The Brillouin limit.

[chrismb]

The Brillouin limit defines the maximum number of particles in non-neutrality conditions, viz. Polywell's central core of electrons.

{L Brillouin, Phys. Rev. 67, 260 (1945)}

This is n=B2/(2umc2) [n:particle count, B: mag field, u:permeability]

For a 1T field, as per the 'fusion reactor' in http://www.askmar.com/Fusion_files/Poly ... oncept.pdf, you get n = 4.8E18, which means in the central core of radius 1cm there would be a maximum total population of 1.5E13 electrons at any one time.

Presumably, then, the total population of ions within the device cannot exceed this 1.5E13 else total charge in the device would go positive, rather than negative, thus stifling any further ion generation.

Is the Polywell designed to exceed the Brillouin limit for electron confinement, and if so what makes it special that it can do so?

best regards,

Chris MB.

[Art Carlson]

This has been a common point of confusion. I believe that the original blame belongs to Bussard. In fact, a polywell must be quasi-neutral. The Brillouin limit tells you how big the *difference* between the number of electrons and the number of ions can be. (Not a very useful number, actually.)

[TallDave]

Yes, I think Bussard said in his Google speech the difference between ion and electron populations is something like 1/1,000,000. They're very close to equal.

[chrismb]

So, presumably, there are intended to be no 'slow' ions in the central electron core, else they would recombine, and we are looking at balancing the total population of ions that happen to be passing through the core at any given moment to within this 5E18 Brillouin limit.

But this still leaves all the other ions in the device, not counting the core. These have to be confined by the remainder of the charge, this 5E18 charges = 0.8 Coulombs-worth of charge at the core.

Is this right, then? Is there 0.8C of charge in the centre to retain all the other ions not passing through this nearly-neutral core at some moment in time?

[mattman]

Hey,

I just want to double check that formula.





Is that correct?

If so, how do I get a density from this?

[D Tibbets]

The uncertainity of the applicability of the Brillouin limit
has been discussed before.

A few references that include Brillouin limit considerations, and some with formula for same:


http://www.deepdyve.com/lp/american-ins ... g6z38tXRaD

http://mr-fusion.hellblazer.com/pdfs/al ... nement.pdf

http://athena-positrons.web.cern.ch/ATH ... l74_90.pdf

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADP012563

http://pop.aip.org/resource/1/pfbpei/v3 ... horized=no

http://sites.apam.columbia.edu/CNT/publ ... ylimit.pdf

Dan Tibbets

[hanelyp]

If I'm reading that formula correctly, it ignores particle energy unless as an effect of electric potential from net charge. Doesn't look like it applies to a plasma of mixed particle types. In an operating polywell the total number of electrons is large compared to the electron excess that gives the plasma a net charge. I'm thinking that you'd get better results treating the plasma according to the kinetic theory of gases.

[KitemanSA]

The thing to remember is that the ions are NOT trapped by the magnetic field but by the electro-static field of the excess electrons. And then the electrons are electro-statically effected by the ions. You assessment needs to take that into account or you will lead yourself astray.

[mattman]

Kiteman,

Sorry, good point - Electrons only.

I was just going off what ChrisMB said.

Also, this limit is WAY higher than what I expect any polywell will reach in density.

However, people will raise this as an argument against.

[D Tibbets]

The pressure that needs to be contained by the magnetic field is, I think dependent on the electron density and energy. The ions don not contribute, at least to a significant extent. I think Bussard, etel. stated this in the patent application, which is an interesting read.

http://www.askmar.com/Fusion_files/Pate ... 187086.pdf

Dan Tibbets

[hanelyp]

I'm not sure how fast the ion population fades at the wiffleball boundary, but with average ion energy nearing zero at that boundary the ion contribution to pressure should be negligible. As opposed to the electrons which are at peak energy and high density there.

[D Tibbets]

PV=nRT

The ideal gas law states that the pressure (P) is proportional to the temperature (T). If the temperature is close to zero, the pressure will be close to a minimum. At absolute zero the pressure would always be zero, but this is a theoretical minimum. Still a temperature of a few eV at the Wiffleball border for ions compared to tens of thousand eV for electrons implies that the ion contribution to the edge pressure is trivial. How the dynamics of the ion kinetic energies increasing towards the center while the electron kinetic energy is decreasing is intriging. At some radii the ion pressure will exceed the electron pressure at that radii. How all of this communicates (integrates?) as the electrons and ions do not exchange much KE through collisions due to the differences in momentum may allow for separate consideration without averaging of the two species energy at any given radii. Note that energy collision mediated ion - electron energy transfer is poor. The space charge represented by the potential well is a different story. As stated in the patent application , apparently the border pressure can be considered as the pressure against the magnetic field, ie: the electron pressure.

Dan Tibbets