New FAQ - What are Cusps and what kind does a Polywell Have?

[icarus]

Art, it was a fine quote, funny too, I found. I wish I'd thought of it myself ... don't mind me, I 'm not here for the charity. Rough, tumble and bruised egos seems to go with territory of theoretical physics ... now truly only god knows why that would be .... but if you haven't been bruised you are probably not even in the game.

[TallDave]

I would posit that having the electric field orthogonal to the magnetic field at the plasma-field beta=1 surface is a crucial key to the enhanced electron confinement. The conformal cans for the MaGrid has done the trick, not only because of the reduced intersection of field lines out at the physical magnets, but critically down at the plasma surface it will keep the electron velocity vectors pointing away from the loss cones, resulting in an enhanced mirroring effect that is better than simple cusp confinement.

Yes, there was a similar argument made re the geometry of the field and the effect on cusps, though less completely, a while back. I can't remember if it was here or the topic on the Physics forums.

[kbaugh]

Pardon me for being a simple-minded electrical engineer, but I seem to recall that impedance for an EM wave is defined as the ratio of the transverse components of the E-field and the H-field. In a lumped-element circuit, impedance is similarly defined to be the ratio of the voltage (a thing that is related to the E-field) and the current (a thing that is related to the H-field).

Is there a similar notion of "impedance" for the flow of free electrons off of the surface of the beta=1 plasma, and if so does it vary over the surface of the plasma sheath? In particular, is there some notion of "surface impedance" that shows that the impendance is "high" for electrons flowing out through the corners and line cusps, but is "low" for recirculating current throuh the point cusps?

[Art Carlson]

I'm not talking about any Debye sheath here. I'm talking about the transition layer between the beta = 1 plasma and the the near vacuum outside the ball.

That's not the whole story though. Assume the electron density has some profile (determined at least in part by the interaction of electrons with the magnetic field). What do the ions do? They will (hardly) see the magnetic field and will keep going where the electrons stop. But once they get outside the electron profile they will see an electric field trying to pull them back in. On the other hand, the existence of a large ion population outside the electron region is what creates the electric field (with proper consideration of boundary conditions). How the electric field is related to the charge density is given by Gauss's law. The result is that the ion density is shifted relative to the electron density by sqrt((epsilon_0*E)/(n*e^2), where E is the component of the ion energy perpendicular the the surface. Hello! That is our old friend the Debye length, only with the ion energy playing the role usually played by the electron temperature. I'll tell you, the fundamental plasma parameters simply insist on having their say.

[D Tibbets]

I'm not talking about any Debye sheath here. I'm talking about the transition layer between the beta = 1 plasma and the the near vacuum outside the ball.

That's not the whole story though. Assume the electron density has some profile (determined at least in part by the interaction of electrons with the magnetic field). What do the ions do? They will (hardly) see the magnetic field and will keep going where the electrons stop. But once they get outside the electron profile they will see an electric field trying to pull them back in. On the other hand, the existence of a large ion population outside the electron region is what creates the electric field (with proper consideration of boundary conditions). How the electric field is related to the charge density is given by Gauss's law. The result is that the ion density is shifted relative to the electron density by sqrt((epsilon_0*E)/(n*e^2), where E is the component of the ion energy perpendicular the the surface. Hello! That is our old friend the Debye length, only with the ion energy playing the role usually played by the electron temperature. I'll tell you, the fundamental plasma parameters simply insist on having their say.

I'm uncertain of what you're implying, is it that the ions will pile up outside the electron cloud (makes sense from a electrostatic viewpoint if there is a potential well) and therefor effect how the electrons interact with the periferal magnetic field. This sounds counter to the idea that the ions stay too deep within the Wiffleball to see the magnetic field- in which case they would need to be too far away to have a dominate effect on the electrons as they do interact with the magrid magnetic field border (?). Perhaps the dynamic nature of the electron population modifies your argument- slow electrons spend most of thier time well within the Wiffleball, while the electron population is relative less dense as they accelerate outward, turn at the B=1 border and then zip back twoards the center (slowing as they enter more dense electron regions near the center).* Any ions would be attracted to the more dense electron cloud in the center and acumulation near the electrons turning at the border would be impeaded, at least for a time. I suppose a similar effect to what you are describing might contribute to an excessive central anode formation if ion density is to great.

