Significance of Electron Recirculation Revisited

[bcglorf]

Sorry, I seem to keep asking stupid lay person questions.

And Coulomb says, if electrons are in the cusp exhaust, then ions are there, too.

Is that still true if the electrons in the core outnumber the ions by a sufficient amount? From my really limited understanding I don't see why the negative charge in the cusps MUST be greater than that from the center. Doesn't the core just need enough excess electrons to hold more charge than the cusps to prevent ions getting pulled out with the electrons?

I'm trying to extract myself gracefully from this forum, but I feel honor bound to answer direct and sincere questions, as long as I can make any sense out of them. This one in borderline, I'm afraid. I'm not sure what you're getting at, but the simple answer is, the only connection I have made to the core plasma is to derive a minimum density and assume that the cusp plasma will have a similar density (say within a factor of 2). If the cusp contains primarily electrons at this density, then the electric potential of the cusps will be tens ov MV. That wouldn't change, even if you also manage to produce tens of MV in the core plasma. The point is, you don't have any way to produce tens of MV either place, so the system will find a way to neutralize most of the charge of the electrons by putting ions there as well.

That makes sense to even a layperson like me, thanks .

If I'm not entirely lost, your saying the volume and density of the cusps is such that the potential there is impossibly high? If I'm allowed a followup question, are there theoretically possible(even if improbable) values for the cusp volume and density relative to the core that aren't impossibly high? One of Bussard's main claims was the 'shrinking' of the cusps as voltage was applied, which as I understand would reduce the volume(an maybe relative density) of the cusp region. Or is Bussard's claim and your statement a chicken and egg kind of argument?

[TallDave]

If I'm not entirely lost, your saying the volume and density of the cusps is such that the potential there is impossibly high?

I asked 93143 that question a while back, and his response was that it's hard to see how you could drive MV potentials (what would drive it?), which I found a very convincing argument against an electron-dominated edge/cusp/exterior. That means the difference between ion density and electron density can't be very large anywhere in the device (but it doesn't say they can't have very different energies in a given area). But I don't think quasineutrality in the cusps is a death knell (except for cusp-plugging, which it more or less drives a stake through).

If WB confinement is a geometric effect, we stipulate the existence of a well, and you're carrying a small (1/1e6) excess of electrons in the interior, then ion pressure at the edge will be low (notice Rick ignored the term entirely in his ITER comparison equation) and the ions around the cusps won't be energetic enough to get out of them very often. Those that do get out will probably amble over to the wall, never to be seen near a fusion again, but how many will upscatter that far? Maybe not enough to keep you from reaching useful Q values.

[Giorgio]

If WB confinement is a geometric effect......

That's the reason why all of these discussions are pretty useless.

The whole Polywell system is an Electro-Geometric machine, in which the various forces will interact in such ways that it will be more easy just to build the machine and see how it behaves than to try to calculate it's behavior in a mathematical way without the experimental model.

As a pure example, one of the factor that I never see anyone considering is that while the increase in magnetic field gives life to an increase in magnetic pressure (B^2/2*u_0) in the two directions "perpendicular" to the magnetic field, it also gives a decrease in pressure equal to the same amount in "parallel" direction, i.e. a Magnetic Tension.
How (if at all) will this tension influence the behavior of our fluid-Plasma inside the geometric confinement of a polywell?
This is of course just a rhetoric question, no need to try to answer it.
It's just to point out that first of all we should question if all the various hypothesis and the related formula that we try to apply do have any meaning and validity in a machine like Polywell.

My guess is NO. After all all of they come from observations done on machines and systems completely different from Polywell.

[icarus]

Giorgio

As a pure example, one of the factor that I never see anyone considering is that while the increase in magnetic field gives life to an increase in magnetic pressure (B^2/2*u_0) in the two directions "perpendicular" to the magnetic field, it also gives a decrease in pressure equal to the same amount in "parallel" direction, i.e. a Magnetic Tension.
How (if at all) will this tension influence the behavior of our fluid-Plasma inside the geometric confinement of a polywell?

Would you like to describe your derivation for these two emboldened statements? I'd be interested to see how you arrived at these conclusions, particularly the tension effect along the field lines from an increasing magnetic field strength. (I'm assuming you are talking about when the plasma kinetic pressure expands the magnetic field, i.e. 'pushback')

[bcglorf]

I don't think quasineutrality in the cusps is a death knell

I think it is, or is so close as to be hard to distinguish. At the narrowest point in the cusps, the potential voltage must be biased negatively leading back to the center. If it isn't, as Art has pointed out, you have nothing more than basic magnetic confinement, with unacceptable cusp loses. Given that the ions will be at very low energy in the cusps, the potential towards the centre doesn't need to be great, but it absolutely can't be neutral, or worse, drawing ions out where the magrid will slam them into the walls.

