Why people are so optimistical to Polywell?

[KitemanSA]

But beta parameter is used for magnetic confinement devices -not for IEC. Yes, it (words) have not a big matter, but beta there used for estimation of stability criteria. Stability is not the favorite issue here like to discuss.

Polywells are a sort of magnetic/IEC hybrid. They have good magnetic curvature everywhere, so no ELMs, etc. Plus, the ion pressure is low at the edge.

Indeed, AFAIK, in the Polywell, the pressure comes almost TOTALLY from electrons, fusion products adding a bit perhaps but fuel effectively not at all.

[Joseph Chikva]

Indeed, AFAIK, in the Polywell, the pressure comes almost TOTALLY from electrons, fusion products adding a bit perhaps but fuel effectively not at all.

I think that this is not a totally correct description. If you consider magnetic mirror as solid. Because in fact significant part of particles (including fuel particles) pass through that.

[TallDave]

For TOKAMAKs there was proved theoretically that in case if beta exceeds 0.4 then various types of instabilities will occur.

See the point on good curvature above. It's not really an issue for mirror machines. In mirrors, the issue is cusp losses. The WB is meant to solve that problem.

Thermalization
I also do not see any mechanizm to avoid the thermalization. As that mainly caused by ion-ion collisions. No thermal energy dissipation mechanizm, no any forces returning scattered ions on previous direction.

Electron thermalization is handled by injecting hot electrons as they are lost. As I recall this is an area of concern because it's easier in small machines (the thermalization time is less than the confinement time, but this is less favorable in larger machines).

As for ion thermalization... well, as Rick pointed out above, they don't really need much ion focus. But they expect to get it, because at the edge the collision cross-section is high and radial velocity is low, so they'll tend to end up being focused at the core. Quoting Rick once again:

2. The general rule of thumb on ion collisions is that ion collisions in the core add angular momentum to the ions (thermalization) while collisions in the edge remove angular momentum. The reasons edge collisions remove angular momentum is that as the ions reach their radial turning point, their angular velocity exceeds the radial velocity. Consequently, thermalization takes energy from the angular direction and puts it in the radial direction. The collision rate gets big because the velocities are small. The upshot of this is that if you want to look at the effect of collisions on ions, you have to do something like bounce-averaged Fokker-Planck where you take into account the collisions at all points in the ion orbit. There are two places this is discussed in the literature. The original work is:

M. ROSENBERG and N. A. KRALL, Phys. Fluids B, 4,1788 (1992)

There is also a 1993 paper by these authors (I don’t have good access to Journals here) but I think the correct one is the one above. Of course, the Chacon paper also looks at this.

[D Tibbets]

If by definition Beta cannot exceed one, then it might be more accurate to describe the Polywell of reaching 0.9999... Beta. If it manages to reach 1.000000.... the cusps open up and any additional electron current is wasted. This description does ease my ignorant concern about balancing at a Beta of one.

As far as ion thermalization, certainly they will thermalize over their expected lifetime if there is not some restoring force. This has been debated here multiple times. The claimed restoring force is edge annealing. It makes perfect physical sense, at least if the ion motions are primarily radial, as they would initially be expected to be. If the MFP for the ions is greater than the machine diameter for most of each transit, during the time the ions are at very slow speed at the Wiffleball border/ top of the potential well, the ions local MFP plummets due to tremendously increased Coulomb collisionality at low speeds/ energy. Because of this the ions do very quickly thermalize in this edge region, but at a Maxwell- Boltzman distribution around this very low energy. This energy spread is much smaller than the energy of the ions as they approach the bottom of the potential well, so the local thermalized edge spread is small in proportion to the maximum energy in the core- thus ~ monoenergetic ions in the core (non edge regions) is maintained for the milliseconds needed. The spherical geometry also means that angular momentum changing collisions that occur in the core do not generate as much angular deflections as you might expect as any angle from the center is still radial.

As far as magnetic surfaces, in the Polywell all of them are curved outward- convex towards the center. This is only possible with cusps, and supposedly prevent MHD instabilities- , macro instabilities. These can form with concave fields that cannot be avoided with any type of solenoid magnet arrangement. I suppose a perfect sphere or oval magnetic surface might be stable, but piratically impossible to form or maintain. If the magnetic windings/ magnets are spaced close enough together there may be some quantum effect that manifests to modyfy this(?). All you would need would be magnet spacings of perhaps 1 nanometer or less,
My weak understanding of Tokamaks is that while these macro instabilities cannot be avoided, there may be some periodicity to them so that manipulations may minimize their effect.