If my cognitation is not to far off, then the dynamic nature of the machine- with excess high energy electrons continually being injected would impead the equlibrium condition that you stress adversly effects containment, at least for a significant amount of time. The argument then becomes dependant upon the relaxation (?) or equilibrium time (verses the ion lifetimes?), not the end condition that would be untenable.


* Just a restatement of my understanding of why the electron cloud is concentrated twoards the center- driven by new high energy electron injection coupled to whatever removes the low energy electrons that would otherwise concentrate more near the Wiffleball border(thereby attracting more ions and setting up the condition you describe?).


Dan Tibbets

[alexjrgreen]

The result is that the ion density is shifted relative to the electron density by sqrt((epsilon_0*E)/(n*e^2), where E is the component of the ion energy perpendicular the the surface. Hello! That is our old friend the Debye length, only with the ion energy playing the role usually played by the electron temperature.

Would that produce concentric shells of positive and negative charge?

[TallDave]

I'm not talking about any Debye sheath here. I'm talking about the transition layer between the beta = 1 plasma and the the near vacuum outside the ball.

That's not the whole story though. Assume the electron density has some profile (determined at least in part by the interaction of electrons with the magnetic field). What do the ions do? They will (hardly) see the magnetic field and will keep going where the electrons stop. But once they get outside the electron profile they will see an electric field trying to pull them back in. On the other hand, the existence of a large ion population outside the electron region is what creates the electric field (with proper consideration of boundary conditions). How the electric field is related to the charge density is given by Gauss's law. The result is that the ion density is shifted relative to the electron density by sqrt((epsilon_0*E)/(n*e^2), where E is the component of the ion energy perpendicular the the surface. Hello! That is our old friend the Debye length, only with the ion energy playing the role usually played by the electron temperature. I'll tell you, the fundamental plasma parameters simply insist on having their say.

I think the standard Polywell view of this is that because of the well, the ions never get far enough out to see the electron "sheath, " which is largely the result of the plasma being eletron-rich and non-ambipolar -- which also raises the question of how the plasma could both be spitting out excess electrons and having ions follow them.

I've been wondering for a while how one describes and calculates the force that ejects electrons. Presumably it also pulls on ions.

I'm left once again with the impression one needs sophisticated dynamic modelling rather than simple equations to describe Polywell.

[TallDave]

The argument then becomes dependant upon the relaxation (?) or equilibrium time (verses the ion lifetimes?), not the end condition that would be untenable.

Rick addressed this at one point, iirc. I believe he said for small machines it was not an issue, but in larger machines it may start to be a problem because the times get closer.

[icarus]

TallDave:

I think the standard Polywell view of this is that because of the well, the ions never get far enough out to see the electron "sheath, "

Is there truly such a thing as "the standard Polywell view"?

I'd be most interested to read it in a FAQ, for instance.

But seeing as you seem to be the most prominent standard bearer of it ... I'll ask you directly ... is there any evidence we can point to that the ions never get far enough out of the potential well to see the electron sheath, i.e the beta=1 surface?

Surely some of them will become energetic enough to rise to this region? and the proportion of ions that do are obviously not confined in the same way by the mag. field at the interface as the electrons .... e.g. for ions and electrons having the same energy their velocity ratios are sqrt(m_e/m_i) which means their momentum ratios are sqrt(m_i/m_e) and when it comes to the forces felt by the ion from the magnetic field this is the relevant ratio ... i.e a big difference in physics.

Also you wrote:

I'm left once again with the impression one needs sophisticated dynamic
modelling rather than simple equations to describe Polywell.

This sounds like a cop out, you yourself have resorted many times to simplistic equations when it suits your cause. In the above statement, the inclusion of the word "dynamic" is a non-sequitur that may be more an attempt to bamboozle than add any useful information.

