Remind me - why 10T field?

[icarus]

what are the mechanisms that cause the limits?

Sounded like Bussard (and Lignon) are already aware of what these are, no?

Might get hand-wavvy if you ask for numbers though.

[hanelyp]

As I recall, the density limit on a polywell is from a requirement of a mean free path large relative to the machine size for annealing to work correctly. A matter of ions needing to avoid to many collisions between time in the outer regions being annealed. That being the case, I'd think that a smaller machine could manage higher density before reaching that limit.

[D Tibbets]

.....

At 10T, this means the outer edge is at 10MeV plasma temp and 1E19 density. But that's insane for the EDGE to be at those conditions. Or let's say it is at 10keV and 1E22, and with the supposed compression factors between the edge and the core, then you're trying to tell me that you are containing a plasma at 10 x atmospheric and that is at 10keV?



So, can Polywell achieve beta=1, or not? And if so, then why are the operating conditions not ALWAYS going to be at beta=1.

I'd still like an answer to the question [that I said I didn't think I'd get an answer to]: What are the density and temp conditions in the edge supposed to be?

I don't know where you get a density of 10X atmospheric. 10^22 particles / M^3 is ~ 0.001 atmospheres*
If there is an equivalent density increase towards the center due to convergence, it is due to the dynamic motion of the ions not separate zones of static density. I'm not sure how this would work out. In any case, I believe that 10^22 number comes from Dr Nebel. Whether this represents the average density within the Wiffleball or the effective density considering some degree of confluence is unknown (by me). It does fit well with the reported Wiffleball trapping factor and the vacuum limits allowable outside the magrid. ChrisMB says the 10 Tesla magnetic field can contain 10 MeV charged particles, or restated, 10MeV particles at a density of 10^19/M^3. Again, that doesn't mean the particles have to have that energy, or the ~10KeV energy of WB6. Again, Beta is determined by the temperature AND the density. Why ChrisMB insists on only quoting conditions at the opposite extremes and ignores the entire range of combinations in between is amazing.
A more reasonable querry, would be how much variation in the density and temperature could have been tested in WB7 as it presumably had similar magnetic field strengths and volume. I wonder if they could have packed a few more wire turns into the casings, and powered the magnets at higher currents for shorter times(to limit the heating). Also, they could have operated at higher drive voltages. This would have increased confidence intervals in the actual fusion rate as they would have had higher counts. I suspect any B^4*r^3scaling results would have been subtle at best.

What drive voltages, and densities could be tested in WB8 considering the size, and 8X B field increase and the desire to maintain Beta= one conditions.
Lets see, to keep Beta=1 the density * Voltage would have to increase by a factor of 64 (change in B ^2). eg: a density 10.4X greater and a voltage 6X greater, or a density 32X greater and a voltage 2X greater. As I said above, any combination giving a product of 64 would work. Presumably they may need some fudge factor to accomidate volume / magnet size considerations. As the fusion rate increases at the square of the density, I'm guessing they would get the most gain by keeping the voltage near, or only slightly higher (say 18 KV (15 KV potential well)) than WB6 and pushing the density to ~ 40X. That would result in ~1600X from the density increase * ~5X from voltage increase * 8X from the size increase. That would scale WB6 1 milliwatt fusion output to ~ 64 watts for this configuration of WB8 (at least if the scaling predictions hold true).


Concerning the need for Beta =1 for fusion, it is true that it is irrelevant for the actual fusion rate. But, it is necessary to have Beta=1 for Wiffleball formation, and the Wiffleball is necessary for two reasons. Without it the losses to the magrid exterior would be faster and it would be much more difficult, if not impossible to reach the internal densities necessary for useful fusion before external arcing occurred - which is intolerable. Actually, it would be tolerable to stay at lower densities, and grow the size of the machines, but using size scaling alone would probably result in machine sizes greater even than Tokamaks before breakeven could be reached. Secondly, if you could somehow pack enough ions into the magrid, despite the losses (and subsequent arcing) the energy costs of doing so would be so great that breakeven could never be reached.

