Significance of Electron Recirculation Revisited

[Art Carlson]

Are you saying that one can find in those pictures a structure where the ratio of ion to electron density differs significantly from unity, and where the density, potential difference, and size differ significantly from the relationship I gave?

Basically, yes. The model/picture there satisfy the Coulomb law/Gauss law div E=-rho/e0 and satisfy the densities specified by Bussard - as I calculated in my previous message. In contradiction to your general statement. Now what happens when things are scaled to densities at 10T I don't know.

Would you mind giving some numbers?

• n_e
• n_i
• the geometry of the structure (smallest dimension, and whether it is more spherical, cylindrical, or slab shaped)
• the potential difference within the structure

Anyways let me point out the error in your thinking. The rest I don't follow. Do you still think you found an error in my thinking or not?

Take a +5V battery. Attach a large metal plate to one of the electrodes. How much charge moves into the plate? Hardly any. Now. Attach a second metal plate to the battery's second electrode and bring it close to the first plate. Something amazing happens. Large quantities of charge move into the plates. The net charge in individual plates is humungous, despite them only being at +5V.

But you just proved this can't happen. You just proved capacitors can't work.

And I didn't bring out this ridiculous example of capacitors for nothing. The polywell (as an ideal) is a sort of a capacitor. One plate is the coils. The other plate is the magnetic field against which the (net) electrons squeeze.

Could you give a little more detail of the problem you see? There are no particles at all, and hence no non-neutrality, in the space between the capacitors. With the metal of the capacitor plates, there is no electric field and therefore no net charge density, ergo no non-neutrality. The only non-neutrality in the system is an excess of electrons in a thin layer near the surface of the plates. And the thickness of that layer will indeed be very tiny.

That's true it is thin in a capacitor. Does it have to be thin in the polywell? I can't say. Where is it located. My conjecture is closest to the coils. Which brings me back to the reason why I don't think polywell will work (read my messages before).

However, electrostatics models show that without breaking the Coulomb law it could be somewhere else. What's the physics that puts it there? I have no idea.

The layer of surface charge in a polywell can be much larger than in a capacitor because the density is much, much smaller than solid density. That's why I talk about microns and not Angtroms.

[Indrek]

I took B = 10 T (oops, I think I said I took 1 T), so the magnetic pressure is B^2/2mu_0 = (10)^2/(2*4*pi*1e-7) = 3.98e7 Pa (or 40 atm). (I apologize for the ASCII math, but (a) I don't know a better way to do it, and (b) as long as I am only doing four function arithmetic plus an occasional sqrt, you should be able to follow me anyway.) If beta = 1, then the plasma pressure n*k*(2/3)*<E> (since <E> = (3/2)*k*T in a thermal plasma, but I am not worried about factors on the order of unity here) is equal to the magnetic pressure, so let's take <E> = 1e4 eV to get n = (3.98e7 Pa) / ((1.6e-19 J/eV)*(2/3)*(1e4 eV)) = 3.73e22 m^-3.

About math. If there are any code monkeys around. The way to modify this forum to support math is:
a) write a plugin to catch the [math][/math] tags.
b) fetch an image from texify.com and store it locally
c) replace the [math][/math] with the link to the locally stored image.

In my code monkey hay days this would take about an hour to code and test. And if texify breaks - the old images won't break down as they are cached locally on this server. Also texify sometimes tends to deviously send the error image I fell upon before (based on referer so you probably have to fake it). If texify won't work - there is another service - codecogs.com. Probably there are others.

This is a really simple mod to do. No need to install latex to this server. Only local storage required. When I look at most of math in Art's messages I personally feel like beating my head against a brick wall to a bloody pulp. And this is just from counting the parentheses and slashes. I can't even get to the meaning.

[Indrek]

Would you mind giving some numbers?

• n_e
• n_i
• the geometry of the structure (smallest dimension, and whether it is more spherical, cylindrical, or slab shaped)
• the potential difference within the structure

• WB6 dimensions, 0.1T
• sphere of uniform charge, 0.1m radius
• Effective well depth ~4000V
• <E>=12kV
• (N_e-N_i)e=5.4e-8C

[TallDave]

This is beautiful. In response to an elementary physics argument, you don't present a counter argument, you don't even express your own well-founded skepticism, and you don't cite the skeptical argument of others - you "recall skepticism".

Heh, whoa, easy there big guy. I just wanted to note this discussion has been had, not rehash it (my point was just if you're deriving the Debye equation in a context where calculating the Debye length that way may not work, you may be making some bad assumptions in said derivation (I know there are different Debye equations that are appropriate depending on whether the mobility of ions is negligible compared to the process's timescale, though I'm not sure how relevant that is here without some more analysis...)). Do I really need to go look up the argument and cite it, or can I just say...

Done that. Check the archives.