I can tell you from experience that if this thing cannot be reduced to a set of equations that engineers can use, it will never make it to market, ask MSimon.

It smells unfortunately like the same line that the climate science charlatans and tokomak jobsworths are spinning. If you don't understand why the hell build it?

Oh yeah, the computer told us how it works .... uh-huh.

[MSimon]

If you don't understand why the hell build it?

Because the numbers that you get from experiments look promising?

BTW James Watt didn't have Carnot. But he managed.

We don't have to understand Polywell to make it work (it would be helpful though). What the engineers need most is: what will it do?

[D Tibbets]

...I can tell you from experience that if this thing cannot be reduced to a set of equations that engineers can use, it will never make it to market, ask MSimon.

It smells unfortunately like the same line that the climate science charlatans and tokomak jobsworths are spinning. If you don't understand why the hell build it?...

Climate models have equations that they are trying to shoehorn the data into. Polywell expermental data apparently needs refinement of theory *, a different perspective. And, understanding (at least at a fundamental level) is not required for utilization of a technology. Fire was very usefull for thousands of years befor any real undestanding of the process was obtained. Also, a blacksmith could/can achieve remarkable results with no theoretical knowlogy of the crystaline structures of iron and it's alloys. On the opposite side is String theory, which has eligant math, but very little if any testable link to reality.



*Expermental data aviable to EMC2 and it's sponsers at least. We (or at least those on this forum with the nessisary physics and math skills) are left in limbo without in depth knowledge of the data or predictive theory. As such, we are all hand waving, weather we are pessimistic or optemistic about the technology. As has been stated here multiple times, experment always trumps theory- so long as you can convince others that your data is real (and you make it aviable). In the meantime, the uncertainity, combined with the promise is what makes this topic so entertaining and educational.


Dan Tibbets

[rcain]

gentlemen, esteemed professionals, fellow enthusiasts

ive been following so far as i can the debates here.

might it be possible to simplify the model whilst preserving its overall nature?

might it be (topologically) possible to model a pollywell cavity/sheath/wb-process into a scaled, (attenuated/tuned, infinitely long) 2D penning trapp? perhaps a radial cellular/compound array of such? wouldnt we expect this instrument to project an equivalent electro-intertial distribution/filter? can be made nonlinear, stockastic, pumpable (and zapable?).

aplogies if this sounds a little abstract. i just thought the numbers involved might be easier to work with, with fewer unknowns. any thoughts?

[KitemanSA]

might it be possible to simplify the model whilst preserving its overall nature?

I was under the impression that this is basically what DrB meant by his 1.5D analysis program (radial plus rotations).

[Solo]

Art, about those boundary conditions: we are expecting an electric field at the edge of the plasma which confines the ions, so the field ought to point inward, which implies a net negative charge in the plasma, not a positive charge as you imply with the ion density being greater than the electron density at the edge (and presumably identical in the central plasma).

But then I can see that the ions would indeed tend to move beyond the electrons by momentum, so I'm not sure how that all matches up.

[rcain]

might it be possible to simplify the model whilst preserving its overall nature?

I was under the impression that this is basically what DrB meant by his 1.5D analysis program (radial plus rotations).

..likewise. just guessing there was some harmonic/eigenstate analysis in there also. 1.5D seems fine (enough) - to my limited thinking.

so probablistically (quasineutrality aside), can we not just consider N radial (& categorised) ion impedence chanels co-tangent to the B=0 surface? ( / else similar constructed manifold normal to electrical/charge centre).

(ftr: i can visualise a (compresses) shell of +ve ions, surrounding a (somewhat compressed electrons, with some neutrals percolating out (and drifting off?) and some percentage of charges particles wandering out though 3 types of capture cone/cusp(....meanwhile toping the mixture up all the time from both ends of the well, to desired scale. repeat until meet desired cross section/Lawson. nuclear collisions and thermalised components to be recirculated/output - the other bit of it). mathematically, something like - http://en.wikipedia.org/wiki/Orbitrap perhps.