New FAQ - What are Cusps and what kind does a Polywell Have?

[KitemanSA]

KitemanSA:

I was under the impression that in both the analyses they used square plan-form magnets turned the WRONG WAY.

Your impressions are all turned the WRONG WAY. Indrek and I used an analysis with circular (toroidal) electromagnets. The cubic projection of lines of low magnetic field onto the sphere are exactly how you would see them, IF the plasma would be spherical. This is a simple geometric consequence of projecting a cube (the faces that the polywell magnets lie upon) onto a sphere.
...
As far as I know, kcdodd;s simulations were for circular toroidal electromagnets (close to the physical ones) and the plasma ball had infinitesimal current loops tangential to it's surface and allowed to relax until beta=1 ... i.e. internal pressure balanced field strength at the surface (current in loops goes to zero, I think).

My apologies, I could have sworn I read that due to some difficulties the loops were square. Then I went to kcdodd's web sit where the graphic was stored and I found this:

and what was I to think.

I am under the impression that kcdodd did the bag calc, no? If so, I kind of think the coil was square there. I could be wrong.

Re the sphere, I truly didn't intend to insult anyone. And I guess I can sort of see how a 6 toroidal magnets in a quasi-cube, with six image magnets below could make the interesting pattern shown. But it does look a lot like there was a set of square magnets making it.

[KitemanSA]

Don't make it so complicated. Just give up ion convergence, which even Rick Nebel says would be nice but is not essential. Then you can let the plasma take whatever exact shape it wants, as long as it is convex, which shouldn't be hard to achieve with polywell coils.

Ok, you are once again confusing me. In an earlier post in this forum you seem to say that MHD stability is provided by the field bulging INTO the plasma (i.e. the plasma is conCAVE) and then you say you can let the plasma do anything as long as it is conVEX. Wha???

[Art Carlson]

Don't make it so complicated. Just give up ion convergence, which even Rick Nebel says would be nice but is not essential. Then you can let the plasma take whatever exact shape it wants, as long as it is convex, which shouldn't be hard to achieve with polywell coils.

Ok, you are once again confusing me. In an earlier post in this forum you seem to say that MHD stability is provided by the field bulging INTO the plasma (i.e. the plasma is conCAVE) and then you say you can let the plasma do anything as long as it is conVEX. Wha???

I'm a fast draw, but sometimes I end up holding the gun the wrong way. The best defense my lawyer could think of is that convex and concave depend on which side you're on. Typical lawyer. I meant the plasma has to be conCAVE, i.e. spikey and spiney and scooped out, not smooth and voluptuous.

[IntLibber]

So a big question remaining for me is does the wiffle-ball look more like this

[a colorful ball]

or this??

[a spikey alien]

Although the proponents sometimes contradict themselves, the spikey version corresponds closer to what they claim, and - in a rare convergence - to the way I think it must work. The beach ball version, at least, is not consistent with a sharp-boundary, beta = 1 plasma in equilibrium. The alien is.

My impression is that they are representing the same thing, the colors on the first show the magnetic field strength at the surface of a virtual sphere inside the reactor, the second is a topology of the same field, at a given field strength.

[icarus]

Art wrote:

The net electrostatic force on a quasi-neutral plasma isn't very big. You can calculate an equivalent (negative) pressure from 0.5*epsilon_0*E^2. For 100 kV/m, for example, this works out to 0.04 Pa. To get this pressure with magnetic fields you only need a few mT.

That's what I would have thought but I was wondering if it was possible for there to be some kind of shielding effect due to the electron sheath being on the exterior of the rest of the plasma? I.e. the net charge of the scalloped out blob is "quasi-neutral" but on the surface, closest to the MaGrid, it is largely negative. Shouldn't this make for a much greater electrostatic attraction between the plasma sheath and MaGrid than if that outer layer was equally populated by ions and electrons?

Just checking so I can put this one behind us. I suppose a better question is
i) What density (total number?) of electrons would the plasma need to contain before electrostatic attraction pressure on the sheath becomes large enough to compete with the repulsive magnetic field gradients?

Consider the case where the plasma is purely made up of electrons. How many electrons would you need in there before the magnetic field would begin to distort outwards, due to the electrostatic attraction between the plasma and the MaGrid?

Another point that is raised here, that strikes at the heart of the conceptual understanding is this; are we now going to consider the plasma to be a continuum of ions and electrons?

Initially, I thought from reading the original material, that the electrons were held in a continuous plasma state but the ions were diving back and forth through that electron plasma ball (but not continuously connected to the plasma in the sense of a connected potential field) as the ions were not affected by the weaker magnetic field strength (~0.1T).

Now, when we move to high magnetic field regimes (>3T) where the ions are forced magnetically (not electrostatically) to be exclusively in the same central region as the electrons then won't that just create a continuous, quasi-neutral plasma state? I think at this point you can let go of any tenuous hold you had on non-Maxwellian assumptions and you are sucked back down in to the vortex of the thermalised plasma game (i.e. tokomaks), turbulent "transport" and all that entails.

The beauty of Bussard's concept is to disconnect the fields of the ions and the electrons and give a control knob over each of them (magnetic field adjustment for electron control and drive voltage adjustment for ion control). Workable control theory we have, turbulent transport theory we don't, that's an engineering fact.