Your only prediction I can recall was an ion current to the wall, which Rick says we don't see. OK, so from there we can assume Rick is lying or wrong or we can adjust our assumptions and make some more predictions for WB-8. Maybe something specific as a number for the current?

Do you know how to plug numbers into a formula?

Do you? If so, why haven't you done so to test their meaningfulness? They're your equations, after all, and for those of us who don't encounter rho or T_e on a daily basis they're a tad obscure, esp. when you don't explain what your terms represent.

[Giorgio]

Do you? If so, why haven't you? They're your equations, after all, and for those of us who don't encounter rho or T_e on a daily basis they're a tad obscure, esp. when you don't explain what your terms represent.

I assume that he means:

RHO= Plasma mass density
T_e= Electron temperature

[Indrek]

@Indrek: I can read your equation now, but I still don't know how to do it myself. When I edit your post I only find " http://img69.imageshack.us/img69/2749/52808308.gif ", which leaves me as high and dry as ever.

You have to turn your equations into a gif or jpg somehow. I don't know the secret sauce for that.

Go to texify.com. Type your equation. Right click and download it to your computer.

Go to imageshack.us, upload the image. You get a link. Paste it into your message here. The down-upload cycle takes 1 minute of your time. But it takes us 20 minutes to understand the parentheses mess you would use instead.

No need for this if you write something simple like a=b*c of course. But if you do things like (sqrt((a/b)*(c*d)/b/d))*d)/b)*a^3c then either don't write this crap at all or do the steps I outlined.

[TallDave]

Thanks Giorgio, those were just examples of common terms. Phi and mu_0 was where I had to decide if I care enough to go out and find a definition and value.

Just saying it's a bit of a struggle for some of us. But I know several here are considerably more familiar with the various constants and etc, so I try not to complain too much.

[TallDave]

I'm assuming that the thermalization time is dependant on the unrecirculated lifetime, as recirculation resets the electron to the original energy and direction.

Why would you assume that recirculated electrons are reset? Electrons in the cusps could be low energy. In fact it seems more likely they would be, at least in my understanding of electron confinement as a function of geometry -- since the electron population at the edge will tend to be dominated by low-energy electrons (as it's the only place low-energy electrons can get to) there would be more of them in the cusps, too.

They may just sit in the cusps oscillating and blocking other electrons from leaving (the "cusp-plugging" that's been discussed here).

How the electrons are distributed within the wiffleball is another matter. A. Carlson assumes that they would be in a thermalized cloud (I think) with resultant square potential well. If they preserve some portion of thier radial motion over their lifetime there would be a greater time dependant concentration near the center (travelling slower there) and an elliptical potential well would result.

That sounds about right to me. Nice calculations btw.

I think a common misconception about keeping the electron distribution nonthermal is that it supposedly happens for free -- it's actually the main input requirement. Upscattered electrons make it to the wall, downscattered end up at the casings, and they all have to be replaced to keep the mix slightly electron-rich and confine the ions. Essentially the main sources of loss are put to work cleaning up the ends of the distribution.

[Giorgio]

Thanks Giorgio, those were just examples of common terms. Phi and mu_0 was where I had to decide if I care enough to go out and find a definition and value.

Just saying it's a bit of a struggle for some of us. But I know several here are considerably more familiar with the various constants and etc, so I try not to complain too much.

Ops.. sorry, I didn't understand it was a rhetoric question, I thought it was a real request
After re-reading the post I got your point, which I fully agree with. It's quite difficult to follow the reasoning and application of the formula in this section of the forum even when you know what they are talking about, let alone when you are not familiar with it.

It might be useful to have a sticky post with the list of the terms and symbol commonly used in the formula. Also the use of texify as Indrek suggest might really make the difference to better understand ones thought and to pinpoint eventual errors.

Just for the sake of it, I do not agree too with Art Carlson calculation of the Debye length.
Anyhow, until we will have some real and solid experimental data, we will not know if the Polywell will work or "why" it will not work.
Mathematically we can prove and disprove almost anything, but only trough experiments will know the truth.

[D Tibbets]

It is really just as basic and nearly as simple as Coulomb's Law, which establishes a relationship between charge, potential, and geometry. If you choose any two of these, the third is automatically and unavoidably determined. It does not depend in any way on the velocity distribution of the particles or on whether or not things are changing in time.
...
As a simple consequence of Coulomb's Law, coupled with an upper limit for the potential and a lower limit for the density, non-neutral structures in a polywell reactor can never be bigger than a few microns.....

... But, what is important is the dynamic / time dependant nature of the beast. In a static or steady state situation A. Carlson's arguments may apply. But the Polywell is in an unsteady state. ...

Somebody is not paying attention.
In Faraday's law there is an explicit time dependence. In Ampere's law there is an explicit time dependence. Gauss's law ( = Coulomb's law) just sits there being true at every instant, without caring about any time derivatives.

