## The potential on the grid is irrelevant

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

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Art Carlson
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### The potential on the grid is irrelevant

Since somebody asked me a couple days ago to make I sketch of what I thought the spacial structure of the electric potential looked like, I've been trying to tap all the pieces of my model into place. There may be an easy way to think about it.

I have been arguing that the electrons and ions will stream out the cusps together and these beams/fans will extend to the wall. This is a result of the quasi-neutrality required by the densities, geometry, and potentials of relevance here and does not require the fluxes to be ambipolar. These beams, however, attach the central plasma ball to the wall electrically through the Debye sheath, so that the relative potential is determined by the current. Specifically (within a factor of 2 or so),
I = n*e*sqrt(kT/m_i)*A*exp( (V_1-V_2) / (kT_e/e) )
In addition there will be a "pre-sheath" voltage drop that accelerates the ions to the speed of sound. If the current is controlled by the sources (i.e. the electron beam), then the voltage of the plasma ball is fixed. When the current is near zero, the power loss will be minimized, which sounds like a good idea.

What about the potential of the magrid? The plasma will react with a surface charge density to patch together the potential it wants to have internally with what the magrid and other structures want to have externally, i.e. in the vaccum regions. You might want to use the voltage on the magrid as part of your electron gun, but you don't have to. It is irrelevant for confinement of the ions for the same reason I give to (almost) every question about plasma physics: quasi-neutrality. If you manage to (magnetically) confine the electrons, the ions will not have any choice but to stick around in their neighborhood.

The density and temperature within the plasma ball and cusp beams will be roughly constant. There will be about a factor of 2 drop in the density from the center to the wall.

I believe this picture is self-consistent and that a real polywell will not look too much different. If anyone can find inconsistencies I would appreciate hearing about them.

Rick Nebel, if he ever shows up again, will say that's all wrong because it assumes a thermalized plasma. In other threads I have calculated the thermalization rate and shown that draining off and re-injecting the electrons at a rate sufficient to maintain a non-Maxwellian distribution will require an unbelievably efficient machinery (>99.96%), and even given perfect engineering there are probably physics reasons why that cannot be achieved. On top of that, Rick has never explained just how a non-Maxwellian distribution will change anything in its essence. Sometimes it does, but often it doesn't. Until somebody shows why it matters and how the power balance works out, I'm sticking to the straightforward conclusion that the plasma is very nearly Maxwellian.

TallDave
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What would this look like in WB-7? WB-8? Real theories make predictions.

I think 93143 probably has it right: layered, not locally quasineutral.

chrismb
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The prediction it makes is clear: it will result in a discharge plasma, exactly as it looks to be in that "test plasma" photograph on emc2 homepage.

TallDave
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In other threads I have calculated the thermalization rate and shown that draining off and re-injecting the electrons at a rate sufficient to maintain a non-Maxwellian distribution will require an unbelievably efficient machinery (>99.96%),
It was hard to square that with this.
rnebel wrote:For present generation machines the electron confinement time is less than the electron collision time so thermalization isn't an issue. For reactors, the electron collision time and the confinement time become comparable. Electron distributions are expected to be isotropic, but not thermal. Thermalization is a global process because electron orbits cover the entire interior. If electrons lose their energy (kinetic + potential), they will accumulate near the coil cases until they leave the system.

Art Carlson
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TallDave wrote:
If anyone can find inconsistencies I would appreciate hearing about them.
What would this look like in WB-7? WB-8? Real theories make predictions.
And real experiments publish measurements. The problem is not that my model doesn't make predictions (specifically of the minimum energy loss), but that there is nothing to compare the predictions to.
Yeah. A lot of people around here like to make guesses. I'm only interested in talking physics.
TallDave wrote:I think 93143 probably has it right: layered, not locally quasineutral.
If that's what you call thinking, you'd better stick to guessing. A layered plasma would exhibit plasma oscillations, which would be damped either by drag between the electrons and ions or by Landau damping. You know people have learned a thing or two about plasmas in the last 80 years. Hypotheses can be examined in that light and some of them ruled out.

alexjrgreen
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### Re: The potential on the grid is irrelevant

Art Carlson wrote:If you manage to (magnetically) confine the electrons, the ions will not have any choice but to stick around in their neighborhood.

