Spheroidal Foci and POPS?

[TallDave]

I was hoping you might expand on your reasoning. The holes are (almost) symmetrical, so most processes contributing transverse momentum will cancel out.

Hmmm? What do the cusps have to do with ion oscillation? Does your picture have ions mostly oscillating across the center from the cusps, or forming a shell around the WB at the top of their orbits?

Everywhere between the WB boundary and the casings is an area where the B field is pushing charged particles at right angles to the coils (except inside the cusps of course). I think having the ions spending a lot of time in that area is not going to be good for ion focus. So it's another reason I don't like that picture (in addition to it seeming unlikely ions in an electron-rich plasma are going to go outside the electron cloud).

I think it's more likely only a few ions get to the WB boundary, where they get bounced back.

[alexjrgreen]

What do the cusps have to do with ion oscillation? Does your picture have ions mostly oscillating across the center from the cusps, or forming a shell around the WB at the top of their orbits?

At the top of their orbits the ions form a shell around the electrons in the wiffleball, except where they escape through the holes.

Everywhere between the WB boundary and the casings is an area where the B field is pushing charged particles at right angles to the coils (except inside the cusps of course). I think having the ions spending a lot of time in that area is not going to be good for ion focus. So it's another reason I don't like that picture (in addition to it seeming unlikely ions in an electron-rich plasma are going to go outside the electron cloud).

I think it's more likely only a few ions get to the WB boundary, where they get bounced back.

If Gauss's Law applies, the ions have to be outside the electrons to be confined by them.

[TallDave]

If Gauss's Law applies, the ions have to be outside the electrons to be confined by them.

How do you figure? Where do they get the energy to do this?

At the top of their orbits the ions form a shell around the electrons in the wiffleball,

That means they're picking up lots of transverse momentum from the magnetic field. Bad.

[TallDave]

As far as the magnetic interface adding transverse motion, I'm not sure that the half spiral that an ion makes when turning on the Wiffleball border introduces any significant lateral motion because each magnetic turning may contribute only a tiny lateral motion. Also, because of the convex surface of each lobe, the field will turn the ion slightly away from the center, or if it hits the other half of the lobe, it will turn slightly towards the center, eg, on the left side of the lobe the magnetic turning might be 179 degrees relative to the Wiffleball center. On the right side the ion may turn at 181 degrees (both ions starting from the Wiffleball center and hitting an equal distance from the center of the lobe). The net effect may be zero.

That's fine for a few ions gently bouncing off the WB boundary, not so fine for a picture where the ions all form a shell outside the WB boundary at the top of their orbits turning radial velocity into transverse. Even if the effects cancel out overall, they don't cancel out very well for individual ions and you'll end up with an ugly spread of transverse velocities and not much fusion.

Also, the ions suposedly stays out of the magnetic domain, which means it is reversed by the electrostatic field, and only upscattered ions would see the magnetic field . Finally, this periferal region of slow ions is advertised to be the reigon where annealing occurs.

I like this picture a lot better.

I just don't see how the ions can turn radial momentum into transverse out in the B field on every orbit and still make it out there. Where do they get the energy to keep doing this? Something would have to keep adding radial momentum. It seems much more likely they settle in inside the edge.

[KitemanSA]

If Gauss's Law applies, the ions have to be outside the electrons to be confined by them.

Actually, they have to be outside the main concentration of the electrons to be restrained by them. That main concentration is the place at the center of the reactor where the "virtual" electrode exists. Since the same virtual electrode slows the electrons, most of their time, therefore most of their concentration , is down in the middle of the reactor. The well slopes up from there, not from the wiffleball. Thus the ions do not NEED to go beyond the wiffleball. They may actually do so, but I don't see it as an absolute.

The main question(s) here seem(s) to devolve to "does the useful well extend beyond the wiffleball? And if so, by how much?"

[alexjrgreen]

I just don't see how the ions can turn radial momentum into transverse out in the B field on every orbit and still make it out there. Where do they get the energy to keep doing this? Something would have to keep adding radial momentum. It seems much more likely they settle in inside the edge.

How do the electrons manage it, then?

[TallDave]

I just don't see how the ions can turn radial momentum into transverse out in the B field on every orbit and still make it out there. Where do they get the energy to keep doing this? Something would have to keep adding radial momentum. It seems much more likely they settle in inside the edge.

How do the electrons manage it, then?

It's the bottom of the well for them. The less radial momentum electrons have, the closer to the edge they have to stay.

[alexjrgreen]

If Gauss's Law applies, the ions have to be outside the electrons to be confined by them.

Actually, they have to be outside the main concentration of the electrons to be restrained by them. That main concentration is the place at the center of the reactor where the "virtual" electrode exists. Since the same virtual electrode slows the electrons, most of their time, therefore most of their concentration , is down in the middle of the reactor. The well slopes up from there, not from the wiffleball. Thus the ions do not NEED to go beyond the wiffleball. They may actually do so, but I don't see it as an absolute.

The main question(s) here seem(s) to devolve to "does the useful well extend beyond the wiffleball? And if so, by how much?"

Art calculated that the ions stop a Debye Length beyond the electrons.

You're suggesting a root mean squared value for the effective radius of the electron orbit...

[TallDave]

Art calculated that the ions stop a Debye Length beyond the electrons.

