The problem with ion convergence

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Art Carlson
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The problem with ion convergence

Post by Art Carlson »

I've started threads that are still running on cusp/whiffle confinement and recirculation. I think the only other really big stomach ache I have with the polywell is the idea of ion convergence. Rick Nebel has suggested that convergence may not actually be necessary, but it is usually invoked. (I am also interested in the idea because it is one of the few loopholes in the virial theorem.)

After mulling over a number of effects, I believe that one dominates all the others: the shape of the potential well. The usual picture is ions in a spherical electrostatic well, which reflects the out coming ions back into the middle thousands of times. But the polywell well will not be very close to spherical. Even at high beta, the magnetic field will push on the plasma ball with different strengths in different places, making it lumpy. (I believe Bussard also used this word somewhere.) If an ion bounces off a surface that is not tangent to a sphere, it will return off-center. Even if the discrepancy is only a fraction of a degree (I would expect several degrees.), the ions will bounce only a few times before convergence is destroyed. In fact they don't even have to bounce once, because the initial acceleration after ionization will already be off center.

I also don't believe you can maintain a monotonic ion energy distribution, much less a bi-modal one, but I think this is not so important. It only costs you a factor of 2 or 3 while losing convergence costs you a factor of 10 or 20.

tonybarry
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Post by tonybarry »

Pardon me for asking this Art, but if the ions are not oscillating through the centre of the potential well, then they must be orbiting in some elliptical orbit. If they orbit in this fashion, will not their energy of rotation be leeched by the EM field they travel through, causing them to spiral back down into the centre?

Regards,
Tony Barry

Art Carlson
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Post by Art Carlson »

tonybarry wrote:Pardon me for asking this Art, but if the ions are not oscillating through the centre of the potential well, then they must be orbiting in some elliptical orbit. If they orbit in this fashion, will not their energy of rotation be leeched by the EM field they travel through, causing them to spiral back down into the centre?
Leeching is not a concept I learned in grad school, at least not in relation to electric fields. The electric potential is a conservative field, so the sum of potential and kinetic energy is conserved. The ions could lose energy through drag on electrons, for example, and sink to the bottom of the well. If they do, they will no longer have the energy they need to fuse.

StevePoling
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Post by StevePoling »

Art Carlson wrote:
tonybarry wrote:Pardon me for asking this Art, but if the ions are not oscillating through the centre of the potential well, then they must be orbiting in some elliptical orbit. If they orbit in this fashion, will not their energy of rotation be leeched by the EM field they travel through, causing them to spiral back down into the centre?
Leeching is not a concept I learned in grad school, at least not in relation to electric fields. The electric potential is a conservative field, so the sum of potential and kinetic energy is conserved. The ions could lose energy through drag on electrons, for example, and sink to the bottom of the well. If they do, they will no longer have the energy they need to fuse.
Pardon me if I'm mistaken (most likely given my far remove from my undergraduate physics minor), but doesn't an elliptical orbit entail acceleration in the sense of change of direction, and doesn't a charged body undergoing acceleration in this sense radiate energy? Isn't this what's called synchrotron radiation? If so, then conservation of energy should dictate something that appears to the layman (which I am) to be a leaching of the particle's velocity. Wouldn't that reduce the size of the body's orbit?

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Post by TallDave »

Even at high beta, the magnetic field will push on the plasma ball with different strengths in different places, making it lumpy. (I believe Bussard also used this word somewhere.) If an ion bounces off a surface that is not tangent to a sphere, it will return off-center.
I don't think ions bounce off the B field; in fact I don't think the vast majority of ions ever see it, due to the WB effect of pushing the B field out of the core. By far the dominant effect should be the electric field, which is a quasiphere that focuses on a point (this focused well has been observed experimentally).

