaling numbers?
High beta operation squeezes down the width of a cusp to a few gyroradii (rho). Point cusps get sqeezed in two dimensions, line cusps only in one. If there are only point cusps in the machine then the size of the effective hole is a few times rho^2. If there are line cusps, the hole is a few times rho*R. The difference is a factor of several thousand. I thought we could at least agree on this much.

TallDave
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Post by TallDave »

Art, do you mean line cusps along all the edges, between the coils? I got the impression these "line cusps" were essentially closed, and it was only the corner "funny cusps" that were a few gyroradii wide.
If WB-7 works as predicted, what is the scale factor to a power reactor? A million? That's a long row to hoe.
Yep, that's the biggest worry. Hard to say if everything will scale to ITER power. OTOH, it's 100 times cheaper than ITER to build one and find out, which makes it a relatively good risk/reward ratio, both because you're out less if it doesn't work and because if it does work it's a lot more useful than the ITER/DEMO chain as you could use it for a reasonably-priced power source in a decade or so versus several decades (and maybe never) for ITER/DEMO.

kcdodd
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Re: Why is polywell supposed to be better than cusp confinem

Post by kcdodd »

Art Carlson wrote: High beta operation squeezes down the width of a cusp to a few gyroradii (rho). Point cusps get sqeezed in two dimensions, line cusps only in one. If there are only point cusps in the machine then the size of the effective hole is a few times rho^2. If there are line cusps, the hole is a few times rho*R. The difference is a factor of several thousand. I thought we could at least agree on this much.
If line cusps have the same throughput as point cusps, yes; but I just posted a plot showing that the point cusps are the major loss factor. Line cusps are not contributing 1000s of times to the loss, just the opposite in fact. At least at low beta, 99.99% of the electron loss occurs in the point cusps and funny cusps. If what you say holds then my plot would have almost nothing through the faces or funny cusps, as 99.99% of the electrons would have already escaped through the line cusps.
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93143
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Post by 93143 »

Okay, I think I see something. The Valencia paper seems to be saying that the fractional loss area is the key to mitigating line cusp losses. This makes intuitive sense given the picture of the trapping effect as a "wiffleball" (and one can easily realize that the same is probably true for point cusps). Now, it may well be true that the line cusps dominate the losses at a larger machine size. However, I don't think that this would preclude good confinement even if true.

Power loss is not a big issue due to recirculation (if you can accept that for the sake of argument). The primary goal is to keep the density ratio high, and for this purpose we can put up with a trapping factor maybe 1/1000 of what a closed-box machine would need. Given that, and considering that the holes stay a few gyroradii wide and that the gyroradius drops substantially as the machine radius increases (due to higher B, because of course you're increasing B as fast as you can as you make the machine bigger), is it not reasonable to expect that confinement would be better in a big machine than in a small one?

Thanks for that picture, kcdodd. That's very interesting. It is possible that the line cusps would become more leaky relative to the point cusps as beta=1 approaches, but if the data says we're in wiffleball mode, I suspect there's something about this geometry that mitigates the effect of the line cusps. Bottom of page 5 in the Valencia paper implies this.

Now, how do the electron losses scale? They are much smaller than in a non-recirculating machine, but they do dominate the power requirements. With linear scaling of B with R, the line cusp loss area remains constant irrespective of the machine size. This means that non-recirculating machines should have losses proportional to the electron density. For recirculating machines, um... the fractional unshielded target area is independent of R (roughly), so the losses should still be proportional to the electron density. See the RHS of Valencia pg. 7 for an empirical take on what the losses actually are.

Even if the line cusps wind up adding a power of R to the predicted losses, we can just make the machines bigger by a power of 5/4, right? That's not that bad...

seedload
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Re: Why is polywell supposed to be better than cusp confinem

Post by seedload »

Art Carlson wrote:High beta operation squeezes down the width of a cusp to a few gyroradii (rho). Point cusps get sqeezed in two dimensions, line cusps only in one. If there are only point cusps in the machine then the size of the effective hole is a few times rho^2. If there are line cusps, the hole is a few times rho*R. The difference is a factor of several thousand. I thought we could at least agree on this much.
I am not very technical, so please forgive me if I start by restating. It helps me :)

OK. So, you are supposing that in WB mode, the point cusps are reduced in two dimensions and the line cusps are only reduced in one. Eventually, the point cusps don't matter anymore because they become merely intersections of the line cusps. Electron escape opportunity is defined by the line cusps. The dimensions of which are defined by (~2rho)*R*N where R is the length of each line cusp and N is the number of them.

I guess this depends on what the heck funny cusps exactly are. My speculation is that they must by real line cusps between the coils. If not, then why did Bussard have to space the coils away from each other. He HAD to to let the electrons recirculate in the places where they were hitting metal - on the line cusps.

Bussard also says that the "semi-line-cusps ... allow much greater throughflow per unit area than through the point cusps of the polyhedral faces." which seems to agree with them being true line cusps and having an R dimension to them that doesn't reduce in WB mode.

In another post you point out that you think that "Bussard is back peddling because he realized it is not possible to obtain point cusps so he is now relying on even better recirculation" I read it that way too, except to say that I would use the term "engineering" over "back pedding". His theory had a flaw and he thinks he found a solution. I would also add that the solution was proved through experimentation to be more efficient at making neutrons.

So, what are you getting at as to the implications of line cusps vs. point cusps? Something to do with linear scaling of the line cusps vs. the surface area of a sphere?

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