Significance of Electron Recirculation Revisited

[bcglorf]

I think Bussard's idea that the density in the cusp outside the magrid is very much lower than inside is based on (wrongly) neglecting quasi-neutrality in the cusps. My working picture of the cusps is just holes (or more precisely a straw or a slit between two parallel plates) that let plasma out. In fluid dynamics you usually don't get more than a factor of 2 drop in the density in those circumstances. A somewhat more sophisticated way to look at, that is also found in the literature, is that there is a "sheath" around the plasma ball that gets bled off into the cusps, whereby the flux tubes have a constant magnetic field, at least as long as they run along the plasma ball. This would also lead to a cusp density close to the density in the plasma ball, again dropping by a factor of 2 or less.

In the theory of plasma-wall interactions, including Langmuir probes, the density drop would be called the "pre-sheath". The value can depend on various conditions, particularly on how the plasma is replenished, but a drop by a factor of 2 is very typical.

A few more questions come to mind then. What is a ballpark density difference between core and cusp needed for things to work as Bussard envisions? A factor of 10, 100, 1000? The obvious follow on being if a factor of 2 is typical, what is the atypical extreme and is there a theoretical limit that can be placed there as well?

[D Tibbets]

I think Bussard's idea that the density in the cusp outside the magrid is very much lower than inside is based on (wrongly) neglecting quasi-neutrality in the cusps. My working picture of the cusps is just holes (or more precisely a straw or a slit between two parallel plates) that let plasma out. In fluid dynamics you usually don't get more than a factor of 2 drop in the density in those circumstances. A somewhat more sophisticated way to look at, that is also found in the literature, is that there is a "sheath" around the plasma ball that gets bled off into the cusps, whereby the flux tubes have a constant magnetic field, at least as long as they run along the plasma ball. This would also lead to a cusp density close to the density in the plasma ball, again dropping by a factor of 2 or less.

In the theory of plasma-wall interactions, including Langmuir probes, the density drop would be called the "pre-sheath". The value can depend on various conditions, particularly on how the plasma is replenished, but a drop by a factor of 2 is very typical.

A few more questions come to mind then. What is a ballpark density difference between core and cusp needed for things to work as Bussard envisions? A factor of 10, 100, 1000? The obvious follow on being if a factor of 2 is typical, what is the atypical extreme and is there a theoretical limit that can be placed there as well?

The question of ion and electron proportion in the cusps is dependent on several assumptions which A. Carlson is resistant to consider as valid options. But, the density of the charged particles (weather ion or electrons within the Wiffleball and outside the magrid seems straight forward, at least from a fluid dynamics approach. The wiffleball holes are reportedly tiny compared to the rest of the wiffleball surface. Consider a tank holding water . Place ~ 14 tiny holes in the wall, and equip it with a high pressure pump to continually replace the water (and maintain the pressure)that is lost through the holes. Place this tank inside a second tank that is also equiped with a pump (lower pressure but higher capacity). As the water squirts out the tiny holes in the inner tank it will eventually fill the external tank tilll it eventually fills up and the pressure equilibrates. But, if the external pump is continually removing the leaked water, the external tank will never fill up. The ratio of internal -vs- external pressures will depend on the leak rate compared to the external pumping rate. Ratios of up to several thousands do not seem unreasonable.
Certainly the pressure in the narrow cusp may be near to the internal pressure, but once the cusp opens up and dumps into the realitively large volume of the continually evacuated vacuum vessel, the pressure quickly drops. The limits are the leaking rate and the pumping capacity. As Bussard has claimed this large differency in internal -vs- external densities is nessisary for usefull fusion rates to be achived while preventing arcing outside the magrid (external pressure dependant). Certainly arcing inside the magrid is also important, but presumably the magnetic shielding and carefull attention to surface chariteristics manages this.

Note that I have not said anything about input/ output energy balance, only density issues and it's importance to fusion rates and arcing (Pashin discharge).