If my understanding above is correct, the only real hope I see is reducing the density and volume at the cusps enough that is possible. Bussard and Nebels comments leave me hopeful the WB effect may be doing that, but I'd like to hear more from Art on the hard theoretical limits on that. He seems pretty convinced they are a dead end, but at the same time Nebel doesn't strike me as deliberately deceptive and Art's argument should be elementary enough to Nebel that he has reason to disagree which I wish I knew enough to understand. I've been following in the hopes of a long shot, but also in the belief that nothing about the basic principles in the Polywell violated known physics.

[TallDave]

bcglorf,

Well, you can have both quasineutrality and a well or gradient. You just can't have a very large disparity between the electron/ion populations, because that would require MV potentials.

It's true cusp confinement isn't good enough, but we don't really know for sure where the WB effect comes from. Bussard seems to have believed it was a geometric effect resulting from the electron pressure,

Rick seems pretty confident he's seen a WB effect. I'm generally more interested in explanations that don't rule out what Rick and Bussard claim to have measured.

[bcglorf]

bcglorf,

Well, you can have both quasineutrality and a well or gradient. You just can't have a very large disparity between the electron/ion populations, because that would require MV potentials.

It's true cusp confinement isn't good enough, but we don't really know for sure where the WB effect comes from. Bussard seems to have believed it was a geometric effect resulting from the electron pressure,

Rick seems pretty confident he's seen a WB effect. I'm generally more interested in explanations that don't rule out what Rick and Bussard claim to have measured.

But at the very least, the portion of the cusp outside the magrid has to be electron dominated, meaning the density and volume of that region needs to be balanced from the inside with more electrons. It's a pretty good place to look for a basic sanity check, for a given drive voltage, the cusp size and density must be smaller than x.

[Giorgio]

Giorgio

As a pure example, one of the factor that I never see anyone considering is that while the increase in magnetic field gives life to an increase in magnetic pressure (B^2/2*u_0) in the two directions "perpendicular" to the magnetic field, it also gives a decrease in pressure equal to the same amount in "parallel" direction, i.e. a Magnetic Tension.
How (if at all) will this tension influence the behavior of our fluid-Plasma inside the geometric confinement of a polywell?

Would you like to describe your derivation for these two emboldened statements? I'd be interested to see how you arrived at these conclusions, particularly the tension effect along the field lines from an increasing magnetic field strength.

It's pretty straightforward, that is the Maxwell Tensor, it will be a mess to type here the way you reach it, but you can check it on Wikipedia for a simple summary:
http://en.wikipedia.org/wiki/Maxwell_stress_tensor

(I'm assuming you are talking about when the plasma kinetic pressure expands the magnetic field, i.e. 'pushback')

Quite the opposite, it's a compression in the directions perpendicular to the magnetic field and a traction parallel to the field (notice the negative sign in the Maxwell Tensor).

[Art Carlson]

If I'm not entirely lost, your saying the volume and density of the cusps is such that the potential there is impossibly high?

Right.

If I'm allowed a followup question, are there theoretically possible(even if improbable) values for the cusp volume and density relative to the core that aren't impossibly high? One of Bussard's main claims was the 'shrinking' of the cusps as voltage was applied, which as I understand would reduce the volume(an maybe relative density) of the cusp region. Or is Bussard's claim and your statement a chicken and egg kind of argument?

Of course, if you lower the density or the thickness enough, then the potential of a mostly-electron cusp eventually gets down to a value we can speculate about.

The thickness constraint is pretty hard, and I am pushing it already to consider point cusps with radius on the order of the electron gyroradius. I have given some strong arguments (although not quite as watertight as Coulomb's law), that the effective radius will be larger by a factor of (R/rho) or (R/rho)^2, and I strongly suspect by an additional factor of sqrt(m_i/m_e).

The choice of B = 10 T, on the other hand, was pretty arbitrary. It is a technological limit I took over from other discussions. It would be interesting to do the math the other way around: Assuming good confinement requires that the cusp plasma contain predominantly electrons (and retaining for the first round the optimistic assumption of point cusps with radius rho_e), what is the maximum permissible density? If this value is not smaller than the density of ITER, for example, one might still have a hope of economic power production.

[TallDave]

But at the very least, the portion of the cusp outside the magrid has to be electron dominated

But maybe only by enough to balance out the Magrid (what else is there to drive such potentials?).

What seems likely is a bowl-like gradient from bottom of the well at the center, peaking mid-Magrid at the cusps and then falling off to the wall. Ions that get out of the "bowl" are lost, but do enough low-velocity ions on the edge upscatter though the cusps to prevent Polywells from reaching useful Q values?

I have to agree with Giorgio too. Bussard called this electrodynamic as opposed to electrostatic. Tom Ligon's experience with PZLx-1 (built to study hydrodynamic stability) seems to argue something interesting happening...

[bcglorf]

But maybe only by enough to balance out the Magrid (what else is there to drive such potentials?).
That is just rephrasing what Art is saying. The limit on volume and density of electron dominated cusps is hard limited by the Magrid potential. What follows is the problem, density in the cusps is related to the density in the core. The question is does the upper limit on cusp density still leave room for viable density in the core? If I understand things at all, this is just a less accurate phrasing of Art's assessment:

Assuming good confinement requires that the cusp plasma contain predominantly electrons (and retaining for the first round the optimistic assumption of point cusps with radius rho_e), what is the maximum permissible density? If this value is not smaller than the density of ITER, for example, one might still have a hope of economic power production.

