Why is polywell supposed to be better than cusp confinement?

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

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Indrek
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Post by Indrek »

Are you sure your calculations are stable? I think I saw similar "weird" behavior with ephi if I reduced calculation resolution too much.

- Indrek

kcdodd
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Post by kcdodd »

Yes I don't think it integration error. I think the field itself is weird there.
Carter

sdg
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Post by sdg »

More basically, it looks like the polywell should be classed as high beta cusp confinement. I'm not familiar with the details, but I know that this idea is as old as the hills and was rejected very early. Why is the polywell supposed to be better? Possibly it is the idea of using point cusps instead of line cusps. If that is the case, then I will amplify the reasons I have already indicated for believing that line cusps are unavoidable.
Hi Art,

Is the above still a main concern? If not, could you please articulate your main concern/contention?

In answer to the question you pose which started this thread:

The relaxed constraints of the polywell approach make it superior to traditional high beta cusp confinement.

To elaborate slightly more:

The polywell differs significantly from traditional high beta cusp confinement in two very important ways:

1) The confinement is primarily of electrons, not a neutral plasma. This significantly reduces the necessary B field strength.

2) The purpose of confinement is significantly different: Confinement is for the purpose of maintaining a suitably large electrostatic charge so as to energize a smaller number of protons to fusion levels. Traditional cusp confinement requires confinement of thermally energized particles, which brings substantial additional constraints (e.g., recirculation is proscribed).

Assuming that you concede that there are important fundamental differences between "old as the hills" cusp confinement, we can move on to more specific and focused objections to IEC fusion.

This is relevant to the discussion of point/line cusp issues, because it is important to avoid talking past each other. For instance, in theory, for IEC to work, the goal of confinement is merely to create a greater than 10^4 or so difference in the electron density of one focused area compared to another, in a way that permits non-destructive proton collisons (as opposed to the destructive collisions in Farnsworth approach). This is a significantly different goal than in traditional neutral cusp confinement.

The superiority of the polywell design does not arise from its use of point cusps (it obviously also has line cusps). Polywell's superiority presumes that it can produce high enough concentrations of light weight electrons to cause heavy protons to collide without destroying the container in the process. Achieving the sufficiently high concentration of electrons depends in part on electron recirculation. Interestingly, the candidate protons also "get" to recirculate, being attracted by the cloud of electrons over and over again until ion-ion collisions happen. (They also do not require confinement in the traditional sense, and recirculate in ways that are not possible in neutral cusp confinement). The whole process is of a fundamentally different topology.

I'm sure you already know all this, but I hope that this may somehow help focus the discussion to areas of specific contention. Which, BTW, I think most here find tremendously valuable, and to which your participation is greatly appreciated. My hope is that clarifying these differences/objections/concerns will result in a discussion that can inform a broader audience.

Assuming you agree to the above, is it fair to say that your current proposed concern/objection is now that the line cusp problem may result in inadequate confinement to maintain sufficient electron density?

And of course there are hopefully many more problems/objections you wish to raise.

Indrek
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Post by Indrek »

Art Carlson wrote: 1) I think I need some numbers, though. If I understand Bussard (and if he is right), the confinement is much worse at low beta, so it is possible that the line cusps are spewing out their R*rho worth, but the corner cusps are for some reason much much worse in this regime. Can you count up the particles exiting each of the three regions and express that as an effective loss area?
I can provide you some data. If you trust my data. I think I can provide electron paths and field values with reliability. But you need to specify what you need exactly and I'm afraid in quite simple terms (as some things you talk about are way above my head;).

In the very early days I did something on the lines of this:
http://www.mare.ee/indrek/ephi/confine1/
and this
http://www.mare.ee/indrek/ephi/pierce/
These characteristics are for you probably self-obvious but for me they were interesting experiments :)

- Indrek

tombo
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Post by tombo »

kcdodd
I have thought about that too. Every coil reinforces the point cusps of the adjacent coils. You can see though that the face coils all point out at the edges, and the corner coils all point in at the edges. They interfere each other on all of the line cusps, and you are left with very week fields there.
Oh. Yes. Now I remember why it did not work when I looked at it before.
It is so obvious that if it worked it would be mentioned and used already.