The density and temperature within the plasma ball and cusp beams will be roughly constant. There will be about a factor of 2 drop in the density from the center to the wall.
chrismb wrote:The prediction it makes is clear: it will result in a discharge plasma, exactly as it looks to be in that "test plasma" photograph on emc2 homepage.
In the "test plasma" photograph the higher density regions have a shape.

Does the theory predict what this shape will be?
Ars artis est celare artem.

TallDave
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And real experiments publish measurements. The problem is not that my model doesn't make predictions (specifically of the minimum energy loss), but that there is nothing to compare the predictions to.
Now who's hiding behind the lack of data? Let's have a prediction for WB-7, so I can laugh at the idea they funded WB-8 with your predicted confinement.
Yeah. A lot of people around here like to make guesses. I'm only interested in talking physics.
You mostly seem interested in vague physics that doesn't make predictions about actual real-world machines. Which isn't much different than guessing.
If that's what you call thinking, you'd better stick to guessing.
Temper, temper.
A layered plasma would exhibit plasma oscillations, which would be damped either by drag between the electrons and ions or by Landau damping.
Maybe. I'd like to see some modelling.

chrismb
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### Re: The potential on the grid is irrelevant

alexjrgreen wrote: In the "test plasma" photograph the higher density regions have a shape.

Does the theory predict what this shape will be?
yes. a discharge plasma in a magnetic field will flow into the regions of minimum magnetic flux, according to grad B drift, just as you can see in that photo and also just like dan dt's efforts with the permanent magnets in a pressure cooker. it's nothing special, i am afraid to say. the density of the shape follows inversely the mag flux.

Art Carlson
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TallDave wrote:
And real experiments publish measurements. The problem is not that my model doesn't make predictions (specifically of the minimum energy loss), but that there is nothing to compare the predictions to.
Now who's hiding behind the lack of data? Let's have a prediction for WB-7, so I can laugh at the idea they funded WB-8 with your predicted confinement.
Yeah. A lot of people around here like to make guesses. I'm only interested in talking physics.
You mostly seem interested in vague physics that doesn't make predictions about actual real-world machines. Which isn't much different than guessing.
From Feb 9: viewtopic.php?p=16258&#16258

TallDave
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And Rick's response was:
Here's where I'm coming from. Obviously, I know what's in the data and I know what it is consistent with. We've known that for several months. However, just because a piece of data is consistent with one model doesn't mean that it's inconsistent with another model. When you compare data and theory, the best you can say is "it's consistent with...." .

I know that the confinement in the WB-7 is much, much better than ballistic. I also believe that the dominant energy flowthrough is in the electrons, not the ions. Glen Wurden (whom you probably know from LANL) has taken some fast framing pictures of the plasma, and the hot spots are on the coils, not the walls. While this isn't a proof, it's a pretty strong indicator.
Like I've said, this debate is entertaining, but ultimately a sideshow.
You know people have learned a thing or two about plasmas in the last 80 years.
No doubt Bussard would voice similar sentiments, were he able.

But thanks for the objections, I'll have to look into the oscillations. Rick Nebel is of course already very familiar with the concept of oscillations in a plasma...
Last edited by TallDave on Wed Dec 16, 2009 3:45 pm, edited 3 times in total.

alexjrgreen
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### Re: The potential on the grid is irrelevant

chrismb wrote:
alexjrgreen wrote: In the "test plasma" photograph the higher density regions have a shape.

