WB-7.1 pulsed, WB-8 continuous?

[WizWom]

I'm speculating, but if the cusps open back up gracefully once Beta exceeds one

I don't think it works that way Dan. Its more like overfilling a balloon. Think of beta =1 being the point where the balloon pops. The wiffle ball will have to operate at beta almost equal to but < 1. For beta < 1, the magnetic forces are greater than the plasma forces leaving the plasma no where to go but to stay confined. For beta > 1 the plasma forces are greater than the magnetic forces so the plasma can escape to the magrid.

That would be the case if the plasma itself didn't modify and enhance the magnetic fields. The simple fact is, it's more expensive to model than to build a test unit, and without one or the other, you're just spinning B.S.

[Aero]

I'm speculating, but if the cusps open back up gracefully once Beta exceeds one

I don't think it works that way Dan. Its more like overfilling a balloon. Think of beta =1 being the point where the balloon pops. The wiffle ball will have to operate at beta almost equal to but < 1. For beta < 1, the magnetic forces are greater than the plasma forces leaving the plasma no where to go but to stay confined. For beta > 1 the plasma forces are greater than the magnetic forces so the plasma can escape to the magrid.

That would be the case if the plasma itself didn't modify and enhance the magnetic fields. The simple fact is, it's more expensive to model than to build a test unit, and without one or the other, you're just spinning B.S.

That's true but one BS is as good as another. Fact is, since we don't know how it works in detail, any model must remain suspect until confirmed by experiment. Don't fall into the trap of believing the simulation is truth, it's not.

[D Tibbets]

I don't think Beta > one leads to the charged particles hitting the magrid. The fields will be compressed more and more closely approach the magrid casings, but within limits (conformal casings , sufficient field strengths, etc) they will not hit them (except through secondary transport mechanisms). My, understanding is that what mostly changes with Beta is the geometry of the cusps. As Beta approaches one the cusps become more pinched and the throat of the cusps are smaller (the Wiffleball analogy). Once Beta exceeds one the cusp throats start opening again. If this is the case then, so long as there was a modest excess of electrons, the cusp would be self regulating. If the electron supply is not keeping up the Beta will drop, the cusps will open and losses will feedback in an increasing manner till simple cusp confinement is reached. But, if the electron supply is in excess (of the simple cusp losses- see below), as Beta= one is exceeded, the cusps will open and increase electron losses. Within limits this might maintain Beta very slightly over one.
If the Beta> one results in the loss of convex magnetic field lines towards the center, that is bad. But, if it results in only graceful opening or miner burp like openings of the cusp throats then the Beta = one (or very slightly> one) would be stable with modest excess electrons. In fact, I think, this excess supply of electrons may be necessary to prevent a runaway drop in Beta due to a shortage of electron pressure.
I'm guessing that the ~ 40 amps provided by the electron guns in WB6 was slightly more than that required to maintain low Beta. As the pressure built up the cusps closed, till Beta= one was reached, and then maintained due to the feedback changes in the cusp.

A better analogy than inflating a balloon, may be having a fixed volume tank with a variable valve. This valve effectively senses the pressure in the tank. If the pressure is just right (Beta= one) the valve is as closed as it can get. With pressures below or above this the valve progressively opens up. To increase the pressure in this tank at the start, you would need to input gas faster than it leaks out. This 'current' would have to be only slightly more than the valve losses (cusp losses). Because the valve closes progressively, the pressure would build quickly until this equilibrium was reached. There is an absolute minimum current that will progressively fill the tank, but there is more leniency in the maximum current. WB 6 at certain conditions may have required exactly 40.000 amps to maintain Beta= one. But to get there you might need to supply 40.1 amps. Initially simple cusp losses would allow the vast majority of this current to escape, but there would be a progressive slight increase in density which would very gradually (in electron transit time perspectives) close the cusp initially. But, this process has a positive feedback so the effect would accelerate rapidly.
I think this has several consequences (if this BS has any validity ). The input current needs to be enough to just slightly exceed the simple cusp losses. The Beta=~ 1 condition then maintains itself. Secondly, the Beta= one condition is the mean condition. It would be represented by a bell shaped curve. Because the process may be logarithmic this curve may be fairly narrow, but not exactly Beta= one. It may have a standard deviation of something like 0.9 to 1.1. There may also be some oscillation involved. This may or may not be useful. If this speculation has any validity, the 'Beta=0ne' in WB6 may be more accurately be described as Beta=1 +/-0.1. If this is the case, subsequent machines with tighter feedback controls (fine tuning current) may be able to maintain Beta= one conditions within tighter limits and therefor benefit from greater Wiffleball trapping factors than those obtained in WB6.

