non-uniformly charged magrid?

[happyjack27]

i think part of the problem w/the funny cusps is it's at a region where the coils are very close and the coils have a positive charge so they love electrons.

is it possible to just put a negative (or at least neutral) charge on the magrid where the coils approach?

i suppose maybe then the particles would turn towards the positively charged part, and then the cross of that with the magnetic field would cause the lorentz force to pull them closer or push them further from the coil, depending on whether they're traveling clockwise or counter-clockwise. and that's probably something you want to avoid. but maybe magnetic mirroring will save you?

anyways, just an idea. has anyone tried this? are there reasons not to do it?

[TallDave]

Bussard tried negative repeller plates at the cusps, but he found it generated massive ion leakage. I suspect any similar scheme will suffer the same fate. Ions are a few orders of magnitude heavier than electrons for D-D and commensurately harder for the B field to confine, and it's even worse for more exotic fuels...

[happyjack27]

what if they were just neutral?

[KitemanSA]

what if they were just neutral?

Per Gauss' law they ARE neutral (or effectively so), until the electron LEAVES the cusp. No?

[happyjack27]

what if they were just neutral?

Per Gauss' law they ARE neutral (or effectively so), until the electron LEAVES the cusp. No?

if it were a hollow sphere... but it's not. from the ephi models and my sims it's clear that that fact becomes important, especially as you get closer to the grid.

[hanelyp]

Given conductive magrid shells I wouldn't expect a uniform charge distribution on the magrid, but a uniform voltage. Positive charge will try to spread itself out as much as it can, away from areas where individual coils approach each other.

[D Tibbets]

Most of the above points seem somewhat reasonable. I have asked how far away you have to deviate from a perfect hollow sphere before Gauss's law starts to break down a significant amount. The answer is ... Umm ...
A grid, even with large holes and even some asymmetry will still perform well for direct current. As the frequency increases these discrepancies become more relevant. That is why FM radio will penetrate a Faraday cage that completely blocks a low frequency radio signal. I don't know how an electron current that is oscillating at several million Htz in the system would compare. Also, if there is no synchronization (waves) in the electron current the net current would be steady. Keep in mind that the magnetic fields and the voltage potential on opposite sides of the cusps are balanced. The electron will be closer to a magnet surface at the 'funny' cusp, but it is also in a region where the opposing magnetic fields are the greatest. The greater electrostatic attraction is balanced by greater resistance from the magnetic field (gyroradius will be smaller) I suspect the net effect is neutral. It would be possible to place the positive potential only in selected areas, but with recirculation, if the charge is only on the corners , and electron that exits just to the side of one funny cusp, will be pulled towards the closer corner, so it would not travel directly towards the center but on a more tangential direction.

As for induction pushing the charge away from the closest surfaces, I had not considered it, but so long as the voltage did not droop in those areas I don't think it would matter. If there was a small amount of voltage droop, it would compete against / compensate for the effects of the closer surfaces at the 'funny' cusps. Again, I suspect the net effect would be neutral so long as all of the magnets were of the same shape. If you have square coils next to round coils, etc. there may be some imbalance (?)

D. Tibbets

[icarus]

hanleyp:

Given conductive magrid shells I wouldn't expect a uniform charge distribution on the magrid, but a uniform voltage. Positive charge will try to spread itself out as much as it can, away from areas where individual coils approach each other.

Good point. So a full solution would have to solve for the charge distribution on the MaGrid as well as the magnetic field due to plasma 'wiffleball'.

I suppose that whatever shape the MaGrid, the internal charge distribution on the cans would tend to approximate that of the inside of a hollow sphere as best it could ...? or?

[93143]

So a full solution would have to solve for the charge distribution on the MaGrid as well as the magnetic field due to plasma 'wiffleball'.

If you want to account for current transients and induction in the shell, yes. Otherwise a constant-potential Dirichlet boundary condition should be fine; you can then simply calculate the charge distribution based on what the local electric field is doing.

[KitemanSA]

what if they were just neutral?

Per Gauss' law they ARE neutral (or effectively so), until the electron LEAVES the cusp. No?

if it were a hollow sphere... but it's not. from the ephi models and my sims it's clear that that fact becomes important, especially as you get closer to the grid.

Hmmm, ok to a point, but I THINK it actually applies to a hollow convex polyhedron where the charges are free to distribute themselves. And plane-wise it applies to any convex polygon where ditto; no?
For some reason I was thinking X-Cusp design which sort of fits that description. Knee jerk reaction to others' adverse comment to the X-Cusp design.

[happyjack27]

Hmmm, ok to a point, but I THINK it actually applies to a hollow convex polyhedron where the charges are free to distribute themselves. And plane-wise it applies to any convex polygon where ditto; no?

yes i see your point about charges free to distribute themselves. but with enough free charges flying around to fill up divergences, ANY configuration is going to become quasi-neutral at near the speed of light. after all, that's how electric circuits work. (electrons flow to try to reduce voltage potentials) but,

a) that's in the absence of a magnetic field. we have a magnetic field here that's making the charge distribution (static efield + dynamic efield) non-uniform.
b) we're talking about the static efield only (i.e. produces by the coils only), particular so we can understand how the dynamic efield moves to fill up any voltage discrepancies.

and while the static efield approximates that of a hollow sphere while you're near the center, the closer you get to a wire, the more its field approximates that of, well, a wire.

[KitemanSA]

If you shoot an electron (or release it even) toward a loop of wire with a positive static charge, it looks to the elctron like a point charge at the center of the loop until the electron gets into the region of the plane of the wire and then the charge effectively disappears, doesn't it?

[happyjack27]

If you shoot an electron (or release it even) toward a loop of wire with a positive static charge, it looks to the elctron like a point charge at the center of the loop until the electron gets into the region of the plane of the wire and then the charge effectively disappears, doesn't it?

that sounds about right. if you're shooting a charged particle directly through the center of a charged loop...

[D Tibbets]

The charge is equal in every direction inside the sphere, or grid. As a charged particle gets closer to a wire or point charge on a hollow sphere. it experiences a greater attraction to that point. But, as this is happening the particle is passing increasing areas of the sphere/ wires- these surfaces are in the rear view mirror. They are increasingly further away, but there are a lot more of them. These competing forces exactly cancel out. That is why Gauss's law applies. I have asked how how much distortion and porosity of the shell/ wire grid can have before this starts to break down. My impression was that it can be a lot so long as the system is low frequency.

So, it doesn't matter whether the internal charged particle is approaching the center of a loop, or more towards an edge of the loop. The particle experiences attractive and repulsive forces that completly cancel out. This persists until the particle passes the mid line of the closest external wire (or hits it). Then the process becomes unbalanced and the particle 'sees' the charge on the grid.

So long as the grids are connected to each other this is unavoidable. With separate grids (like WB8) each with its' own power feed and no physical connection between the grids (within the vacuum chamber) this may not hold if there is some variation in the supplied voltage. This might be a knob that needs to be carefully controlled (merely connecting the leads outside of the chamber would probably do it), or perhaps manipulated for some purpose.

Dan Tibbets

[KitemanSA]

With separate grids (like WB8) each with its' own power feed and no physical connection between the grids (within the vacuum chamber) ...

What information do you have that indicates that WB8 has no physical connections between coils?