I'm not trying to claim that you are not concidering time in jour derivations, I'm argueing that you are not concidering the imbalance in the electron and ion inputs. If cusp flows of electrons are matched by cusp flows of ions then the system is in balance, so the input current of ions would equal the input current of electrons, or the system would exceed coulomb limitations. But input electron current exceeds input ion current (at least that is the basis of my arguement) so the escape rate of electrons have to exceed the escape rate of [EDIT- ions ] or the system would violate Coulomb's law.

I believe you use debye arguments to justify ambi-polar flows, but I believe this applies to neutral plasmas (and the need to maintain this neutral plasma within quasineutral limitations*). I don't see how this would limit you in establishing a biased plasma so long as you expend energy to do so. The Polywell is not a neutral plasma, but a net negative plasma by a factor of ~1 ppm thanks to the continous input of excess electrons that have to perfectly match the excess loss of electrons through the cusps or some other mechanism.

* My understanding of quasineutrality is that it is a limitation of how large a local imbalance in charge can exist within an overall neutral plasma. I think that the bias in the Polywell plasma could be realitively neutral if a well insulated container had an equal but opposite charge(within quasineutral limits). If a conductive path is established (like a cusp) the current will be predominatly the EXCESS charged particles, I don't see how this behavior would be much different from a rechargable battery or capacitor. The mobile charge carriers (electrons ) flow/ drain, while the fixed ions stay behind. This will eventually be limited by the system moving towards neutrality (chemical reaction in a battery or bias in a capacitor), but if the battery or capacitor is recharged, the process can be unlimited. This is what I understand is occuring in the Polywell. As has been stated before it is essentialy a resupplied capacitor draining current through a conductor (a cusp in this case). The resistance of the conducter (confinement time of the electrons) and the potential bias determinbes the current amplitude and direction.

The debye sheeth acts like a diode (or perhaps a vacuum tube rectifier would be a better analogy) limiting unbalanced flow of one charged species compared to the oppositely charged species (if one flows through a circuit, the other must flow to ground- or more acuratly, the same mobile species must be replaced from ground)). Again, this is controllable by appying a biased potential (provided by excess electron input in the Polywell). In a plasma, there are two oppositly charged current carriers to consider, but the same rules apply.

Dan Tibbets

[TallDave]

But input electron current exceeds input ion current (at least that is the basis of my arguement) so the escape rate of electrons have to exceed the escape rate of electrons or the system would violate Coulomb's law.

Yes, thank you.

I'd really like to know what the cusps look like: if there's a 3-4 order of magnitude change in density from interior WB to exterior, what does the density and potential gradient look like over the length of the cusp? Does the entire fall off happen right at the edge of the WB (the cusp entrance) due to the WB geometry? Does it fall off gradually toward where the cusp opens up on the outside, because cusps are being plugged by oscillating electrons building up a slightly larger imbalance at the back end, pushed there by the current, where ions in the WB aren't pulled in because the larger imbalance is in a density 1e4 times smaller than that in the interior?

[KitemanSA]

... For a sphere with radius R and a uniform charge density rho, the potential difference between the center of the sphere and infinity is

Phi = 0.5*(rho/epsilon_0)*R^2

I do hate to expose my ignorance, but if you are talking a sphere with radius R, shouldn't that be R^3 for volume? After all, this isn't the r^2 seperation in most of the equations.

[Betruger]

When I look at most of math in Art's messages I personally feel like beating my head against a brick wall to a bloody pulp. And this is just from counting the parentheses and slashes. I can't even get to the meaning.

Here you go. FWIW I got some website suspiciously looking like a malware portal when I went to www.textify.com. No text input window, and an advertisement overlay you can't close on top of everything.

Also where does this 1e22m^-3 pop out from?

I took B = 10 T (oops, I think I said I took 1 T), so the magnetic pressure is

(or 40 atm).

If beta = 1, then the plasma pressure



(since in a thermal plasma, but I am not worried about factors on the order of unity here) is equal to the magnetic pressure, so let's take <E> = 1e4 eV

to get

.

Hope I didn't mangle it. The powers of ten "e" don't look right when near the e's of eV and exponential, but I didn't want to risk editing the original.

[Indrek]

... For a sphere with radius R and a uniform charge density rho, the potential difference between the center of the sphere and infinity is

Phi = 0.5*(rho/epsilon_0)*R^2

I do hate to expose my ignorance, but if you are talking a sphere with radius R, shouldn't that be R^3 for volume? After all, this isn't the r^2 seperation in most of the equations.

See
http://hyperphysics.phy-astr.gsu.edu/hb ... ce.html#c2
And calculate in the middle of the sphere.

[mad_derek]

FWIW I got some website suspiciously looking like a malware portal when I went to www.textify.com. No text input window, and an advertisement overlay you can't close on top of everything.

That's because the site you want is http://www.texify.com ...