Thanks for your patience with me Art, I think that's exactly the question I wanted to get at, without knowing enough to even figure out how to ask it . I don't imagine you have an equally clean answer to go with? Is there any set of circumstances that meet those criteria without violating known physics, even if the window is ridiculously small? I'm searching for the difference between violating the laws of physics, and merely pushing them to the utter edges of what is theoretically possible.

[Art Carlson]

Assuming good confinement requires that the cusp plasma contain predominantly electrons (and retaining for the first round the optimistic assumption of point cusps with radius rho_e), what is the maximum permissible density? If this value is not smaller than the density of ITER, for example, one might still have a hope of economic power production.

Thanks for your patience with me Art, I think that's exactly the question I wanted to get at, without knowing enough to even figure out how to ask it . I don't imagine you have an equally clean answer to go with? Is there any set of circumstances that meet those criteria without violating known physics, even if the window is ridiculously small? I'm searching for the difference between violating the laws of physics, and merely pushing them to the utter edges of what is theoretically possible.

I thought this would produce an interesting number, but the answer is actually even more interesting than that. This post of mine has the most details. I had forgotten, but the 10 MV figure does not depend on the value assumed for the magnetic field. It is essentially the 500 keV rest mass of the electron plus a few factors. Reducing the magnetic field will reduce the density, which will in turn increase the Debye length, but it will increase the electron gyroradius to the same degree. I'm very sorry, but I can find no loopholes.

Bussard's and Nebel's picture of the way a polywell does or could work is flawed, not just in the details, but in the fundamental physics. Why don't you all just give it up and set your hopes on FRCs?

[TallDave]

The limit on volume and density of electron dominated cusps is hard limited by the Magrid potential.

No, I'm rejecting that "electron-dominated" notion entirely and assuming quasineutrality.

What follows is the problem, density in the cusps is related to the density in the core.

But how strongly are they related? If you have a well with ion focus, what's the corresponding drop-off in density at the edge, and what is the further drop-off due to the WB's unique geometry?

Sorry, I just don't find analyses that contradict what the experimenters are telling us very interesting. If Art wants to assume Rick hasn't actually seen WB confinement, fine, he's certainly entitled to do that given that nothing is published. I'm much more interested in analyses that would tend to explain what we're told has been measured, and how those might scale in larger machines.

[bcglorf]

Assuming good confinement requires that the cusp plasma contain predominantly electrons (and retaining for the first round the optimistic assumption of point cusps with radius rho_e), what is the maximum permissible density? If this value is not smaller than the density of ITER, for example, one might still have a hope of economic power production.

Thanks for your patience with me Art, I think that's exactly the question I wanted to get at, without knowing enough to even figure out how to ask it . I don't imagine you have an equally clean answer to go with? Is there any set of circumstances that meet those criteria without violating known physics, even if the window is ridiculously small? I'm searching for the difference between violating the laws of physics, and merely pushing them to the utter edges of what is theoretically possible.

I thought this would produce an interesting number, but the answer is actually even more interesting than that. This post of mine has the most details. I had forgotten, but the 10 MV figure does not depend on the value assumed for the magnetic field. It is essentially the 500 keV rest mass of the electron plus a few factors. Reducing the magnetic field will reduce the density, which will in turn increase the Debye length, but it will increase the electron gyroradius to the same degree. I'm very sorry, but I can find no loopholes.

Bussard's and Nebel's picture of the way a polywell does or could work is flawed, not just in the details, but in the fundamental physics. Why don't you all just give it up and set your hopes on FRCs?

And I'm afraid your referenced post is the point where you lose me. Rather, more accurately, where I get lost. My physics isn't strong enough to follow through your argument and understand it properly. I'm afraid there probably isn't any way to dumb it down enough for someone at my level to grasp, so just let me know if my question simply doesn't make sense to the problem. If I really want the answers I can take the time to school myself back up on the physics.

I can't follow how/where you map the density of the main plasma to the density in the cusp cylinder. If I'm not mistaken, Bussard seemed rather confident in claiming the density varied by as much as a factor of 4 from inside to outside the magrid, or is that my misunderstanding? Is there not any rational reason to expect a significant density decrease in the cusp cylinders the further you are from the main plasma? Again, if these questions are all irrelevant or foolish if you can follow the math you've already given just let me know that too. At least I know then where to start with my own study.

[TallDave]

If I'm not mistaken, Bussard seemed rather confident in claiming the density varied by as much as a factor of 4 from inside to outside the magrid, or is that my misunderstanding?

Not 4, 1E4.

I think this is the most accurate assessment:

The whole Polywell system is an Electro-Geometric machine, in which the various forces will interact in such ways that it will be more easy just to build the machine and see how it behaves than to try to calculate it's behavior in a mathematical way without the experimental model.

Back to paid work for me.