PS:
Ambipolar flow implies neutral plasma has to flow through a portal. There is no electron/ ion seperation. If this was always the case things like ion rocket engines, electron guns, etc. would be impossible. I look at the Polywell cusps as electron guns. The electrons are accelerated outward due to electrostatic effects, and focused to beams by magnetic fields. Fortunatly, if the Polywell works, the electron guns are very ineficient. They produce only feeble beams despite the high voltage and high electron densities maintained within the 'gun'.

Dan Tibbets

[Art Carlson]

A few more questions come to mind then. What is a ballpark density difference between core and cusp needed for things to work as Bussard envisions? A factor of 10, 100, 1000? The obvious follow on being if a factor of 2 is typical, what is the atypical extreme and is there a theoretical limit that can be placed there as well?

I won't be able to answer all your questions, but I can make a few more comments.

Start with the Bohm criterion, which says that the ions entering a sheath must do so with at least the speed of sound, c_s. The usual derivation assumes cold ions, so c_s = sqrt(kT_e/m_i). There is much discussion in the literature (part of it by me) about how to generalize this condition to warm ions. Usually you write c_s = sqrt((kT_e+gamma*T_i)/m_i), with the heat capacity ratio gamma equal 5/3 for 3 degrees of freedom or 3 for 1 degree of freedom (which is probably closer to the truth). If we take T_i = T_e and gamma = 3, then c_s = 2*sqrt(kT_e/m_i), twice the value for cold ions. To accelerate the ions to this speed requires a potential drop of 0.5*m_i*c_s^2 = 2*kT_e (compared to 0.5*kT_e for cold ions). With Maxwellian electrons, the Boltzmann relation holds, in which case this potential drop will be associated with a drop in density by a factor e^2 = 7.4 (compared to e^0.5 = 1.6 for cold ions). The polywell mythology assumes the ions are cold at the edge of the ball, but if you want to overthrow this view (which you will have to do sooner or later anyway), you might want to consider a density drop on the order of 7 or 8 as an extreme value. This would reduce the potential of a cusp with unbalanced charges from 10 MV by a factor of 4 to 2.5 MV.

We still need an additional factor of 100 or more. How can we further reduce the density? Since particle flux is conserved, I can only see two possibilities: either spread out the channel or speed up the ions.

Spreading the channel hardly makes any difference at all. For a cylinder (point cusp) of uniform charge density and given charge per unit length, the potential drop from the center to the edge is independent of the radius. The drop from the edge to the outer boundary (magrid) depends only logarithmically on the radius. For a slab (line cusp) of uniform charge density and given charge per unit area, the potential drop actually increases with the thickness.

To reduce the density by a factor of 100 would require an increase in velocity by the same factor. This acceleration would require a potential drop (now parallel to the magnetic field of the cusp, if that is even possible) by a factor of 100^2, which introduces a problem significantly worse than the one we are trying to solve.

[rcain]

Art, forgive me for asking such a dumb question, but isn't 'ions entering the sheath' precisely what we dont want?

alslo

...How can we further reduce the density? Since particle flux is conserved, I can only see two possibilities: either spread out the channel or speed up the ions.

i come back again to the possibility of pulsed plasmas. thermalisation aside, (for a moment), is this not a further possibility? (looking at eg. http://en.wikipedia.org/wiki/Lower_hybrid_oscillation and the Bolttzmann relation).

ps. i seem to be zeroing-in on Landau damping i think.

[bcglorf]

Thanks for your reply again Art, unfortunately it's now far enough over my head I can't make heads or tails of it. In layman's terms, is the required density in the cusps theoretically impossible, or more positively a condition that is nearly impossible? I know, objectively simplifying that much is probably equally impossible but you've been so generous so far I'll just keep asking and get what I get .

To reduce the density by a factor of 100 would require an increase in velocity by the same factor. This acceleration would require a potential drop (now parallel to the magnetic field of the cusp, if that is even possible) by a factor of 100^2, which introduces a problem significantly worse than the one we are trying to solve.