Dan Tibbets

[D Tibbets]

....... Electron thermalization is handled by injecting hot electrons as they are lost. As I recall this is an area of concern because it's easier in small machines (the thermalization time is less than the confinement time, but this is less favorable in larger machines).
......

Don't forget that the electron life time for thermalization concerns is the primary magnetic confinement of the electrons- generally a fraction of a millisecond. Recirculation modifies the input energy needed, but not this primary lifetime of the electrons in determining thermalization limits.

Also, the efficiency of fusion / over input power (Q) for D-D peaks at ~ 15 KeV (Joel Rogers mentioned this in his evaluation- this is the steepest portion of the D-D fusion crossection curve). But Bussard expected drive energies of ~ 80 KeV. This reduces output/ input efficiency (everything else being ignored), but it also significantly decreases the electron Coulomb collisionality rate, thus MFP increases proportionately by ~ 30X in this example. Another example: 10 KeV 0.3 M WB6. If the electron thermalization was tolerable, then a 80 KeV 3 M WB100 should perform ~ 5 times better from an electron thermalization standpoint, at least at the same densities.

[EDIT] I think the the electron lifetime in terms of passes or orbits is unchanged in larger machines (proviaded B field increases proportionatly). In terms of time the lifetime in a WB100 machine would be ~ 10 times longer (cusp hole size maintained and diameter (distance per pass) is increased 10 fold). The lifetime would be ~ 10 times longer, the MFP would be ~ 30 times longer. So the larger machine should actually perform better from an electron thermalization viewpoint with this comparison between 15 KeV and 80 KeV drive energies.

As Bussard reportedly was careful and through in his evaluations, this drive energy was probably close to the best compromise necessary to optimize fusion AND thermalization characteristics in the anticipated sized machine. Or, another view- under this best compromise, the appropriate size machine was determined.

Dan Tibbets

[TallDave]

Dan -- here's yet another of my incessant Rick quotes, fwiw:

For present generation machines the electron confinement time is less than the electron collision time so thermalization isn't an issue. For reactors, the electron collision time and the confinement time become comparable. Electron distributions are expected to be isotropic, but not thermal. Thermalization is a global process because electron orbits cover the entire interior. If electrons lose their energy (kinetic + potential), they will accumulate near the coil cases until they leave the system. Since the spherical geometry (coupled with conservation of angular momentum) will itself change the distribution functions, l.t.e. doesn't make a lot of sense.

[Joseph Chikva]

For TOKAMAKs there was proved theoretically that in case if beta exceeds 0.4 then various types of instabilities will occur.

See the point on good curvature above. It's not really an issue for mirror machines. In mirrors, the issue is cusp losses. The WB is meant to solve that problem.

I do not understand how a few short solenoids have a better mag field topology in comparison with other mirror machines. For example "yin-yang" design.

[Joseph Chikva]

If by definition Beta cannot exceed one, then it might be more accurate to describe the Polywell of reaching 0.9999... Beta. If it manages to reach 1.000000.... the cusps open up and any additional electron current is wasted. This description does ease my ignorant concern about balancing at a Beta of one.

By my understanding of process you will add and add electrons and ions into reaction zone and by approaching to beta=1 particles losses will increase. If you see at mag mirrors as 100% effective confining device, that's wrong.

[D Tibbets]

For TOKAMAKs there was proved theoretically that in case if beta exceeds 0.4 then various types of instabilities will occur.

See the point on good curvature above. It's not really an issue for mirror machines. In mirrors, the issue is cusp losses. The WB is meant to solve that problem.

I do not understand how a few short solenoids have a better mag field topology in comparison with other mirror machines. For example "yin-yang" design.

No, a mirror machine, at least in this context, is two opposing magnets, with two polar cusps and one line or equatorial cusp. It is a dfifferent morphology than a solenoid arrangement where the poles are lined up in the same direction.

Dan Tibbets

[D Tibbets]

If by definition Beta cannot exceed one, then it might be more accurate to describe the Polywell of reaching 0.9999... Beta. If it manages to reach 1.000000.... the cusps open up and any additional electron current is wasted. This description does ease my ignorant concern about balancing at a Beta of one.

By my understanding of process you will add and add electrons and ions into reaction zone and by approaching to beta=1 particles losses will increase. If you see at mag mirrors as 100% effective confining device, that's wrong.

