Diffusion and Osmosis- an argument against ion cusp losses

[D Tibbets]

I have heard and tried to follow arguments from A. Carlson and others about ions always following electrons through cusps in equal proportions due to basically electrostatically driven diffusion processes. But, without using plasma formulas, but instead fluid/ gas arguments; the Polywell has magnetic confinement of electrons. This is in effect a semipermiable membrane- ions can pass through, but electrons cannot. This results in a buildup in negative charge within the magrid untill a balance is reached- the osmotic pressure if you will. This will contain a number of the ions at a number less than the number of electrons. Since the semipermiable membrane is not perfect (cusp losses, etc) some electrons will leak out and normally the ions would leak out with them to maintain the relative concentrations within the Polywell. But, new electrons are pumped back into the Polywell through the electron guns, so the concentration of electrons inside is maintained and therefor the ions are contained in equal proportion. ie- the ions will not follow the electrons out of the cusps so long as the lost electrons are replaced. Otherwise the osmotic gradiant would be increasing (electrostatic potential would be increasing). So, by maintaining an excess of electrons inside the Magrid the ions are effectively contained and do not follow the electrons through the cusps- unless you add energy to the system- effectively increasing the osmotic potential/ pressure. The system is similar to reverse osmosis, in which the driving force is the excess pumped electrons.

This chemical/ biological (and nerve impulse) analogy should, I think, be equally valid for plasmas. The only way I see for non upscattered ions (upscattered high energy escaping ions would increase the internal potential, so allowing room for replacement with a new low energy injected ion- thus in effect recycling the ion energy (?)[EDIT- upon reflection, this peticular idea is nonsensical, so please ignore]) to escape is for them to first combine with an electron and then diffuse out as a neutral atom without effect on the potential gradiant.


Dan Tibbets

[Art Carlson]

I have heard and tried to follow arguments from A. Carlson and others about ions always following electrons through cusps in equal proportions due to basically electrostatically driven diffusion processes. But, without using plasma formulas, but instead fluid/ gas arguments; the Polywell has magnetic confinement of electrons. This is in effect a semipermiable membrane- ions can pass through, but electrons cannot. This results in a buildup in negative charge within the magrid untill a balance is reached- the osmotic pressure if you will. This will contain a number of the ions at a number less than the number of electrons. Since the semipermiable membrane is not perfect (cusp losses, etc) some electrons will leak out and normally the ions would leak out with them to maintain the relative concentrations within the Polywell. But, new electrons are pumped back into the Polywell through the electron guns, so the concentration of electrons inside is maintained and therefor the ions are contained in equal proportion. ie- the ions will not follow the electrons out of the cusps so long as the lost electrons are replaced. Otherwise the osmotic gradiant would be increasing (electrostatic potential would be increasing). So, by maintaining an excess of electrons inside the Magrid the ions are effectively contained and do not follow the electrons through the cusps- unless you add energy to the system- effectively increasing the osmotic potential/ pressure. The system is similar to reverse osmosis, in which the driving force is the excess pumped electrons.

This chemical/ biological (and nerve impulse) analogy should, I think, be equally valid for plasmas. The only way I see for non upscattered ions (upscattered high energy escaping ions would increase the internal potential, so allowing room for replacement with a new low energy injected ion- thus in effect recycling the ion energy (?)[EDIT- upon reflection, this peticular idea is nonsensical, so please ignore]) to escape is for them to first combine with an electron and then diffuse out as a neutral atom without effect on the potential gradiant.

Dan Tibbets

I think your way of looking at the system is essentially correct and not too different from the way I look at it. I'm not so clear on what conclusions you are drawing.

Let me clarify one point before Rick Nebel starts scolding us. I don't really say "ions always follow electrons through cusps in equal proportions". What I'm saying (at least up to this point in the argument) is that the ion density must be very nearly equal to the electron density, not only in the bulk of the plasma, but also in the cusps. In fact, the arguments I have brought so far (in this round) would be satisfied by a population of ions that just sit around in the throat of the cusps without going AWOL at all.