* One atmosphere of a gas has 6.02 *10^23 particles / 22.4 liters at STP. Converting this to particles per cubic Meter yields 2.7 *10^25 particles / M^3.

Dan Tibbets

[Aero]

* One atmosphere of a gas has 6.02 *10^23 particles / 22.4 liters at STP. Converting this to particles per cubic Meter yields 2.7 *10^25 particles / M^3.

Oh what fun! Now we have the reactor operating at standard temperature and pressure. It's not such a stretch from here to the ideal gas law.

PV=nRT, or easier yet, http://www.chemicool.com/idealgas.html

This gives me 27 atmospheres of pressure, but then I don't know how that is applicable so I'm not quoting initial conditions.

[D Tibbets]

* One atmosphere of a gas has 6.02 *10^23 particles / 22.4 liters at STP. Converting this to particles per cubic Meter yields 2.7 *10^25 particles / M^3.

Oh what fun! Now we have the reactor operating at standard temperature and pressure. It's not such a stretch from here to the ideal gas law.

PV=nRT, or easier yet, http://www.chemicool.com/idealgas.html

This gives me 27 atmospheres of pressure, but then I don't know how that is applicable so I'm not quoting initial conditions.

Obviously,the reactor is not operating at STP. I included that to be complete in my calculation of the number of particles (molecules or atoms) contained in one cubic meter. The STP only applies to the conversion from the volume of one mole of gas to cubic meters. Obviously, at higher temperatures the pressure exerted by that number of gas molecules would be greater. But, I'm calculating DENSITY, not pressure. The actual pressure exerted under eg: 100,000 eV temperatures and 10^22 ion/ M^3 would be a large number. That is why you need very strong magnets to contain them.
Using the equation I showed several posts earllier, at room temperature (~0.01 eV ) and a density of 10^22 charged particles/ M^3, the magnetic field strength needed to obtain Beta= 1 condition would be ~ 10 ^-6 Tesla, or ~ 0.001 Gauss This calculation should be close enough to be in the ball park (I hope).

Dan Tibbets

[MSimon]

Using the equation I showed several posts earllier, at room temperature (~0.01 eV ) and a density of 10^22 charged particles/ M^3, the magnetic field strength needed to obtain Beta= 1 condition would be ~ 10 ^-6 Tesla, or ~ 0.001 Gauss This calculation should be close enough to be in the ball park (I hope).

Which explains why the Earth has an atmosphere.

[kcdodd]

Why does that explain why the earth has an atmosphere?

[MSimon]

Why does that explain why the earth has an atmosphere?

.5 gauss field.

[icarus]

Dan:

That is why you need very strong magnets to contain them.

I think you are starting from the wrong place. The beta=1 condition applies to the electron kinetic pressure, (that is not necessarily the ion partial kinetic pressure but might be related (?)). The electrons are 'confined' by the magnetic field but not the ions, they are attracted to the virtual anode potential well ... or so the hypothesis goes.

You'll need to find a link between optimal fusion ion density, i.e. mean free path, ion pressure, electron pressure, magnetic field strength and 'annealing' behavior. Beta=1 is just the start of your problems.

[D Tibbets]

Bussard stated that there is an upper limit to density.

Above that limit the mono-energetic assumption breaks down and, even with 'annealing', the plasma essentially thermalises as there are too many 'low energy' ion collisions occurring before a fusion event (high energy collision).

If there is an upper limit for density (based on fusion conditions), there is an upper limit on pressure and thus an upper limit on edge magnetic field strength.

There's your anchor.

