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

[KitemanSA]

Ok, I can do that. Does anyone argue against his proposed change?

Does anyone have any other proposed changes?

[Roger]

Kiteman its awesome you've tackled this, the faq so needed to be done. One thing I might mention beyond the technical discussion, is how well can the layperson grasp some of this. When I describe Polywell cusps to someone (I hope this has been correct /sheepish grin), it goes like this:

I hold up 2 fingers in a ring, and point to the middle, thats one kind of cusp, then there is the "3" finger Pinch", 8 of them at the 8 corners of the cube, then finally there is the "2 Finger Flat Pinch", should be 12.

And does an occasional graphically illustrative turn of phrase belong in a/this FAQ.

[TallDave]

For MHD stability, the field strength must increase moving away from the plasma

But it does, doesn't it? Moving away from the plasma means moving towards the coils. The electron pushback is altering the shape of the containing fields the plasma sees, but in some sense that's just an illusion created for the plasma by the motion of electrons across the convex magnetic fields.

[TallDave]

If I have two toroidal magnets positioned along the same axis of rotation, then the fields need to be of opposite sense to get a line cusp in the gap between their coils. In one case "same sense", in the other "opposite sense". In BOTH cases, the current in the parallel conductors are running in opposite directions. It is the single descriptor that I can find that works al the time. Do you have a better one?

First off, I'm not sure what you mean by "toroidal." Are you just talking about a wound electromagnet? Also, can't you create a cusp between permanent magnets?

But I think what's most confusing about that portion of the definition is that it doesn't mention electromagnetism. That definition would also apply to two straight copper wires side by side, carrying current in opposite directions but obviously not generating a cusp. This will probably be confusing to people trying to understand the FAQ.

It's probably easiest to talk in terms of magnetic polarity, which people generally understand (i.e. "a line cusp is formed by the meeting of N-N or S-S fields"). Positionality is probably something we can leave to the experts.

[Art Carlson]

For MHD stability, the field strength must increase moving away from the plasma

But it does, doesn't it? Moving away from the plasma means moving towards the coils.

Probably. But if so, then the surface of the plasma is concave. It's not close to spherical, but is a weird shape with spines in some places and scoops taken out of others.

[TallDave]

For MHD stability, the field strength must increase moving away from the plasma

But it does, doesn't it? Moving away from the plasma means moving towards the coils.

Probably. But if so, then the surface of the plasma is concave. It's not close to spherical, but is a weird shape with spines in some places and scoops taken out of others.

Hrm. Well, maybe Rick will let us know at some point.

[charliem]

Funny Cusps occur when multiple pairs of fields with opposing directions meet at a common vertex. This field configuration is a patented feature of Polywell systems. A funny cusp is generated when two or more conducters with current in opposite directions meet at the vertex and the receed. The current flow must be "in out in out, etc. around the pattern of conductors. The problem here is that there is metal conductor at the vertex where the field is null, so the metal is in the excape path of the electrons. This forms a significant loss path.

"fields with opposing directions"? They'd tend to cancel, shouldn't it be "not opposing directions"?, or just "where two fields meet"?.

Beyond that, what I understand of this definition is that a funny cusp is generated whenever two (initially parallel?) conductors, carrying current in opposite directions start to diverge, that is, when the (initial) line cusp widens.

Is that so? Doesn't anyone have other definition?

Maybe we should search for a diferent term, because intuitively "funny cusp" seems to refer to any non simple geometry cusp. How about "wedge cusp"?

And another proposal. To evade confusion I propose also to name the corner cusps: what about "tristar cusps" (for cubes or dodecahedrons, "star cups" for others).

[Art Carlson]

But it does, doesn't it? Moving away from the plasma means moving towards the coils.

Probably. But if so, then the surface of the plasma is concave. It's not close to spherical, but is a weird shape with spines in some places and scoops taken out of others.

Hrm. Well, maybe Rick will let us know at some point.

Whatever he tells us, I hope it doesn't violate Maxwell's equations.

[Betruger]

Kiteman its awesome you've tackled this, the faq so needed to be done. One thing I might mention beyond the technical discussion, is how well can the layperson grasp some of this. When I describe Polywell cusps to someone (I hope this has been correct /sheepish grin), it goes like this:

I hold up 2 fingers in a ring, and point to the middle, thats one kind of cusp, then there is the "3" finger Pinch", 8 of them at the 8 corners of the cube, then finally there is the "2 Finger Flat Pinch", should be 12.

And does an occasional graphically illustrative turn of phrase belong in a/this FAQ.

Couldn't you either use a simple java animation like this one, or capture it to a video file?

[TallDave]

Probably. But if so, then the surface of the plasma is concave. It's not close to spherical, but is a weird shape with spines in some places and scoops taken out of others.

Hrm. Well, maybe Rick will let us know at some point.

Whatever he tells us, I hope it doesn't violate Maxwell's equations.

I bet it violates local quasineutrality, though.

[MSimon]

I bet it violates local quasineutrality, though.

Isn't that how vacuum tubes work. ;-)

[KitemanSA]

Beyond that, what I understand of this definition is that a funny cusp is generated whenever two (initially parallel?) conductors, carrying current in opposite directions start to diverge, that is, when the (initial) line cusp widens.

Is that so? Doesn't anyone have other definition?

No. What you are describing is the line like cusp that replaces the funny cusp in the WB6 and WB7 machines.

Picture an infinity sign where the cross-over is with straight lines crossing at right angles to each other. Place a clockwise current in BOTH loops. What you get in the middle is a funny cusp. You will have North in fields in the loops and North out fields on either side of the loops, two pairs of opposing fields meeting at one point. They go in-out-in-out around the cross-over. Funny cusp.

[icarus]

Art said:

Let z be the direction of the field on the surface of the plasma, and y the normal to the surface pointing away from the plasma. The x component of the curl is d(B_y)/dz-d(B_z)/dy, so d(B_y)/dz=d(B_z)/dy. For MHD stability, the field strength must increase moving away from the plasma, i.e. d(B_z)/dy>0. This implies d(B_y)/dz>0 as well. This part is a little tricky - a sketch might help - but this last condition implies that the center of curvature is on the vacuum side.

Using the same logic from the other end, you can also show that a spherical plasma will be MHD unstable.

Art, this is not exactly so but only mostly, it's a rule of thumb of vectors you are using, in actuality MHD stability in general has to do with gradients and curvatures of the surfaces of scalar magnetic field strength, not just curvature of vector field lines. We covered it already a bit back here,

viewtopic.php?t=650&postdays=0&postorder=asc&start=15

I'm glad you are thinking about this because it has had me baffled for some time, i.e., how spherical is the wiffle-ball and what are the implications for containment, stability and convergence??

As the wiffle-ball pushes back it bunches up the field lines between it and the coils (i.e. higher scalar field strengths). It is hard to visualise but an area of increasing field strength is not necessarily rigidly concave or convex ....

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



or this??

[KitemanSA]

The second, IMHO.

[icarus]

The second result above includes no calculation for the additional pressure forces due to the electrostatic attraction between the electron layer on the plasma surface and the MaGrid.

How much of a contribution does this electrostatic attraction make? Interestingly, it will be largest exactly where the MaGrid magnetic field is pushing back hardest, due to conformal MaGrid cans, orthogonality of conjugate harmonic B and E fields and etc.