But, I am confused about the analogous escape path.
There seems to be a contradiction between.
1. The electron's orbit follows a flux tube. The flux through the orbit is conserved. So, the orbit radius exceeds the coils major radius as the flux tube goes out of the magrid.
2. The particle passes through the very highest fields in the device which should give them the smallest gyro radius in the device at those points, not a gyro path that takes it clear around the outside of the face coil.

The RH rule seems to say 1. but how can it pass through the highest fields in the device while maintaining a very large gyro radius?
-Tom Boydston-
"If we knew what we were doing, it wouldn’t be called research, would it?" ~Albert Einstein

Art Carlson
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Post by Art Carlson »

sdg wrote:
More basically, it looks like the polywell should be classed as high beta cusp confinement. I'm not familiar with the details, but I know that this idea is as old as the hills and was rejected very early. Why is the polywell supposed to be better? Possibly it is the idea of using point cusps instead of line cusps. If that is the case, then I will amplify the reasons I have already indicated for believing that line cusps are unavoidable.
Is the above still a main concern? If not, could you please articulate your main concern/contention?
Yes, this is still a good summary of my main concern.
sdg wrote:1) The confinement is primarily of electrons, not a neutral plasma. This significantly reduces the necessary B field strength.

2) The purpose of confinement is significantly different: Confinement is for the purpose of maintaining a suitably large electrostatic charge so as to energize a smaller number of protons to fusion levels. Traditional cusp confinement requires confinement of thermally energized particles, which brings substantial additional constraints (e.g., recirculation is proscribed).
This mantra has been repeated often, but it still doesn't make any sense. In what sense does a polywell "primarily" confine electrons while a traditional cusp primarily confines a neutral plasma? The polywell is "quasi-neutral", meaning that the fractional difference between the electron density and the ion (charge) density is tiny. It has to be this way in order to get a density high enough to be relevant for practical fusion power production. Bussard and Nebel realize this. It's not an issue.

Looking at it from another perspective, you may, if you choose, ignore the effect of the magnetic field on the ions, but then the same electrostatic force that acts to pull the ions back in will act to pull the electrons out. If the magnetic field acts only on the electrons, it has to be twice as good because it has to not only counteract the tendency of the electrons to fly apart by thermal motion, it also has to counteract the indirect effect of the ions trying to fly apart and pulling the electrons along.

sdg wrote:... For instance, in theory, for IEC to work, the goal of confinement is merely to create a greater than 10^4 or so difference in the electron density of one focused area compared to another, in a way that permits non-destructive proton collisons (as opposed to the destructive collisions in Farnsworth approach). This is a significantly different goal than in traditional neutral cusp confinement.
Nonsense. It's trivial to produce a large ratio of density inside compared to outside. Just make sure the plasma outside has zero confinement. The total loss rate from the inner plasma has to be below some minimum, otherwise you need more power to maintain the plasma than you get back from fusion. This is the Lawson Criterion.
sdg wrote:Assuming you agree to the above, is it fair to say that your current proposed concern/objection is now that the line cusp problem may result in inadequate confinement to maintain sufficient electron density?
As you see, I don't agree with you, but your restatement of my concern is nonetheless (nearly) valid. Comparison of the polywell to traditional cusp machines is a shorthand for saying that confinement by line cusps is inadequate to satisfy the Lawson criterion. I am not concerned about achieving sufficient density by itself, but about achieving adequate energy confinement time for a given density.