There are also other ways of enhancing ion focus; see this paper on "Experimental Observation of a Periodically Oscillating Plasma Sphere in a Gridded Inertial Electrostatic Confinement Device" by some guy named Nebel.

http://scitation.aip.org/getabs/servlet ... s&gifs=yes

Roger
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Re: The problem with ion convergence

Post by Roger »

Art Carlson wrote:I believe that one dominates all the others: the shape of the potential well.
Dr Carlson, a belated welcome, just a layman here. It looks like you are indeed getting up to speed.

I think you have hit a very vital point, the shape of the well.

IIRC Todd Rider assumed a broad flat well & Bremsstrahlung radiation. On the far other end, we might consider a central spike in the well, or something in the middle, a parabolic well. And then fuel richness.

I'm guessing shape of the well is one of those "knobs" that can tune the carburetor. Also can the carburetor be adjusted to "rich" or "lean" fuel mixes, and what are the resulting effects on the well ?
I like the p-B11 resonance peak at 50 KV acceleration. In2 years we'll know.

Art Carlson
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Post by Art Carlson »

TallDave wrote:
Even at high beta, the magnetic field will push on the plasma ball with different strengths in different places, making it lumpy. (I believe Bussard also used this word somewhere.) If an ion bounces off a surface that is not tangent to a sphere, it will return off-center.
I don't think ions bounce off the B field; in fact I don't think the vast majority of ions ever see it, due to the WB effect of pushing the B field out of the core. By far the dominant effect should be the electric field, which is a quasiphere that focuses on a point (this focused well has been observed experimentally).
I was accepting the approximation that the electrons see the magnetic field and the ions see the electrons through the electric field. But this entails that the ions see the magnetic field indirectly. The reason the term "quaisphere" is used is exactly because the shape of the electrostatic well is lumpy.

@Roger: I'm not talking about the shape of the well in the radial direction, whether flat or parabolic. I'm talking about differences in the tangential directions, so that the equipotential surfaces are not spherical.

Roger
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Post by Roger »

@Art, gotcha, thanks.

So the surface of the well that is presented to the MaGrid is lumpy ?
I like the p-B11 resonance peak at 50 KV acceleration. In2 years we'll know.

tombo
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Post by tombo »

Yes the surface of the well will be "lumpy".
It follows the fields which are "lumpy".
Indrek has an interesting plot of it at http://www.mare.ee/indrek/ephi/bfs/

Also it cannot be too spherical. Otherwise the magnetic field would be concave toward the plasma causing an instability.
I think that one of the failure modes is when the plasma pushes the field out far enough to make one of the magnetic arches concave toward the plasma and the well "blows out".

It seems to me that the dodecahedron, the icosahedron and the other higher ordered polyhedrons have more resistance to this failure mechanism than the cube, because they start out with the fields curved more strongly.
-Tom Boydston-
"If we knew what we were doing, it wouldn’t be called research, would it?" ~Albert Einstein

drmike
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Post by drmike »

Yeah - this is a great big hole that needs to be studied well. With luck it won't matter too much or it can be easily controlled. Without luck, it may make the whole thing not work.

Art Carlson
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Post by Art Carlson »

My arguments on confinement and recirculation are more subtle and must be discussed further, but the argument I presented in my original post in this thread seems to be very straightforward. Reading through the other threads again I also found this statement in support of my view:
jmc wrote:There was some hope originally that on top of the shrinking of the line cusps there would be convergence in the centre, that the electric field at the sheath surrounding the polywell, would all point toward the centre of the device, that all the ions would be ionized (created) in this sheath region and would all be accelerated on trajectories that pass through a similar point in the centre, this would lead to peaked densities at the centre and enhanced fusion power while cusps losses would remain unchanged. This would enhance both fusion power and the triple product by the convergence ratio.

