Significance of Electron Recirculation Revisited

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

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MSimon
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Postby MSimon » Sun Apr 04, 2010 5:41 am

POPS used sine waves. The paper on it suggested that a different waveform might produce better results.
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Postby hanelyp » Sun Apr 04, 2010 10:47 pm

Art Carlson wrote:...Where the misconception is dwelling like a stubborn cough is the cusps. The cusps may be very small, but they are not small enough to allow a significant imbalance of ions and electrons. And yet some people seem to think that electrons can make an excursion out the cusps and back in again without taking ions along as hitchhikers. It's important because it means you can't improve on cusp confinement by applying some clever arrangement of radial electric fields. And cusp confinement by itself isn't good enough.

Wouldn't the relative energy of ions and electrons at the cusps make a difference? With an excess of electrons in the plasma the electrons would be at a high energy at the cusps while the ions would be low energy.

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Postby Art Carlson » Mon Apr 05, 2010 10:23 am

hanelyp wrote:
Art Carlson wrote:...Where the misconception is dwelling like a stubborn cough is the cusps. The cusps may be very small, but they are not small enough to allow a significant imbalance of ions and electrons. And yet some people seem to think that electrons can make an excursion out the cusps and back in again without taking ions along as hitchhikers. It's important because it means you can't improve on cusp confinement by applying some clever arrangement of radial electric fields. And cusp confinement by itself isn't good enough.

Wouldn't the relative energy of ions and electrons at the cusps make a difference? With an excess of electrons in the plasma the electrons would be at a high energy at the cusps while the ions would be low energy.

So if you want to confine those high-energy electrons, you have to (say Bussard and heirs) put the magrid at a high positive potential with respect to the wall. If you do this, however, any ions making it through the cusp, even if they start with a low kinetic energy, will be accelerated by the magrid potential towards the wall and have a high energy by the time they get there. And Coulomb says, if electrons are in the cusp exhaust, then ions are there, too.

Of course, that's not the whole story either, because by the same argument, the ions will drag electrons along with them. If you want my professional opinion, the only self-consistent picture is to let the quasi-neutral cusp plasma extend to the wall, where it is finally possible to develop a microscopic region with a large excess of ions - the Debye sheath. I've already given details. Check the archives.

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Postby rcain » Mon Apr 05, 2010 3:54 pm

Art, am I right in thinking that argument wouldnt (necessarily) apply in a pulsed/modulated machine?

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Postby Art Carlson » Mon Apr 05, 2010 7:31 pm

rcain wrote:Art, am I right in thinking that argument wouldnt (necessarily) apply in a pulsed/modulated machine?
I don't know why not.

bcglorf
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Dumb question

Postby bcglorf » Mon Apr 05, 2010 7:47 pm

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?

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Postby TallDave » Mon Apr 05, 2010 8:03 pm

So if you want to confine those high-energy electrons, you have to (say Bussard and heirs) put the magrid at a high positive potential with respect to the wall. If you do this, however, any ions making it through the cusp, even if they start with a low kinetic energy, will be accelerated by the magrid potential towards the wall and have a high energy by the time they get there.


If those excess exterior electrons are balancing the Magrid, wouldn't they also keep the ions from getting too much push towards the wall? (I think we just want our electron current to be much larger than our ion current)

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?


And if your exterior electron density is 1e4 times lower than the interior density, how much bigger does the disparity have to be in the cusps to create an ion current?
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

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Postby TallDave » Mon Apr 05, 2010 9:00 pm

For instance, to horribly oversimplify things, look at the ratio of excess electrons you need on the exterior to match the number on the interior if you accept Bussard's WB trapping factor of 1E-4.

Let's say interior density is 1E+22 ions per cm3, and 1E+22+(1E+22*1E-6) electrons, for a excess ratio of 1E-6 as Bussard says in Valencia.

To get the same number of excess electrons (1E+22*1E-6 = 1E+16) on the exterior, you would need an excess ratio of 1E-2 from 1E+18 ions, 1E+18+1E+16 electrons, 1E+16/1E+18 = 1E-2. That's 1% excess electrons versus one-millionth.

The trapping factor is also the factor by which the exterior electron excess ratio can increase without pulling in ions (at least in this grossly oversimplified example).
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

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Re: Dumb question

Postby Art Carlson » Mon Apr 05, 2010 9:23 pm

bcglorf wrote: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.