Does the theory predict what this shape will be?
yes. a discharge plasma in a magnetic field will flow into the regions of minimum magnetic flux, according to grad B drift, just as you can see in that photo and also just like dan dt's efforts with the permanent magnets in a pressure cooker. it's nothing special, i am afraid to say. the density of the shape follows inversely the mag flux.
I'm assuming that no one would invest in this, much less a peer review group who individually have decades of experience in plasma physics.

Something more constructive must be happening.
Ars artis est celare artem.

chrismb
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maybe. but not from that picture... unless they have been mesmerised by "the pretty light".

well... pretty pictures have been known to get gov ministers investing millions in tokamak - it's easy to get carried away when you've finally got a picture to show someone - after investing millions!

93143
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Art Carlson wrote:
TallDave wrote:I think 93143 probably has it right: layered, not locally quasineutral.
If that's what you call thinking, you'd better stick to guessing. A layered plasma would exhibit plasma oscillations, which would be damped either by drag between the electrons and ions or by Landau damping. You know people have learned a thing or two about plasmas in the last 80 years. Hypotheses can be examined in that light and some of them ruled out.
As far as I can tell, the idea is in fact similar to plasma oscillation, except that at the edge of the wiffleball you have a cold thermal ion distribution and a very fast two-stream electron distribution (that turns around at the diamagnetic boundary without slowing down or increasing in density), which anchors the waveform, so the result is (in my imagination, anyway) standing Langmuir waves with high two-stream particle flux.

The thought process that resulted in this picture assumed a collisionless plasma. Naturally collisionality will damp such an effect, if it exists, but how much? At these energies, the mean free path for ion-ion and ion-electron Coulomb collisions is pretty long, and electron-electron annealing (Landau damping, which in this case is not the opposite of the two-stream instability) could mitigate the effects of head-on collisionality between inflowing and outflowing electron distributions over the timescale of interest. Actually, since for the ions the timescale of interest has to do with fusion, which is related to ion-ion collisionality, the annealing properties of the ion density wave peaks would be important too...

I haven't made a big deal of this idea because I don't have the plasma physics background to support it analytically (that or I'm just too lazy), so I wanted to do a simulation to see if I could observe the effect in a low-density spherically-symmetric system, but Boltzmann's equation is hard to solve even with spherical symmetry... perhaps I should try a collisionless beamlike two-stream system for starters; the solution procedure could be greatly simplified... it might even run on a desktop in a reasonable amount of time...

Experiments with fusors have shown multiple well formation.

On the other hand, this picture is a bit difficult to square with what Dr. Nebel said about the electron distribution being isotropic (but not thermal)... It's still an improvement over the last time I tried to explain the internal structure of the wiffleball plasma, in that this time the potentials and densities are at least physically consistent...

Art Carlson
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TallDave wrote:And Rick's response was:
Here's where I'm coming from. Obviously, I know what's in the data and I know what it is consistent with. We've known that for several months. However, just because a piece of data is consistent with one model doesn't mean that it's inconsistent with another model. When you compare data and theory, the best you can say is "it's consistent with...." .

I know that the confinement in the WB-7 is much, much better than ballistic. I also believe that the dominant energy flowthrough is in the electrons, not the ions. Glen Wurden (whom you probably know from LANL) has taken some fast framing pictures of the plasma, and the hot spots are on the coils, not the walls. While this isn't a proof, it's a pretty strong indicator.
I didn't know what to make of his response back then either. Is he a physicist or a sphinx? Is he trying to say that my model is consistent with the data, too? Afer all, I also predict that the confinement will be "much better than ballistic". You're not only free to guess what the data is, you are also free to guess what Rick is saying about the data.

alexjrgreen
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### Re: The potential on the grid is irrelevant

Art Carlson wrote:Since somebody asked me a couple days ago to make I sketch of what I thought the spacial structure of the electric potential looked like, I've been trying to tap all the pieces of my model into place.
What do you make of Joel G. Rogers' PIC Simulation of Polywell?
Ars artis est celare artem.