Again I'm not sure of your derivations. Neither a simple mirror machine nor a Polywell is a 100% confinement machine. A Tokamak approaches this much more closely, provided that it is huge enough that cross field trasport becomes tiny and macroinstabilities are ignored. These cusp machines leak charged particles- mostly electrons in the Polywells case, much faster (lifetimes ~ 1 ms instead of hundreds of seconds in a large Tokamac). What the Wiffleball / Beta= very close to one results in is a minimum of loss for that machine. Without it the electron confinement time would probably be closer to ~ 10 microseconds. The reason the Polywell can compete with Tokamaks (cuspless confinement) is two fold- increased density, and increased ion participation in fusion (more monoenergetic ion population). There are other side considerations about Bremsstrulung, etc, but that is the two basic differences, with the Wiffleball trapping factor probably being the most important, as a thermalized Polywell would probably work with D-D fusion, though at larger size and lower Q's. Remember the triple product : confinement * temperature* density. The Polywell has low confinement but more than makes up for it with greater density and effective temperature.

To restate WTF vs Beta, The confinement improves up to Beta = 1. This is a maximal condition. Pumping in more electrons will not increase Beta further (as you said) but the confinement efficiency will drop so the electron losses will increase in proportion to the electron injection once a maximum containment efficiency is reached at Beta= 1.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Beta=1 represents a peak in confinement efficiency, not an endpoint. To simply maintain Beta= 1 conditions, you only need to inject a few more electrons than required. The excess will naturally leak out as the peak confinement efficiency is passed. There may be a mild oscillation about this peak containment efficiency, and resulting WTF and this may be good or bad depending on the amplitude, frequency and resulting effects on the plasma (POPS type waves, etc).

Dan Tibbets

[Joseph Chikva]

Beta=1 represents a peak in confinement efficiency...

It's wrong. I also doubt in projected density 10^22 m^-3 that as I see is calculated from condition beta=1 (equality of gas and magnetic pressure). That will be impossible technically.
And if lower density then consequently lower fusion intensity (as square) with the same confinement duration. ~ 10 microseconds you say?

[93143]

Beta=1 represents a peak in confinement efficiency...

It's wrong. I also doubt in projected density 10^22 m^-3 that as I see is calculated from condition beta=1 (equality of gas and magnetic pressure). That will be impossible technically.

Either you're splitting hairs or you haven't understood how this device is supposed to work.

The magnetic field inflates under plasma pressure, and this squeezes the cusps shut. When we say "beta=1" in the context of a Polywell, we mean that the plasma has fully excluded the magnetic field from a quasi-spherical region with maximally-constricted magnetic cusps - a fully-formed wiffleball - and this is the minimum-loss operating point.

This is not something the posters on this forum made up. It is Dr. Bussard's own description of what happens in his invention, and so far the indications are that he was essentially correct.

[D Tibbets]

Chikva, you should read the 2008 patent application, then reread it again. There are a lot of subtle details and reasoning about the various aspects of the Polywell.
As far as the physics, there are essentially two arguments. If the Wiffleball is real and if thermalization can be controlled. Both have accepted physics explanations. There are some gray area about assumptions and extrapolations, but the basic physics is standard. There is no fringe science involved. In areas where the physics theory is uncertain or intrepratations diverge, then experimentation is the final answer. The persistence of the arguments on this forum is driven by the unavailability of definitive data. The released data is sparse and open to accuracy arguments . That was the whole purpose of WB7, to increase the precision and reliability of previous conclusions. As outsiders we unfortunately are not privy to this information. The optimistic vs the pessimistic sides of the argument are often reduced to arguing the motives of those who continue to fund the research as much or more than the merits of the data that is available.

As far as obtainable density. That is very basic plasma physics dependent on the B fields and loss rates. The question of losses to maintain that density is more open. Issues like the Brillion limit, etc have been addressed.
Again, much of this is mentioned in the 2008 patent application (and in the earlier ~1988 patent).

http://www.fusor.net/board/view.php?bn= ... 1237670934

Dan Tibbets

[KitemanSA]

Indeed, AFAIK, in the Polywell, the pressure comes almost TOTALLY from electrons, fusion products adding a bit perhaps but fuel effectively not at all.

I think that this is not a totally correct description. If you consider magnetic mirror as solid. Because in fact significant part of particles (including fuel particles) pass through that.

As DanT suggested, the ions are very cold when they reach the magnetic field, having had to climb out of the well. Indeed, IIUIC, the ions are (or were) expected to be formed INSIDE the well, far enough down the well so that they would never reach back to the edge where the field is. So indeed the fuel should never reach the magnetic field except the upscattered ions. So true, the upscattered ions may add partially to the pressure, but not much. ICBW.

[Joseph Chikva]

Either you're splitting hairs or you haven't understood how this device is supposed to work.

I already understood how this device is supposed to work. Also I assume how it will work in reality.