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Postby TallDave » Mon Apr 05, 2010 9:59 pm

Of course, that's not the whole story either, because by the same argument, the ions will drag electrons along with them


This is a little unclear to me. Assuming they have similar numbers (more or less quasineutral), why can't the electrons just flow past the ions? If you have a potential that moves electrons, why would you expect it to move ions in the same direction? This just goes back to ion pressure being low at the edge.

The exterior starts with neutrals that get ionized. Could there be enough to balance out the electrons that flow by? I agree getting tens of MV doesn't seem to make a lot of sense.
Last edited by TallDave on Mon Apr 05, 2010 10:13 pm, edited 2 times in total.
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 » Mon Apr 05, 2010 10:04 pm

I now have perhaps some comprehension of the debye length and the shielding effects of a plasma, but there are many assumptions that I don't think have been fully considered.
First off, the debye length is calculated with the assumption that there is only a tiny current that can be concidered as zero. In WB6 the electron input current was ~ 40 amps, if the recirculation factor was 100X, then without it the input current(and resulting output current consisting mostly of electrons and/ or ions flowing through the cusps to the walls (ground)) would have been ~ 4000 amps. This would have a presumably large effect on the derived debye length, if it could be derived at all.
Secondly, I don't know if non neutral plasmas make a difference in the derivation.
Thirdly, pulsed current like AC , as has been mentioned, can significantly modify the debye shielding length if the frequency of the input approaches the plasma frequency.
Also, the local Coulomb interactions do not dominate over the collective field effects within fusion type plasmas.

Most of this ramble is based on the following text, starting on page ~120.




PLASMA PHYSICS AND FUSION ENERGY
Jeffrey P. Freidberg
Massachusetts Institute of Technology
© J. Freidberg 2007


One way that helps me is looking at neutral (?) plasmas and voltage measurements / potential fields is to use a wire circuit. The wire = plasma with very good electrical conductivity. The debye sheeth = the resister length that is placed on each end of the wire to limit current flow. The length of this resistor is derived from temperature, density, etc. The strength of the resistor is determined by something. What is important is the length of the resistor as there would be a voltage drop across it if measured by a voltmeter. But if the voltage is measured along the wire between the resisters the voltage reading would be zero- there is no voltage drop, thus no potential field. I believe this would be consistant with a potential well in an IEC device being square with a flat profile except for a curving shoulder several debye lengths long on each end. An argument that this is not the case is represented by several experiments that have measured elliptical electric fields (continous change in potential from the center to the border) in devices much wider than the expected debye length. This suggests to me that the debye length does not give the complete answer, or the derivation of the debye length is at fault in these systems.

Dan Tibbets
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Postby TallDave » Mon Apr 05, 2010 10:10 pm

Nice find Dan, do you have a link or do I have to kill a tree for that?
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

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Postby MSimon » Mon Apr 05, 2010 10:21 pm

TallDave wrote:Nice find Dan, do you have a link or do I have to kill a tree for that?


No.

http://www.filestube.com/6e02fddf2c1b91 ... tails.html
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Postby TallDave » Mon Apr 05, 2010 10:34 pm

darn, I had my axe all sharpened and everything.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

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Postby rcain » Mon Apr 05, 2010 10:40 pm

Art Carlson wrote:
rcain wrote:Art, am I right in thinking that argument wouldnt (necessarily) apply in a pulsed/modulated machine?
I don't know why not.


simply put, because of the differing inertia of ions Vs electrons, they will respond to modulation at different rates.

since electrons lead ions in your scenario, we set the modulation frequency (and duty cycle) such that the device always cycles just short of an ion avalanche out of the cusps. (ions are phase retarded cf electrons).

of course i havent specified in what manner modulation is applied - whether the ion injectors, eV or B, or some 'orchestration' (for lack of a better word). i would also expect to see a 'bunching' effect dominate (observed both experimentally and theoretically in multi-grid fusors) if the modulation is any whole multiple of the bounce frequency or its harmonics. the overall dynamic's around the cusps however, could be made to adhere to a similar pattern.

does that make any sense? (and thanks for sticking around and trying to answer questions you admit you dont know the answer to :) )


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