93143
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Post by 93143 »

Art Carlson wrote:This mantra has been repeated often, but it still doesn't make any sense. In what sense does a polywell "primarily" confine electrons while a traditional cusp primarily confines a neutral plasma? The polywell is "quasi-neutral", meaning that the fractional difference between the electron density and the ion (charge) density is tiny. It has to be this way in order to get a density high enough to be relevant for practical fusion power production. Bussard and Nebel realize this. It's not an issue.

Looking at it from another perspective, you may, if you choose, ignore the effect of the magnetic field on the ions, but then the same electrostatic force that acts to pull the ions back in will act to pull the electrons out. If the magnetic field acts only on the electrons, it has to be twice as good because it has to not only counteract the tendency of the electrons to fly apart by thermal motion, it also has to counteract the indirect effect of the ions trying to fly apart and pulling the electrons along.
It's a quasi-neutral plasma, yes, but the (position-dependent) ion energy distribution is supposed to be such that the slight negative charge of the wiffleball does all the confining necessary (hence the name IEC). The magnetic field doesn't need to be anywhere near strong enough to confine the ions. All it has to do is confine the electrons, and the charge:mass ratio of an electron is so extremely high that it can do this despite the net negative space charge.

That's the idea, anyway. It seems to be working at the current scale.

I am not concerned about achieving sufficient density by itself, but about achieving adequate energy confinement time for a given density.
The idea of recirculation is critical to this. It is true that a closed-box Polywell with cusp leakage = losses will probably never work. But if cusp leakage can be allowed to be a few orders of magnitude above energy confinement losses...?

I attempted to tackle this earlier in the thread. If the current observations of wiffleball formation are correct, I believe I have shown that it is not unreasonable to expect it to scale up more or less as predicted.

Solo
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Post by Solo »

Art Carlson wrote:Looking at it from another perspective, you may, if you choose, ignore the effect of the magnetic field on the ions, but then the same electrostatic force that acts to pull the ions back in will act to pull the electrons out. If the magnetic field acts only on the electrons, it has to be twice as good because it has to not only counteract the tendency of the electrons to fly apart by thermal motion, it also has to counteract the indirect effect of the ions trying to fly apart and pulling the electrons along.
Sure. So running the reactor with a large negative charge means that ions are confined by electrostatic attraction and escape less frequently, with the tradeoff that electrons are repelled by the net charge, and escape more frequently. My impression was that since the electron gyroradius is smaller for a given B-field strength, then that is how the electrons are more easily confined: the cusp loss rate should be lower for electrons compared to ions since the cusp area varies with the gyroradius. (Thus the claim that electrons are 'easier to confine'.) So, even though the electrons need to be confined 'twice as well,' it is possible to confine them 'four times as well,' due to the mechanics of the cusp, so that you come out ahead.

Art Carlson
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Post by Art Carlson »

93143 wrote:
Art Carlson wrote:This mantra has been repeated often, but it still doesn't make any sense. In what sense does a polywell "primarily" confine electrons while a traditional cusp primarily confines a neutral plasma? The polywell is "quasi-neutral", meaning that the fractional difference between the electron density and the ion (charge) density is tiny. It has to be this way in order to get a density high enough to be relevant for practical fusion power production. Bussard and Nebel realize this. It's not an issue.

Looking at it from another perspective, you may, if you choose, ignore the effect of the magnetic field on the ions, but then the same electrostatic force that acts to pull the ions back in will act to pull the electrons out. If the magnetic field acts only on the electrons, it has to be twice as good because it has to not only counteract the tendency of the electrons to fly apart by thermal motion, it also has to counteract the indirect effect of the ions trying to fly apart and pulling the electrons along.
It's a quasi-neutral plasma, yes, but the (position-dependent) ion energy distribution is supposed to be such that the slight negative charge of the wiffleball does all the confining necessary (hence the name IEC). The magnetic field doesn't need to be anywhere near strong enough to confine the ions. All it has to do is confine the electrons, and the charge:mass ratio of an electron is so extremely high that it can do this despite the net negative space charge.