Aside: Along with the above considerations, I have derived a formula relating the cusp electron loss rate to wiffleball radius and total number of electrons in the contained volume, if anyone was interested I'll write it up in a web document when I get some time off work.

[icarus]

KitemanSA:

Re the sphere, I truly didn't intend to insult anyone. And I guess I can sort of see how a 6 toroidal magnets in a quasi-cube, with six image magnets below could make the interesting pattern shown. But it does look a lot like there was a set of square magnets making it.

I did the simulation along with Indrek and I'm telling you the magnets were toroidal. Believe whatever you like, I'm not insulted but consider getting your facts straight before you spread the manure all around.

[icarus]

IntrLibber:

My impression is that they are representing the same thing, the colors on the first show the magnetic field strength at the surface of a virtual sphere inside the reactor, the second is a topology of the same field, at a given field strength.

Close but no cigar. They are different fields, however closely related, although both can be thought to have all field excluded interior to the shown surfaces.

The first has most all it's field lines running tangential to a sphere, however, the field strength at the surface varies, as given by the contour colouring.

The second has field lines tangential to a scalloped out blob but the field strength is constant all over the surface of the blob.

[Art Carlson]

Art wrote:

The net electrostatic force on a quasi-neutral plasma isn't very big. You can calculate an equivalent (negative) pressure from 0.5*epsilon_0*E^2. For 100 kV/m, for example, this works out to 0.04 Pa. To get this pressure with magnetic fields you only need a few mT.

That's what I would have thought but I was wondering if it was possible for there to be some kind of shielding effect due to the electron sheath being on the exterior of the rest of the plasma? I.e. the net charge of the scalloped out blob is "quasi-neutral" but on the surface, closest to the MaGrid, it is largely negative. Shouldn't this make for a much greater electrostatic attraction between the plasma sheath and MaGrid than if that outer layer was equally populated by ions and electrons?

As I recall the derivation, you get the charge density from the divergence of the electric field. More simply, if the field jumps from zero inside the ball to some value in the vacuum region, you can calculate the surface density of electric charge from the size of the jump. The force comes from the electric field acting on the charge density. That is why there is an E^2 in the formula. I believe it is really a quite general result.

[KitemanSA]

... I meant the plasma has to be conCAVE, i.e. spikey and spiney and scooped out, not smooth and voluptuous.

So by this am I to assume you think added sphericity is bad?

[TallDave]

The net electrostatic force on a quasi-neutral plasma isn't very big. You can calculate an equivalent (negative) pressure from 0.5*epsilon_0*E^2. For 100 kV/m, for example, this works out to 0.04 Pa. To get this pressure with magnetic fields you only need a few mT.

Actually, now I'm not sure we're talking about the same thing here. My understanding is that the motion of the electrons along the field lines are what change the shape of the field, as opposed to just the pressure.

[TallDave]

... I meant the plasma has to be conCAVE, i.e. spikey and spiney and scooped out, not smooth and voluptuous.

So by this am I to assume you think added sphericity is bad?

Yes, he thinks it will be unstable for some important MHD modes, but some of us question whether the shape is important as long as long the forces are increasing in the right directions.

[KitemanSA]

... I meant the plasma has to be conCAVE, i.e. spikey and spiney and scooped out, not smooth and voluptuous.

So by this am I to assume you think added sphericity is bad?

Yes, he thinks it will be unstable for some important MHD modes, but some of us question whether the shape is important as long as long the forces are increasing in the right directions.

Dang! Then I guess we should try to find out SOON!

[Art Carlson]

... I meant the plasma has to be conCAVE, i.e. spikey and spiney and scooped out, not smooth and voluptuous.

So by this am I to assume you think added sphericity is bad?

Yes, he thinks it will be unstable for some important MHD modes, but some of us question whether the shape is important as long as long the forces are increasing in the right directions.

I think you didn't follow my math. Using Ampere's Law I showed that the forces increase in the right direction if and only if the surface is concave.

[icarus]

Hey Art, since we're on surfaces, curvatures and lines I have a question that I'd be interested on your take on.

First consider tracing along the cusp line radially inwards (say one of the face-centered cusp lines for the simplest case), and by cusp line here I mean the very center line (i.e the mathematical "stagnation" line of the cusp from which all the field strength gradients are increasing perpendicularly away from).

Would you agree that at some radius that this cusp line will terminate on the beta=1 surface of the electron plasma? (And probably as a normal to that surface.)

Is this a valid proposition? Is there any way we could show it to be physically realistic?

[KitemanSA]

KitemanSA:

Re the sphere, I truly didn't intend to insult anyone. And I guess I can sort of see how a 6 toroidal magnets in a quasi-cube, with six image magnets below could make the interesting pattern shown. But it does look a lot like there was a set of square magnets making it.

I did the simulation along with Indrek and I'm telling you the magnets were toroidal. Believe whatever you like, I'm not insulted but consider getting your facts straight before you spread the manure all around.

I was not intending to question your veracity. I believe you that the presentation on the sphere was produced with toroidal magnets. I was actually asking your forgiveness and understanding as to how I could come to the mistaken impression.