Seems reasonable. But I have not heard of thermalization at higher densities being the limiting factor. As the density goes up, the fusion rate goes up at density squared. How fast will the thermalization rate increase? I would guess that the rate would increase in a similar manner as they are both statistical probabilities based on density and temperature. It is true that as the density increases, the temperature has to decrease to maintain Beta=1 at some given B field strength. There is a limit to how much the energy (temperature) could increase before the fusion crossection levels off. The counter argument is that as the temperature increases the coulomb crossection decreases rapidly, so this is a knob that can be adjusted for greatest input/ output considerations, where thermalization time approaches the limiting condition.
I suspect that so long as you can increase the B-field strength, you can increase the fusion rate by increasing the density. At some point the densities and fusion rate could theoretically become almost infinite. Of, course piratically, that is impossible.

My impression has been that the limit on density is the Wiffleball trapping factor, and the resulting density buildup outside the magrid that could lead to arcing*. Density inside the magrid could also lead to arcing, but I got the impression from Bussard was that this could be controlled, thanks to magnetic shielding of the magrids and careful attention to surface smoothness (no points that could concentrate charge).

* External densities of ~ 5-10 Microns or ~ 10^19 particles / M^3 could develop pashin discharge (glow discharge) or what is generally referred to as arcing. The density differential that the Wiffleball trapping factor provides then limits how much addition density can be built up within the magrid. As this number has been reported as a few thousand, the maximum density would be ~ 10^22 particles / M^3, as has been quoted. The only way to increase the density beyond this would be to figure some way to increase the Wiffleball trapping factor. I'm not sure if the claimed 3-5X improvement in performance with a higher number of magnets does this by increasing the Wiffleball trapping factor, or by greater quasi-sphericity and convergence.

Dan Tibbets

[D Tibbets]

Why does that explain why the earth has an atmosphere?

I thought of commenting on this in that post but, for once I restrained myself. But...
Light gasses, like hydrogen leave the atmosphere of a planet most easily. That is one reason why Venus is so dry. As the heat increased, the water vaporized, the small amounts that then made it into the upper atmosphere, was ionized by the sun, The hydrogen ions were then able to escape, while the oxygen left behind then combined with anything available (like carbon) to form more CO2 and cause run away greenhouse heating. If Venus had a magnetic field like Earths' much (?) of the hydrogen ions would have been trapped on field lines and a fair portion would reenter the atmosphere at the magnetic poles. This would have prevented, or at least slowed the loss of hydrogen to space.

Dan Tibbets

[KitemanSA]

which might explain why Earth has a HYDROsphere, not an atmosphere. After all, Venus has amost no magnetosphere but has a hell of an atmosphere (and I mean that literally!)

[kcdodd]

I have never heard that as a reason for our atmosphere. Most of the atmosphere is clearly not in ionic state and won't be affected by the magnetic field. The part that is originates from the sun, not earth. The magnetic field keeps solar plasma from reaching earth and may aid in our atmosphere not being blown away, but I have never heard of it as a containment mechanism.

[D Tibbets]

I have never heard that as a reason for our atmosphere. Most of the atmosphere is clearly not in ionic state and won't be affected by the magnetic field. The part that is originates from the sun, not earth. The magnetic field keeps solar plasma from reaching earth and may aid in our atmosphere not being blown away, but I have never heard of it as a containment mechanism.

Not quite, though I admit it is much closer than what I said. Without a magnetic field, the solar wind can ionize gas in the upper atmosphere and that can lead to increased escape of the light ions. I saw no mention of internal trapping of charged particles due to Earth's magnetic field, though it is reasonable if external ions can be excluded/ deflected. It is the same process in reverse. It may be a trivial contribution though.

http://en.wikipedia.org/wiki/Atmospheric_escape

Dan Tibbets

[kcdodd]

I was also going to weigh in on the topic that I think the wiffleball (ie high beta) may not be a good idea. I think that if beta is increased to the point of making a wiffleball it will become more unstable and lead to larger anomalous transport of electrons, which defeats the purpose of the wiffleball approach. So, in order to increase density and reaction rate higher fields would be needed to suppress it.