IIRC Art also assumed the electrons collapsed into a sheath. It's also tricky to calculate a Debye length in such a dynamic environment.

[KitemanSA]

Art calculated that the ions stop a Debye Length beyond the electrons.

From wikipedia, and values not UNLIKE a tokamak, that results in ~0.0004 m. Maybe so. But does that necessarily mean the entire surface, or just the average? By that I mean, does the well necessarily follow the contour of the wiffleball, or might it be a smoother shape? My reading of Dr. N's limited comments suggest that the well is smoother. One of these days I will index Dr B's and Dr. N's comments on the various issues as best I can and place the comment set in the FAQ. Want to help? Anyone?

You're suggesting a root mean squared value for the effective radius of the electron orbit...

I have seen a number of representations of the "well" and they all had sides sloping up from near the center. I don't pretend to sufficiently up on the mathematics of this to suggest the cause or even the relationship for that, merely mentioning what I have seen. Indeed, maybe I've simply ignored others as not fitting my prejudice.

[D Tibbets]

Keep in mind that there are various assumptions made, and several different arguments made on those assumptions. Concerning the Wiffleball and electron distribution within it, I beleive the magnetic field (Wiffleball border) can be concidered as a hard surface that the radial electrons bounce off of. You can ignore gyroradius away from the cusps and ignore any trasnsverse motion imparted by the magnetic field because it is minor and/ or self canceling (see my earlier post) for the dominate population of radial electrons. The time you can maintain the majority of electrons in this pattern and how much energy it costs to do so is a different argument. The dynamic distribution formes an elliptical potential well. This means there are more electrons per cc near the center rather than being dristributed evenly throughout, or concentrated in a shell near the Wiffleball border- this would form a square potential well (I think) as supported by A. Carlson. You have to dig deep to find evidence of elliptical and double wells in IEC devices, but I have found several sources.
Having most of the electrons well below the wiffleball border means the ions will see most (almost all, or perhaps effectively all) of the well while they remain within the Wiffleball border. How you get the low energy ions to this position initially with ion guns (as opposed to gas puffers) while not destroying the magnetic and effective electrostatic shielding of the guns is beyond me.
At least from an ideal perspective, the magnetic fields can be completly ignored from the fuel ions perspective. The only thing they see is the electrostatic field created by the electrons (which are concentrated near the center).

Another idea with unknown (by me) merits is that low energy ions introduced into the magnetic domain just above the Wiffleball border are initially traped by the magnetic field lines, but they are quickly pulled off of the field lines and into the interior of the Wiffleball due to the electrostatic well. This would apply to new ions or upscattered ions.The energy used to pull the ions out of the magnetic field takes energy and this automatically sets the top of the ions well right at the Wiffleball border(vigorous hand waving here). I have to scratch my head some more when I try to apply this reasoning to cusps.

Dan Tibbets

[TallDave]

Concerning the Wiffleball and electron distribution within it, I beleive the magnetic field (Wiffleball border) can be concidered as a hard surface that the radial electrons bounce off of.

Well, remember, the WB effect exists only because of the electron pressure. As the electrons move along the field lines, they deform the field (the motion of a charged particle).

and ignore any trasnsverse motion imparted by the magnetic field because it is minor and/ or self canceling (see my earlier post) for the dominate population of radial electrons.

I think you can ignore it more because we don't care as much whether electrons have lots of radial momentum and little transverse. We're not fusing electrons, so the focus isn't as important; as long as there are lots of electrons somewhere near the center the ions still see a well. And we're constantly injecting 10MW of happy new electrons with lots of radial velocity to make sure there are.

Having most of the electrons well below the wiffleball border means the ions will see most (almost all, or perhaps effectively all) of the well while they remain within the Wiffleball border

That shouldn't be necessary. When you drop in a ball at the edge of a bowl, it doesn't roll out of the bowl again. The ion population as a whole is going to lose, not gain radial momentum; some of the initial radial momentum will become transverse (hopefully not too much). A few ions will upscatter to the point of being gently shoved back at the WB boundary, but the bulk should be well contained.

[KitemanSA]

Well, remember, the WB effect exists only because of the electron pressure. As the electrons move along the field lines, they deform the field (the motion of a charged particle).

This is 90 degrees out of line with what I understood to be the case. It is not the motion "along" the field lines, but "normal to" the field lines that inflates the wiffleball and pinches the cusps.
With "normal to", you get a half orbit and a return in the direction from whenst it came (radial). "Along" causes the electrons to be at the edge of the well, not contributing to the well at all, no?

[TallDave]

Yes I think it's technically the gyration around the field lines. I'm a little fuzzy on exactly how the deformation happens, and I haven't found much online. Maybe 93143 or someone can educate me beyond "motion of a charged particle." I'm guessing it's something like a current flowing around a coiled wire.

"Along" causes the electrons to be at the edge of the well, not contributing to the well at all, no?

Well, sure. Not all the electrons are always in the middle, else there'd be no electron pressure and no WB. It's just the place they're most likely to be on average.

[Aero]

Correct me if I'm wrong, (often happens) but I thought that the electrons spiraling around the field lines were what caused the polywell to form. That is, the electrons repel each other and those spiraling around the field lines drag the field lines outward. They don't escape the field lines, (until later) but they drag the field lines away from the center of the BFR, creating and maintaining the polywell.