Recent simulations and evidence suggests that achieving this will be difficult in the extreme, due to the equipotentials in the sheath not all pointing spherically inward and it being hard to ionize the atoms at a sufficiently similar energy for annealing to take place, and while it may perhaps not be impossible, it will probably be impossible in the absence of a far larger budget and a great deal more research.
May I take the lack of response as indicating a consensus that convergence is probably not possible? Does Rick Nebel or Tom Ligon want to jump in and defend convergence?

drmike
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Post by drmike »

Radial currents can be forced. It's not supposed to be necessary. I think the comparison to Farnsworth fusors should lead to the assumption that convergence is possible. Until I see data though, it's all just speculation.

To zeroth order, convergence should be natural. With a virtual cathode center and positive MaGrid, it is a stable configuration.

rnebel
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Post by rnebel »

First of all, I don't think it is correct to assume that the electrostatic field will collapse into a Debye sheath at the edge. That's an l.t.e. argument applied to a non-l.t.e. plasma. The shape of the potential well depends on the detailed balance of the electrons and the ions in the core. That's one of the peculiar things about these systems.

Secondly, it's worth noting that the power density depends AT MOST linearly on the compression (or convergence) ratio. The Langmuir solutions (no angular momentum) scale like 1/r**2. Unless you have huge convergence ratios (like the Hirsch Poissors) the effect isn't huge. We don't assume huge convergence ratios when we scale the machine.

Finally, the only way to do the "correct" calculation is to do the full bounce-averaged Fokker-Planck like Chacon did. Where the electrons/ions are when they collide makes a huge difference and determines whether or not they gain angular momentum (which is what determines the convergence ratio).

Art Carlson
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Post by Art Carlson »

drmike wrote:Radial currents can be forced. It's not supposed to be necessary. I think the comparison to Farnsworth fusors should lead to the assumption that convergence is possible. Until I see data though, it's all just speculation.

To zeroth order, convergence should be natural. With a virtual cathode center and positive MaGrid, it is a stable configuration.
How can radial currents be forced? Remember I'm not (only) talking about the average motion being in the radial direction. I'm talking about most of the ions having a nearly radial velocity for a long time. If you have physical control over this with a grid electrode, you might be able to get close. In a polywell, you have a virtual electrode of "loose" electrons, confined by a magnetic field formed from a small number of discrete coils. You'd have the same problem if you tried to make a Farnsworth fusor using an electrode made up only of a cubical frame. To zeroth order you may get convergence, but you have no way to keep the first order from killing you.

Art Carlson
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Post by Art Carlson »

rnebel wrote:First of all, I don't think it is correct to assume that the electrostatic field will collapse into a Debye sheath at the edge. That's an l.t.e. argument applied to a non-l.t.e. plasma. The shape of the potential well depends on the detailed balance of the electrons and the ions in the core. That's one of the peculiar things about these systems.
I didn't assume anywhere in my argument that the edge is a Debye sheath. Regardless of the radial form of the well, if it is not spherically symmetric, you will neither get nor maintain convergence.
rnebel wrote:Secondly, it's worth noting that the power density depends AT MOST linearly on the compression (or convergence) ratio. The Langmuir solutions (no angular momentum) scale like 1/r**2. Unless you have huge convergence ratios (like the Hirsch Poissors) the effect isn't huge. We don't assume huge convergence ratios when we scale the machine.
Good thing for you you don't need it. Still, it must hurt to take even a factor of 5 hit.
rnebel wrote:Finally, the only way to do the "correct" calculation is to do the full bounce-averaged Fokker-Planck like Chacon did. Where the electrons/ions are when they collide makes a huge difference and determines whether or not they gain angular momentum (which is what determines the convergence ratio).
Chacon's calculations are not relevant to my argument because he assumed a "spherically uniform electrostatic well". (Adding collisional effects can only make things worse.) My argument is much simpler and does not require "full bounce-averaged Fokker-Planck" calculations: (1) If the electrostatic well is not spherically symmetrical, the initial in-fall will not be radial, and the convergence on the center will get worse with every bounce, and (2) the electrostatic well in a polywell device will not be spherical because it must roughly follow the contours of a magnetic multipole field.

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