That's the idea, anyway. It seems to be working at the current scale.
You haven't addressed why you think you can say these things about a polywell but not about a cusp machine.
I'm not sure what you mean by "The magnetic field doesn't need to be anywhere near strong enough to confine the ions." If you mean, do a good enough job of confining the electrons then they will confine the ions for you, then OK. If you mean the ion energy confinement time is unimportant, that's plain wrong. If you mean that the magnetic field only has to provide force balance against electron pressure, and not against the sum of electron and ion pressure, that's wrong, too.
93143 wrote:
I am not concerned about achieving sufficient density by itself, but about achieving adequate energy confinement time for a given density.
The idea of recirculation is critical to this. It is true that a closed-box Polywell with cusp leakage = losses will probably never work. But if cusp leakage can be allowed to be a few orders of magnitude above energy confinement losses...?

I attempted to tackle this earlier in the thread. If the current observations of wiffleball formation are correct, I believe I have shown that it is not unreasonable to expect it to scale up more or less as predicted.
Then let us hold that thought: Success of the polywell requires good magnetic confinement on the inside *and* good recirculation on the outside. If either one of these is missing, it will fail. I have been calling the good magnetic confinement into question, and I am preparing a post that will question the good recirculation.

Art Carlson
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Post by Art Carlson »

Solo wrote:
Art Carlson wrote:Looking at it from another perspective, you may, if you choose, ignore the effect of the magnetic field on the ions, but then the same electrostatic force that acts to pull the ions back in will act to pull the electrons out. If the magnetic field acts only on the electrons, it has to be twice as good because it has to not only counteract the tendency of the electrons to fly apart by thermal motion, it also has to counteract the indirect effect of the ions trying to fly apart and pulling the electrons along.
Sure. So running the reactor with a large negative charge means that ions are confined by electrostatic attraction and escape less frequently, with the tradeoff that electrons are repelled by the net charge, and escape more frequently. My impression was that since the electron gyroradius is smaller for a given B-field strength, then that is how the electrons are more easily confined: the cusp loss rate should be lower for electrons compared to ions since the cusp area varies with the gyroradius. (Thus the claim that electrons are 'easier to confine'.) So, even though the electrons need to be confined 'twice as well,' it is possible to confine them 'four times as well,' due to the mechanics of the cusp, so that you come out ahead.
Have you tried comparing the loss rates for ions and electrons, assuming line cusps and high beta? The Larmor radius of the ions is bigger by the square root of the mass ratio, so the effective hole they leak out of is bigger by this amount. But the speed at which they leak out (assuming equal temperatures) is smaller by the square root of the mass ratio, so the number of particles lost per unit time per unit length of cusp is the same for ions as for electrons. If you add a strong inwardly-directed electric field, this will cut the ion loss and raise the electron loss. So why don't you expect the electrons to have *worse* confinement than the ions, at least until enough leak out to destroy the potential well?

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Post by TallDave »

So why don't you expect the electrons to have *worse* confinement than the ions, at least until enough leak out to destroy the potential well?
I think we do. The trick getting the interior density 1000+ times higher than the outer.

Again, this doesn't worry me too much, as it sounds like we have experimental data that clearly shows the WB effect.

93143
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Post by 93143 »

Art Carlson wrote:You haven't addressed why you think you can say these things about a polywell but not about a cusp machine.
I may be hampered by the fact that I don't actually know what a cusp machine is. Reference?
I'm not sure what you mean by "The magnetic field doesn't need to be anywhere near strong enough to confine the ions." If you mean, do a good enough job of confining the electrons then they will confine the ions for you, then OK.
Yes, that's what I meant.
If you mean that the magnetic field only has to provide force balance against electron pressure, and not against the sum of electron and ion pressure, that's wrong, too.
I know. But since the ion temperature at the edge of the wiffleball is supposed to be very low, I don't expect that term to be large.
Then let us hold that thought: Success of the polywell requires good magnetic confinement on the inside *and* good recirculation on the outside. If either one of these is missing, it will fail. I have been calling the good magnetic confinement into question, and I am preparing a post that will question the good recirculation.
I attempted a response to your recirculation post. It is a weak response, but fortunately recirculation (well depth+density vs. input current) is the sort of thing they should be able to quantify on WB-7.