Is the potential on the magrid itself significant enough to be a factor in the cusp dynamic? To some degree or another it will be pushing ions out of the cusp, either to the wall or back into the core. I guess I'm blindly presuming that your assessment is ignoring the potential on the magrid as insignificant. I know you'll do that with good reason, and likely reasons I can't follow. I'm curious though if it is potentially a point were your assessment diverges from the more optimistic ones from Nebel and Bussard?

[TallDave]

The question of ion and electron proportion in the cusps is dependent on several assumptions which A. Carlson is resistant to consider as valid options.

I think it's hard to answer these questions without some access to raw data. For instance, we know potential wells form, so there has to be some ion velocity distribution, but what does it look like in WB-8 conditions? Hard for us to say, but with all those ports they should have a lot of data. The Carlson mythology is interesting and some parts are likely applicable, but as with his FRC objections it probably includes a few flawed assumptions about conditions specific to PW, unknown to us, that will come to light when Rick releases results. I doubt that they will allow for net power in the near future, but they should fill in some gaps, such as why we don't see an ion current on the wall.

Joel Rogers' latest simulation (released Monday) seems to point to cusp-plugging behind the WB effect (hopefully Joel doesn't mind me posting this):

Fig. 3 shows a snapshot of the charge density as a function of position inside the tank. The central plasma ball is positive, coded magenta. The positive center is surrounded by a ring of negative charge, coded dark blue.
Outside the negative charge is a ring of positive charge, coded magenta.
External cusps contain negatively charged plasma; green, yellow, red and black code increasingly more negative charge density. The negative charge in the cusps was a surprise. Electrons are apparently attracted into the cusps by the positive voltage on the magnets. Gauss's Law is built into the simulation, which requires the net charge inside the tank be zero. The excess electron charge in the plasma is precisely balanced by positive charges on the magnets. The concentration of electrons in the cusps seems to block the leakage of ions from the core. Cusp plugging provides ion confinement like the WiffleBall was supposed to do.

...but I'll have to ask why that wouldn't require unreasonably large potentials as Art and 93143 have suggested. Is it just a question of degree? Maybe the potential difference necessary for WB confinement isn't as large as expected. Cusp plugging does seem to mesh with Tom's PZLx-1 "flux capacitor" experience.

The most interesting Polywell question imho right now is this: if we assume the WB effect is real in WB-7/6 sized machines and a result of cusp plugging, what can we say about how such an effect might scale to larger machines? This seems to be where Polywell will live or die, and I'm not especially optimistic you can get to net-power densities with good enough confinement.

[rcain]

good post TallDave. great to see preview of Joel's work - please keep them coming if you can. Do you know if and when, he might make his works publicly available?

Cusp plugging, as an alternative to Wiffle ball inflation, as the primary means of achieving Q>1. Has that ever been properly explored I wonder?

maybe we need, have always needed, both cusp plugging and WB for this thing to work. but it woulld be nice to know their relative contributions, where they act sympathetically, and under what conditions they break down.

its a great shame we have no actual data on cusp plugging, only models still. if we had any data to prove this effect is significant, then one of Art's key objections falls over on its side.

[Munchausen]

Joel Rogers' latest simulation (released Monday)

Link please

[mvanwink5]

Joel Rogers' latest simulation (released Monday) seems to point to cusp-plugging behind the WB effect (hopefully Joel doesn't mind me posting this):

Fig. 3 shows a snapshot of the charge density as a function of position inside the tank. The central plasma ball is positive, coded magenta. The positive center is surrounded by a ring of negative charge, coded dark blue.
Outside the negative charge is a ring of positive charge, coded magenta.
External cusps contain negatively charged plasma; green, yellow, red and black code increasingly more negative charge density. The negative charge in the cusps was a surprise. Electrons are apparently attracted into the cusps by the positive voltage on the magnets. Gauss's Law is built into the simulation, which requires the net charge inside the tank be zero. The excess electron charge in the plasma is precisely balanced by positive charges on the magnets. The concentration of electrons in the cusps seems to block the leakage of ions from the core. Cusp plugging provides ion confinement like the WiffleBall was supposed to do.

