The problem with ion convergence

[TallDave]

I think knowing the full distribution function over space and velocity is needed to get a good handle on how the system will behave under given conditions.

When I realized the system was so dynamic, I threw up my hands on simulation, let alone a static equation predicting much that could be useful. I like equations and love programming algorithms, but as a programmer who interfaces with a lot of business users I'm very skeptical of anything that can't be proved empirically, esp. in a complex system with dynamic interdependencies. Give me real-world data or send me home!

In a non thermal system, Debye length doesn't make sense. The derivation is based on an exponential distribution of velocity and space. If that kind of uniformity doesn't exist, you have different length scales as a function of position.

Yeah, I'd been wondering why Bussard rarely seemed to mention it.

[Tom Ligon]

I've not been thru the whole magnetic field article yet, but it all looks familiar. I used Allegro linear Hall Effect devices at EMC2, to good effect, up in the multi-kG range, and I've used Honeywell's dainty little magnetoresistive bridges (a very different technology) down in the > 1G range.

The magnetoresistive bridges can be sensitive as all getout, but they require about as much circuitry to exploit them properly as a fluxgate. The full implementation is zero-stable down to a few hundred nT, but the gain is VERY temperature-sensitive. For simplicity, give me a 3-pin Hall Effect chip. You can get all three axes on a magnetoresistive sensor in a chip not much bigger than a dog tick.

A little rewiring of a Polywell makes a tolerably good approximation of a 3-D Helmholtz coil, BTW.

[Art Carlson]

One of the problems with assuming some formulas are valid when the system is not really thermal ignores the way the formulas were originally derived. I think knowing the full distribution function over space and velocity is needed to get a good handle on how the system will behave under given conditions. It's just a lot easier to do experiments at this point - computers can't follow that many particles in 6D phase space yet.

In a non thermal system, Debye length doesn't make sense. The derivation is based on an exponential distribution of velocity and space. If that kind of uniformity doesn't exist, you have different length scales as a function of position. If 1D models give hints on what to look for, that's great, but full scale experiments are still required to find out if the hints are meaningful.

I think there may be a misunderstanding here. I agree that Debye shielding is a phenomenon that has some subtleties, that the simple form in terms of exponential decay of a potential with the characteristic length of lambda_Debye depends strictly on special circumstances, and that it is not known whether these conditions are met in the polywell. The Debye length, on the other hand, is a combination of variables that turns up in different calculations and can be used - with appropriate interpretation of T_e and n_e - as a shorthand for the relation between charges and potentials. For example, in the thread on recirculation, I used the term Debye length, but the essence of my argument had nothing to do with whether the electron velocities had a Boltzmann distribution. All that mattered was the potential of a sheet of charge with a particular density and geometry. I hope nobody was misled by the terminology I used.

[Jboily]

Dr. Nebel,

If electrons collide and lose all of their angular every time they cycle and all I am looking for is 10:1 convergence (at most, since we both agree that I don't need any convergence) then it seems to me that I have at most a 10% problem. If you want to claim that the collisionality is less, then you should take that up with Nick Krall (see reference 4 in Bussard's note).

I think the Fusion rate gain is hier for the first few convergence ratio because of the reaction that happen outside the core radius are significant in number. A quick calculation yield a 36x Fusion rate gain for a 10:1 ratio. For larger convergence ratio, it would be close to linear, with a gain G(rc) ~= 3*R/rc.

I have ussumed Ions density ~= R/rc^2 down to rc, then constant within the rc core. I end up with 25% within the core, and with about 60% of the reactions happening within 2*rc. Am I wrong here?

It is a simplimplification ofcouse, but it is to show that the first few convergence factor would help a lot.

In one of his patents I believe, Dr. Bussard was claiming that the increase colision rate close to the core would help the convergence. You claim the other way . Not to be disrespectfull, I think Dr. Bussard had some good points there .

I think it depend on how many trips an Ion will make before it is disturbed. It require 10^4 to 10^6 trips before a fusion occure, but what would be the number of trip an Ion will do across the machine before it is disturbed by something?

[Jboily]

Sorry for the previous message, something got wrong with the quote. only the first line in the quote is from Dr. Nebel.

[MSimon]

Sorry for the previous message, something got wrong with the quote. only the first line in the quote is from Dr. Nebel.

I fixed it. Did I do it right?

[Jboily]

Sorry for the previous message, something got wrong with the quote. only the first line in the quote is from Dr. Nebel.

I fixed it. Did I do it right?

Yes, thank you.