Incidentally, what do you think of my take on the scaling properties of pseudo-wiffleball confinement with line cusps? It does require recirculation to work, but that's a separate issue.
So why don't you expect the electrons to have *worse* confinement than the ions, at least until enough leak out to destroy the potential well?
The electrons should have far worse confinement than the ions. Assuming that annealing and/or POPS can be used to maintain a non-Maxwellian ion distribution, ion loss rates should be very very low.

hanelyp
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Post by hanelyp »

Art Carlson wrote:Then let us hold that thought: Success of the polywell requires good magnetic confinement on the inside *and* good recirculation on the outside. If either one of these is missing, it will fail.
A tokomak or other conventional magnetic confinement machine, lacking a recirculation mechanism, needs even greater magnetic confinement quality. Recirculation is effectively a multiplier on the magnetic confinement quality. If 999 electrons out of every 1000 that escape the interior are pulled back in, you can afford to leak roughly 1000 times as much through the cusps. The better the recirculation, the leakier the magnetic confinement may be. The better the magnetic confinement, the less recirculation you need.

Solo
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Post by Solo »

Art Carlson wrote: Have you tried comparing the loss rates for ions and electrons, assuming line cusps and high beta? The Larmor radius of the ions is bigger by the square root of the mass ratio, so the effective hole they leak out of is bigger by this amount. But the speed at which they leak out (assuming equal temperatures) is smaller by the square root of the mass ratio, so the number of particles lost per unit time per unit length of cusp is the same for ions as for electrons. If you add a strong inwardly-directed electric field, this will cut the ion loss and raise the electron loss. So why don't you expect the electrons to have *worse* confinement than the ions, at least until enough leak out to destroy the potential well?
Ok, you make a good point, assuming as you do that we are dealing with line cusps only. And that seems to be the case. So in theory, it shouldn't make any difference whether the potential well is positive, negative or neutral in terms of density confinement, correct? (that is, electrons are not easier to confine, in terms of getting plasma density.)

We expect the electron loss rate in the polywell to be much more than the ion loss rate, but the important question is whether the loss rate of electrons in this configuration will be worse than the loss rate of both species in a neutral plasma in a similar cusp field.

One thought: the electrons ought to have about the same (probably somewhat higher) KE/temp in this system, but the electrons will have this value at the edge of the potential well, where the ions will be fastest in the center (whereas in a neutral plasma both species will have max. velocity at all places). This might mean that the ion loss rate drops off faster than the electron loss rate increases.

Solo
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Post by Solo »

Apologies for the double-post.
Art Carlson wrote:So why don't you expect the electrons to have *worse* confinement than the ions, at least until enough leak out to destroy the potential well?
Remember that the electrons (the high-energy ones we are interested in) are being fed into the machine from an e-gun outside it, rather than produced by the ionization of the plasma inside it. They eventually drain by running into the magrid. So there's not really a question of them leaking out of the whiffleball: they are being force-fed into the cusps by the electrostatic potential outside the magrid caused by the positive charge on the grid. Any leaks (in terms of energy confinement) will be in terms of cross-field transport toward the magrid, or interception by supports/coil-connections, or maybe by upscattering and impact with the walls.

A different way to look at the BFR is like an Elmore-Tuck-Watson fusor, since these fusors actually have a positively charged central grid like the polywell. Then Bussard's idea is to magnetically insulate the grid to prevent electron impacts, and then secondarily to confine the plasma to increase the density in the center. I think that may be a better way to understand the machine, than looking at it from a primarily magnetic confinement perspective. The BFR is after all classified as an inertial electrostatic confinement device.

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