Significance of Electron Recirculation Revisited

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

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TallDave
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Postby TallDave » Fri Apr 02, 2010 1:08 am

If so, then you better be sending ions in and out with your electrons, or you will be violating Maxwell's equations somewhere


Why would your electron current have to match your ion current? You don't have to send any out, they just have be balanced by some combination of the Magrid and the ions already outside the Magrid. The charge doesn't care what the current is.

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.


It was pointed out before this doesn't matter much if there's a lot of them stacked around each other. In any case I recall skepticism calculating the Debye length that way is even valid in a Polywell where there are dynamic currents.

-----------------------------------------------
Yes, the paucity of data is very frustrating, but how about some testable predictions for when we do get data, or using existing data (like Indrek did)? What ion current do you expect in WB-7/8? What's the lowest density that could produce macroscropic non-neutral structures? How does that compare with known experiments that have shown well formation?

I wouldn't be at all surprised if they run into showstoppers as they try to scale up, but I would be surprised if ions flowing into the wall is among them.
Last edited by TallDave on Fri Apr 02, 2010 1:52 am, edited 4 times in total.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

icarus
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Postby icarus » Fri Apr 02, 2010 1:20 am

Chris MB: if you have the time, what kind of magnetic field is your plasma in the pictures confined with?

Rotating toroidal?

TallDave
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Postby TallDave » Fri Apr 02, 2010 1:34 am

Not sure where the lower energy electrons go. Joel seems to have them congregate at the edge of the well, IIRC.


Presumably they're lost to the casings. They would tend to aggregate near there because they don't have the energy to move toward what is the top of the well for them (the center).

Hey. who wants to calculate a density for WB-8? .8T magnets is pretty close to Art's 1T example above. Is the well going to be limited to a few microns? If so, we're probably going to know in a year because WB-8.1 is going to be cancelled and the data most likely released.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

D Tibbets
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Postby D Tibbets » Fri Apr 02, 2010 2:38 am

Art Carlson wrote:
BenTC wrote:To what degree would the positive HV electric field from the coils balance those electrons, rather than needing ions to do it?

If you play through the geometry with some model calculations, you will see that will hardly make any difference at all.

If I am able to get across one piece of plasma physics before I go my way,* I hope it is the way quasi-neutrality works. I've explained it so often, and always somebody pops up that doesn't get it. Let me try one last time.

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.

The way I like to think about it is to set the maximum potential difference allowed, the charge density, and the shape, and then calculate the maximum scale size. Let's assume spherical symmetry because it is simplest and most optimistic, in the sense of yielding the smallest value for the characteristic scale. 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

Take Phi and rho as given, and solve for R:

R = sqrt( 2*(e*Phi) / (rho*e/epsilon_0) )

If we ignore the numerical factor and replace e*Phi with k*T_e, and rho*e with n_e*e^2, then we have - not coincidently - the formula for the Debye length.

If we apply this to a polywell, we might take Phi no larger than 100 kV, and n in the range of 1e22 m^-3 (figuring B = 1 T, beta = 1, <E> = 10 keV). Then we find

R >= sqrt( 2*(e*Phi) / (rho*e/epsilon_0) )
= sqrt( 2*(1e5) / ( (rho/n*e)*(1.6e-19)*(1e22)/(8.854e-12) ) )
= sqrt(rho/n*e) * 3 microns

You can play with the assumptions, but obviously your polywell as a whole is much bigger than 3 microns, so rho = e*(n_i-n_e) will have to be much smaller than n*e. That's the meaning of quasineutrality. If you want to even start a discussion of non-neutral plasmas in a polywell, the best you can do is look at the cusps, but I have given arguments why the thickness of the cusps must be much larger than microns, and the 1-D or 2-D geometry will make things rather worse than the calculation I did here.

In brief:
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.....


