Some comments from reading the last couple of pages. Beta= one is easy to achieve. It is the result of something like KE of charged particles * density / B field. You can play with all three numbers and achieve B=1 with very weak B fields, etc. To achieve Beta =1 conditions with KE and densities useful for practical fusion energy production is another matter. My impression has been that the achievement of Beta= one is not contested. What is contested is if this condition leads to the cusp surface area / total surface area of the plasma 'sphere' decreasing to create a Wiffleball.
As for the swimming pool filled to the brim, where any wave or instabilities could lead to water (plasma) slopping over the side. I would think that this would refer to MHD instabilities due to magnetic surfaces concave towards the center of the plasma. These macro instabilities are supposed to be avoided in the Polywell due to the universal convex magnetic surfaces towards the center. This sloshing is apparently so bad that systems with this instability (like Tokamaks) have to stay below ~ 0.3 Beta, to prevent these waves from sloping over the side to much .
Cusp plugging in some of EMC2's machine was a major effort. like in WB5. I'm not sure of the interactive dynamics in this process, but Bussard, etel apparently abandoned these efforts. Bussard claimed he could not plug the exits to electrons without opening them to ions at the same time. My impression is that cusp plugging consists of holding a collection of like charged particles in the cusp to repel electrons (how would Gauss's law effect this with this quasi spherical machine?). The problem is that if this negative space charge in the cusp repels electrons entering the cusps, it would also attract the ions- or at least lessen the net negative space charge behind the ions and this would allow more up scattered ions to escape without a subsequent opportunity to be edged annealed on the next pass. Instead, he went with electron recirculation instead. I'm not sure if the mechanics is the only difference while the end results are the same, or if recirculation entails significantly different physics. Irregardless, this recirculation approach seems to be the key. Does that mean trying to supplement this process with more mundane cusp plugging have merit? Does it mean there is some inherent cusp plugging, but increasing it further is a disadvantage? I have no idea!
Concerning Coulomb colisionality, thermalizing influences in a larger machine. It is a complex relationship. My impression that in the ~ 10 KeV, 0.3 meter WB6, with its ~ 10^18-19 particles/ M^3 the MFP was somewhere around 100 meters. That would be ~ 300 passes through WB6 before much thermalization occurred. As the lifetime was ~ 200 microseconds, or ~ 10,000 passes or less- this would be the confined passes without consideration for electron recirculation. With an electron average speed of perhaps 5,000,000 M/s (1/2 of speed at 10 KeV) this would be ~ 1000 M traveled/ 200 microseconds. This is within an order of magnitude, and considering my loose approximations of MFP and density, it is reasonable to state that the electrons would not fully thermalize. It might take several multiples of the MFP to fully thermalize.
With a 3 meter WB100 operating at ~ 100 KeV. The distance per pass would increase 10X. The confinement time as a function of passes would not change, but the distance traveled per pass is 10 times greater, so the confinement time would be 10X greater on a time scale. This is why the losses scale at the 2nd power as the volume scales as the 3rd power. And this condition requires that the B field is increased as the square of the radius in order to maintain the same cusp hole surface area in relation to the entire surface area of the Wiffleball. This B vs volume scaling is convient for calculation, though it is not preclude different ratios in an actual machine.
In this larger machine the KE of the electron at 100 KeV would result in a speed increase of the square root of the delta change in the KE, or ~ 3X. The average speed would be ~ 15,000,000 M/s. At 15,000,000 M/s / 3 meter diameter the electron would complete one pass in ~ 1/5,000,000 of a second or ~ 0.2 microseconds. This times ~10,000 transits =~ 2 ms confinement time.
This is ~ 10 times longer than in WB6. The MFP lengthens by a factor of delta energy (KeV) of the electrons squared. This would be 10 squared or ~ 100X. This means that so long as you increased the drive potential 10 X, the MFP will increase so that the net effect is null, or actually negative. That is the thermalization concerns becomes smaller.
I actually think the drop off in Coulomb collisionality with temperature is closer to ~ exponent of 1.75 rather than 2. (I should look it up and store the formula, but that is too much work). But this still illustrates that the problem is not compounded as much as might seam apparent on first inspection, concerns may actually be relaxed within limits.
Note that the coulomb collision rates in this example for D-D fusion still exceeds the fusion rate, but the difference is less. And, since we are talking about electron lifetimes and thermalizing rates, the fusion rate of the ions are mostly irrelavent in this discussion.
Of course if you stayed at 10 KeV electron energies in the larger machine, the thermalization concerns would be magnified. I'm guessing this is why Bussard mentioned 80 KeV for a 3 meter diameter D-D burning demonstrator. It is the best compromise between electron thermalization concerns, fusion power yield and D-D fusion crossection slope. It is not the ideal drive energy from a pure crossection slope viewpoint where Q is maximized (this is ~ 15KeV), nor is it the ideal point if you are considering fusion rate to thermalization rates. Even higher driv energies increase bremsstrulung more, decreases fusion fusion yield per reaction, and increases engineering problems. As in Goldilocks.. it is just right.
I have not considered the effects of increased density on the thermalization times of the electrons. This would throw the thermalization rate/ confinement time issue back into the problem side (the MFP would become much shorter). But the magnitude is mitigated somewhat by the above considerations.
Dan Tibbets
To error is human... and I'm very human.