The osmosis idea is only of limited relevance here because we are not talking about what happens around the "membrane" but about what happens at the "holes" in the membrane, where neither electrons nor ions are inhibited in their radial motion by the magnetic field.

[KitemanSA]

I have heard and tried to follow arguments from A. Carlson and others about ions always following electrons through cusps in equal proportions due to basically electrostatically driven diffusion processes. But, without using plasma formulas, but instead fluid/ gas arguments; the Polywell has magnetic confinement of electrons.

NO!!! Polywell has electro-static confinement of electrons with magnetic enhancement. In all truth, the reflections that the wiffleball give are just gravy. If all the magnets did was nudge the electrons away from the positive MaGrid and direct them thru the cusps, the machine would still be just fine, because the positive potential of the MaGrid would just draw them back in.

Since the electrons that "leak out" of the cusps came in THRU the cusps in the first place, and largely turn around and come back in after "leaking", what violates the quasi-neutrality of the Polywell? What is to draw the ions out?

This large flow of electrons OUT and BACK IN is the non-ambipolar (thanks for the term!) condition Dr. N mentioned in another thread recently.

[Art Carlson]

Since the electrons that "leak out" of the cusps came in THRU the cusps in the first place, and largely turn around and come back in after "leaking", what violates the quasi-neutrality of the Polywell? What is to draw the ions out?

It doesn't matter whether the electrons are streaming out, streaming in, or bouncing back and forth - they still need to be neutralized by ions. Likewise, it doesn't matter whether the ions doing the neutralizing are streaming out, streaming in, or just hanging out. Is anybody still contending this point? The plasma in the cusp throats must be quasineutral.

(Very shortly we sill begin discussing just what it is that those ions do. But I would like to first make sure we all agree they are there.)

[KitemanSA]

The plasma in the cusp throats must be quasineutral.

Sorry Art, I suppose you have defined what you mean by "cusp throat" in another post, but if so, I didn't read it. Is the cusp throat inside or outside the well?

[Art Carlson]

The plasma in the cusp throats must be quasineutral.

Sorry Art, I suppose you have defined what you mean by "cusp throat" in another post, but if so, I didn't read it. Is the cusp throat inside or outside the well?

I didn't really define it and I don't know if it's good terminology. I mean the radial region where (1) the magnetic field is maximum, (2) the electric potential is maximum, (3) physically located closest to (at the same radius as) the magrid.

At the risk of tipping my hand, I am aiming to get myself a population of ions with nothing between them and the wall expect a straight (and moderately expanding) magnetic field and a down-sloping potential hill.

[KitemanSA]

I didn't really define it and I don't know if it's good terminology. I mean the radial region where (1) the magnetic field is maximum, (2) the electric potential is maximum, (3) physically located closest to (at the same radius as) the magrid.

OK, first off, I am assuming you are using the term "potential" as the voltage that causes an electron to move in-radius. Max potential, max inward pull on an electron. Further, I am assuming that at radius = infinity, the "potential" has gone to ground.

With that, and given your quote as your definition of cusp throat, then no, it is not quasi-neutral there. By that location, the ions have escaped the well and are gone.

Now, somewhere in-radius of that point, there is a location where the potential is again at ground. I call this location the edge of the well. Inside of the edge, the ions are in the well. It may be that in the well the plasma is uniformly quasi-neutral, but even there I am not so sure. I don't recall anyone who is involved with the Polywell saying that the plasma is uniformly quasi-neutral. Dr. N. did say that the Polywell was quasi-neutral, but I don't recall him saying the plasma is uniformly so.

[Art Carlson]

I didn't really define it and I don't know if it's good terminology. I mean the radial region where (1) the magnetic field is maximum, (2) the electric potential is maximum, (3) physically located closest to (at the same radius as) the magrid.

OK, first off, I am assuming you are using the term "potential" as the voltage that causes an electron to move in-radius. Max potential, max inward pull on an electron. Further, I am assuming that at radius = infinity, the "potential" has gone to ground.

You don't have to assume anything about the way I use the term "electric potential". That has been well-defined for 200 years. I'd suggest you brush up on the concept because at a maximum of potential there is no force on a charge.