Reasons why I guess that ambi-polar cusp flows are not required in the Polywell.
Art Carlson and others have presented relationships between charge, potential,and density. I won't argue the merits of this. 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. The electrons leak through the cusps, but they are replaced continously, thus the plasma is kept in an unbalanced state.
The quote below , I believe, is saying basically what A. Carlson said except from another direction. The electrons will reach a suddenly exposed ground faster than the ions due to inertia, but very quickly a debye sheeth will form and lengthen untill the electrons are shielded from the ground to an extent that the ion and electron flows match (= ambi-polar flow). The space charge or quasineutrality limits are what drive this final equalibrium .

But, in the Polywell, the continous injection of excess electrons negates this process (or rather stretches it out to infinite time (or at least till the machine breakes down)). I weakly reason that this is similar to reverse osmosis, there a nonequalibrium state is maintained by the application of external energy. Yes, this requires input energy, but so long as the magnetic confinement (and recirculation) is good enough, the costs are reasonable.


Quote from pp 104-105 of:

The Physics of Plasmas
Richard Fitzpatrick


http://farside.ph.utexas.edu/teaching/p ... lasma.html




"3.14 Langmuir Sheaths
Virtually all terrestrial plasmas are contained inside solid vacuum vessels. So, an obvious question is: what happens to the plasma in the immediate vicinity of the vessel wall? Actually, to a first approximation, when ions and electrons hit a solid surface they recombine and are lost to the plasma. Hence, we can treat the wall as a perfect sink of particles. Now, given that the electrons in a plasma generally move much faster than the ions, the initial electron flux into the wall greatly exceeds the ion flux, assuming that the wall starts off unbiased with respect to the plasma. Of course, this flux imbalance causes the wall to charge up negatively, and so generates a potential barrier which repels the electrons, and thereby reduces the electron flux. Debye shielding confines this barrier to a thin layer of plasma, whose thickness is a few Debye lengths, coating the inside surface of the wall. This layer is known as a plasma sheath or a Langmuir sheath. The height of the potential barrier continues to grow as long as there is a net flux of negative charge into the wall. This process presumably comes to an end, and a steady-state is attained, when the potential barrier becomes sufficiently large to make electron flux equal to the ion flux."

Dan Tibbets
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icarus
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Postby icarus » Fri Apr 02, 2010 6:29 am

Hey. who wants to calculate a density for WB-8?


Who would want to calculate anything?

There is no data so where's the motivation?

Time for Open Source Polywell Theory to go on strike methinks, it's a big bunch of "saving humanity BS" .... seen the same the thing in climate change, scientists saving humanity and then refusing FOIAs when curious souls show up with good intentions but difficult questions ... oh yeah, same old crap different pile.

Art Carlson
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Postby Art Carlson » Fri Apr 02, 2010 6:44 am

D Tibbets wrote:
Art Carlson wrote: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.

Art Carlson
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Postby Art Carlson » Fri Apr 02, 2010 6:57 am

TallDave wrote:In any case I recall skepticism calculating the Debye length that way is even valid in a Polywell where there are dynamic currents.
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".
Skepticism about what? "calculating the Debye length that way". Who calculated a Debye length? I derived consequences of Coulomb's law and pointed out parallels to the mathematics of the Debye length. That was an aside. Forget it and try to grasp the central argument.
And as I wearily pointed out to D Tibbets. Dynamics has nothing to do with it.

TallDave wrote:... how about some testable predictions for when we do get data ... ?
Done that. Check the archives.

TallDave wrote:What's the lowest density that could produce macroscropic non-neutral structures?
Do you know how to plug numbers into a formula?

Art Carlson
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Postby Art Carlson » Fri Apr 02, 2010 7:06 am

There seems to be another misconception I should clear up. My statement was about non-neutral structures, not about potential structures. Coulomb's law and my manipulations of it in no way preclude the possibility of large, deep, high-density potential wells. On the contrary, the argument says potential wells are easy to form in the sense that the excess of electrons over ions (or vice versa) only needs to be miniscule.

MSimon
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Postby MSimon » Fri Apr 02, 2010 8:59 am

Just for fun I'd like to do some simple wiffle ball calculations.

Let us start with this:

Radius .5 m - 8,000,000 Amp Turns = 10 T field. Roughly. So we have 8 E6* 6.25 E18 electrons a second passing through a section of coil. = 5 E25 electrons a second. Roughly.