[EDIT] Another consideration is that the Wiffleball trapping factor improvement, if significant, is not the only possible benefit of tighter control around Beta=1. The input electron current would also be smaller once this condition was obtained, improving the input side of the energy balance equation. You might need 40.1 amps to build towards Beta= one, but once there, instead of wasting this current on the high side of Beta= one, the current needed to stay very near Beta= 1 +/- 0.01, may be only 10 amps (a made up number). This would decrease the input energy, and also decreased the charged particle population outside the magrid, which has consequences for the arcing and vacuum pumping concerns.
Lets see, if the Wiffleball trapping factor improves, the obtainable density will improve (within internal arcing limits), the fusion rate will increase, and if significantly lower electron currents are needed to operate very close to Beta=one, then the input energy will decrease. Add this to confluency issues, POPS type effects, and better recirculation from moving the nubs and the WB6 results may represent a very, very conservative indication of the Polywell's potential. - Now I'm definately in the BS territory

Dan Tibbets

[TallDave]

Beta will exceed one and the containment will fall proportionately.

That's an interesting thought. But I don't think the machine can operate usefully at beta > 1. I guess we'd need some data, though, to say whether the WB fails gracefully (proportionately) or catastrophically (immediately back to cusp confinement as soon as beta exceeds 1). My money is on the latter because of how Bussard characterized failure as "blowout".

Hmmm, now I wonder if that's why the runs end when beta exceeds 1 -- beta>1 leads to loss of interior density and greater exterior density, so cusp blowout causes arcing!

For beta > 1 the plasma forces are greater than the magnetic forces so the plasma can escape to the magrid.

I agree with Dan, at beta > 1 plasma doesn't escape to the Magrid, but it does blow out the cusps, which is bad for the gmj factor (remember, this is an open device) and the interior density.

PW is sort of an odd duck -- it doesn't ignite, and achievable density is a function of the achievable interior/exterior ratio. It's really an ETW with a virtual cathode formed by a magnetically compressed volume inside the anode grid.

[D Tibbets]

Rereading WB6 final report and some other sources, I appreciate that my above reasoning, while perhaps not completely irrelevant or wrong, does not match what went on in WB6.

In WB6 the ions came from gas puffing neutral injection. There was a low Beta stream of energetic electrons injected from the electron guns. This primary electron current may have been ~ what would be nessisary to maintain Beta=1, but not to build up to this condition. But, once the neutral gas was injected the primary ionization, and especially the secondary cascading ionization would provide most of the electrons needed for Beta=1 condition. The ongoing heating of these cold secondary electrons by the injected hot electrons builds the to the final density * energy electron population that creates the outward pressure that creates the Beta=1 condition. At this point the electron gun current (which has not changed) is the only source of new electrons and the steady state is maintained (ideally).
The ion gun machine would be a very different beast in this regard as the electron density would be determined purely by the electron gun injection. The initially greater electron gun current would have to be reduced as Beta=1 was reached.

It was mentioned that the photomultiplier signal plateaued as Beta = one was passed- it didn't immediately fall, meaning that the density was maintained for a time, possibly by less efficient confinement balanced by continuing cascading ionization of remaining neutrals. This would confuse confinement measurements, but the density dependent fusion rate could be maintained longer- until the runaway arcing destroyed the potential well, or you ran out of internal neutrals.

So, in the gas puffing mode, WB7 may have been able to maintain near Beta= 1 condition (at least the density equivalent aspect) longer if they had better control of the gas puffer feed.

The gas puffing system vs the ion gun system are very different, with different advantages and disadvantages in terms of controls and feedbacks.

Dan Tibbets

[MSimon]

I forget if it was a simulation or an experiment but a Penning trap required less electron flow as it got larger. So a small machine might need 40 Amps while a larger machine might get by on 10 or 5 amps.

It may be a surface to volume effect.