With that, and given your quote as your definition of cusp throat, then no, it is not quasi-neutral there. By that location, the ions have escaped the well and are gone.

You'll have to do better than that. I presented a calculation that showed any plasma near the (hypothesized) maximum in potential must be quasi-neutral. Either point out a problem with the calculation or hold your piece.

Now, somewhere in-radius of that point, there is a location where the potential is again at ground. I call this location the edge of the well. Inside of the edge, the ions are in the well. It may be that in the well the plasma is uniformly quasi-neutral, but even there I am not so sure. I don't recall anyone who is involved with the Polywell saying that the plasma is uniformly quasi-neutral. Dr. N. did say that the Polywell was quasi-neutral, but I don't recall him saying the plasma is uniformly so.

I assure you that Dr. Nebel meant that any region in the main plasma large compared to the Debye radius (appropriately calculated, given the possibility that the energy distribution is not Maxwellian) is quasi-neutral. Let me beat on him a bit longer and he will make the same concession for the plasma in the cusps.

[Skipjack]

Hmm, maybe there should be a glossary of terms frequently used here somewhere.
It sometimes also seems to me that there is a commonly accepted terminology for all the effects, etc that are being observed, theorized and talked about here frequently.
I dont know, maybe there are already some terms that are "normally" used for some things. Arts "cusp throat" seems to be a good candidate.
In any case having something like this, could make it a lot easier for people to follow conversations on these boards, especially those of us that are already having a difficult time. Then you add in a hand full of abbreviations and spice it up with some self invented terms and people like me will end up looking at you like a deer into headlights.

[TallDave]

I assure you that Dr. Nebel meant that any region in the main plasma large compared to the Debye radius (appropriately calculated, given the possibility that the energy distribution is not Maxwellian) is quasi-neutral. Let me beat on him a bit longer and he will make the same concession for the plasma in the cusps.

Or, since the electron-rich plasma is spitting out electrons and all the well-confined ions are too far away to be pulled ino the cusps, the force just builds up until it reaches a balance where it repels more electrons from accumulating in the cusp throat but isn't so big it requires a massive charge on the Magrid.

[KitemanSA]

Or, since the electron-rich plasma is spitting out electrons and all the well-confined ions are too far away to be pulled ino the cusps, the force just builds up until it reaches a balance where it repels more electrons from accumulating in the cusp throat but isn't so big it requires a massive charge on the Magrid.

??? I thought there was a massive charge on the MaGrid. Isn't 12kV pretty massive?

[hanelyp]

If the plasma at the cusps has a substantial population of positive ions, it would leak those ions rapidly on the outer side of the cusps, driven by the same electric field that recirculates electrons. The rate at which ions reach the electric field peak is a key question of how well the polywell works. As I understand the Buzzard model, ions lack the energy to reach that point.

[Art Carlson]

If the plasma at the cusps has a substantial population of positive ions, it would leak those ions rapidly on the outer side of the cusps, driven by the same electric field that recirculates electrons. The rate at which ions reach the electric field peak is a key question of how well the polywell works. As I understand the Buzzard model, ions lack the energy to reach that point.

What do you mean by "electric field peak"? I suspect you mean the peak of the electric potential. Please, all of you, try to be a little more precise. If we are not careful to distinguish between electric potential and electric field, between density and flux, we can't do any physics.

[Art Carlson]

??? I thought there was a massive charge on the MaGrid. Isn't 12kV pretty massive?

My calculation determined that 10 MV would be needed. (And since I just started a crusade for more precision, that's an electric potential or voltage of 10 MV. Charge is measured in Coulombs.)

[Art Carlson]

Or, since the electron-rich plasma is spitting out electrons and all the well-confined ions are too far away to be pulled into the cusps, the force just builds up until it reaches a balance where it repels more electrons from accumulating in the cusp throat but isn't so big it requires a massive charge on the Magrid.

"Too far away"? Have I ever mentioned that the polywell plasma is quasi-neutral? There are ions everywhere.