...but I'll have to ask why that wouldn't require unreasonably large potentials as Art and 93143 have suggested. Is it just a question of degree? Maybe the potential difference necessary for WB confinement isn't as large as expected. Cusp plugging does seem to mesh with Tom's PZLx-1 "flux capacitor" experience.

The most interesting Polywell question imho right now is this: if we assume the WB effect is real in WB-7/6 sized machines and a result of cusp plugging, what can we say about how such an effect might scale to larger machines? This seems to be where Polywell will live or die, and I'm not especially optimistic you can get to net-power densities with good enough confinement.

WB-7.1 targeted high temperature nubs and better diagnostics, which EMC2 web site implies was successful, (whatever successful means). Any thoughts on why the nubs required better thermal resistance, does Dr. Rogers electron plasma distribution help? If cusps are plugging why are the nubs hot? Perhaps his simulation works if the coil supports are from the wall and nubs as shown in WB-7 are an issue. Perhaps WB-7.1 was intended to see if coil to coil nubs must be dropped in WB-8. Thanks for any thoughts.

[TallDave]

Sorry no link, it was an email list. I don't know if/when Joel is publishing anything, but he seemed open to inquiries and/or sharing his results via his email list.

mvan,

Yes, I agree, any exposed unshielded surface on the Magrid is going to pull in electrons and I'm guessing they wanted to try to figure out how bad that problem was. You can see the WB-8 design eliminates the nubs entirely, as many of us suspected it might. One of the really interesting questions for WB-8 is what electron confinement will look like with no nubs.

[mvanwink5]

mvan,

Yes, I agree, any exposed unshielded surface on the Magrid is going to pull in electrons and I'm guessing they wanted to try to figure out how bad that problem was. You can see the WB-8 design eliminates the nubs entirely, as many of us suspected it might. One of the really interesting questions for WB-8 is what electron confinement will look like with no nubs.

Dave, thanks for the reply. I guess I was a little surprised by the need for high temperature nubs for WB-7.1 as WB-6 reports did not flag nub heating as an issue (perhaps they missed it because of short duration of testing). I was wondering if maybe WB-7 pulses were longer and maybe the nubs were heating more due to high currents. Oh, well, the older I get the less patience I have waiting for data.

In regards to Dr. Rogers' simulations, has he simulated WB-8 conditions?

[rcain]

..., but he seemed open to inquiries and/or sharing his results via his email list...

i wonder if perhaps he'd consider doing a 'guest spot' here on the forum?

i'd be very interested in getting an overview. is there anything we could share by pm's? better still if its served up from his professional website somewhere.

notwithstanding academic and publishing protocols, it seems to me that the more information we have publicly available around this subject, the better the whole 'alt-fusion' race is benefitted.

[MSimon]

good post TallDave. great to see preview of Joel's work - please keep them coming if you can. Do you know if and when, he might make his works publicly available?

From what I can tell he collects his work for a year and publishes at the yearly IEC Confrence.

[rcain]

good post TallDave. great to see preview of Joel's work - please keep them coming if you can. Do you know if and when, he might make his works publicly available?

From what I can tell he collects his work for a year and publishes at the yearly IEC Confrence.

.. if we are to believe Dr's Nebel, Lerner and others, in alt-fusion, right now, a year is a very long time.

[MSimon]

good post TallDave. great to see preview of Joel's work - please keep them coming if you can. Do you know if and when, he might make his works publicly available?

From what I can tell he collects his work for a year and publishes at the yearly IEC Confrence.

.. if we are to believe Dr's Nebel, Lerner and others, in alt-fusion, right now, a year is a very long time.

About 8 months to go.