Let us say that is mirrored by electrons spinning at the speed of light.

Coil circumference 3 meters. Speed of light 3E8 m/sec. so 1 electron could make 1E8 passes/ second. So you need 5E17 electrons roughly to balance the coil field.

That seems within the realm of possibility.
Engineering is the art of making what you want from what you can get at a profit.

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Postby MSimon » Fri Apr 02, 2010 9:10 am

Let me add that if it is ions doing the spinning you are going to have a WHOLE LOT of energy locked up in them.

Some one a while back suggested the Polywell as an energy storage mechanism and I thought the idea was nuts. Now I'm not so sure.
Engineering is the art of making what you want from what you can get at a profit.

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Postby Art Carlson » Fri Apr 02, 2010 9:21 am

@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.

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Postby MSimon » Fri Apr 02, 2010 9:23 am

Art Carlson wrote:@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.
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Postby Art Carlson » Fri Apr 02, 2010 9:52 am

I've had my coffee now, let's give it a crack.

Indrek wrote:
Art Carlson wrote:In brief:
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.

...
What you are saying is basically that my electrostatics simulation is wrong. The one at
http://www.mare.ee/indrek/ephi/pef8/

I'm sorry, but I was not able to divine the full glory of those simulations. 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?

Indrek wrote: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 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.

Indrek wrote:Anyways let me point out the error in your thinking.

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.

Indrek
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Postby Indrek » Fri Apr 02, 2010 11:30 am

Art Carlson wrote:I've had my coffee now, let's give it a crack.

Indrek wrote:
Art Carlson wrote:In brief:
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.

...
What you are saying is basically that my electrostatics simulation is wrong. The one at
http://www.mare.ee/indrek/ephi/pef8/

I'm sorry, but I was not able to divine the full glory of those simulations. 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.
Art Carlson wrote:
Indrek wrote: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 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.

Indrek wrote:Anyways let me point out the error in your thinking.

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.

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Postby rcain » Fri Apr 02, 2010 11:31 am

Blimey, its all kicking off on this thread.

Please dont leave us permanently Art. Look back on us from time to time and give us a good kicking, for old times sake. Who knows, there may even be news to chew over.

Indrek wrote:...Actually. If you run the numbers you'll see that you can't have electron-only plasma generated wiffleball...


not even temporarily? what happens if you cycle it?

MSimon wrote:I have seen a number of simulations of gridded devices and they all show oscillation - bunched electrons leaving and entering the reaction area. Not only that - the electrons seem to self co-ordinate so that the bunches leave an enter the device in synchronization


that sounds a very interesting area to explore. love some more data to make further modelling (speculation?) worthwhile.

the way i see it, there is a magnetic equilibrium manifold, an electrostatic equilibrium manifold, offset, and two species differing in inertia, but (almost) balanced in charge. even without various edge and surface effects, that topology spells a multi-mode resonant system to me. so it will 'pump' in various dimensions, hence Maxwell, Coulomb and quasineutrality happily co-reside, within frame.

the only thing that enables Q>1 is the discontinuity/nonlinearity of the (alleged) WiffleBall - otherwise all Arts prophecies come true.

Art Carlson wrote:...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
....
Gauss's law ( = Coulomb's law) just sits there being true at every instant, without caring about any time derivatives.


so i understand. but, surely at a micro-level, here the 'effects' of Coulombs law are determined by a dynamic, rather than fixed space-geometry in time. If we include POPS approaches, then at macro level too. We havent yet considered how the three Alfven modes might apply within a PW regime either.

chrismb wrote:... how does it manage to invert grad B drift?? By what means does it turn F=-µ.grad(B) into F=+µ.grad(B


precisely the question i would love to see answered (even guessed at). but again, we are looking to dedicated people to show it; experiment first or theory first i'd be equaly intrerested in either.

love the pix Chris - looks most intriguing, but I guess you would rather leave us simply intrigued, rather than informed. got your patent sorted out? seriously love to learn more.


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