Talk-Polywell.org

The electrons that escape through cusps recirculate along field lines because they're attracted to the positively charged MaGrid, right?

Dave, I think the electrons move along filed lines because that's what electrons do ... they follow the path of lowest energy depending on the sum of the forces acting on them at the time. The positive charge on the MaGrid helps. But electrons will move in a magnetic field regardless of this positive charge.

Regards,
Tony Barry

Sure, that makes sense on the inside, where they're confined. But on the outside, wouldn't they just fly off along their merry way without the Magrid pulling them back?

The magnetic field operates on the outside as well as the inside of the donuts. On the inside it is squashed near to the donut surfaces due to the magnetic fields from the other donuts of the MaGrid. On the outside it is expanded somewhat compared to the inside, but it is still there, and the electrons travel through the centre of the donut ring, into the fusion region a bit, then out through the cusp lines / points, out into the chamber, then round and back to the centre of the donut ... recirculating. The magnetic field provides the electrons with this "track" to travel on.

The more complex and complete answer is that the electron path is actually some kind of a spiral, where it follows this simple path but spirals around and along this path. In addition, there are other forces acting on the electrons (such as the charge on the MaGrid) which will distort the simple line further.

Regards,
Tony Barry

The electrons won't just fly off ... the emitters and walls are at about the same potential, and the magrid is positively charged to 10 kV or more. They're strongly attracted to it, and want nothing to do with the walls. They keep moving because of the high kinetic energy imparted by the grid (they'll slow as they leave the vicinity of the grid and approach the walls, but accelerate again as they are drawn back to the magrid).

I think the electrons will fly off. One can only contain the number of electrons that it would take to neutralize the positive charge on the magrid. These will tend to be in a layer of one debye length thick close to the grid. See http://en.wikipedia.org/wiki/Debye_length
Along the axis of the donuts there will be no field, and the electrons will be confined for about one collision time like a mirror machine.

So what causes the electrons to return to the well (and stay there)?

Tom Ligon wrote:The electrons won't just fly off ... the emitters and walls are at about the same potential, and the magrid is positively charged to 10 kV or more. They're strongly attracted to it, and want nothing to do with the walls. They keep moving because of the high kinetic energy imparted by the grid (they'll slow as they leave the vicinity of the grid and approach the walls, but accelerate again as they are drawn back to the magrid).

OK, thanks Tom. I was pretty sure that was the case, but I was updating the Polywell wiki and Art Carlson was saying if they recirculated then the magnetic field had to be concave to pull them back in. I was fairly certain it was the Magrid, not a concave magnetic field, that was pulling them, but thought I'd run it by the crew.

pstudier wrote:I think the electrons will fly off. One can only contain the number of electrons that it would take to neutralize the positive charge on the magrid.

I assume you mean "contain" for recirculation purposes, as the magnetic containment depends on the B field. Presumably we get some help from the fact the grid is further out than the contained electrons (because of the B field).

These will tend to be in a layer of one debye length thick close to the grid.

That's how I always pictured it.

zretawt wrote:So what causes the electrons to return to the well (and stay there)?

In theory, I think, they accelerate back inside while trying to get to the Magrid and then have to find another tiny cusp to get out again, which takes a while.

If there were no collisions, the electrons would be trapped on fixed field lines.
The field lines on cusps and faces are compressed, so the electrons have to eventually wrap back around the coil (assuming you have the walls far enough away - see pictures of WB6).

If an electron were exactly on a cusp line, it would not feel any magnetic force and it could fly straight out. But it is attracted to the MaGrid, so it would bounce between center and wall.

But there are collisions, so some electrons will pick up more than enough energy to fly off the cusp line into a wall. But the probability of being exactly on a cusp line is really tiny. Most electrons are going to be trapped on the field lines, at least for beta < 1.

I'm kind of worried about beta >= 1 though. At that point the plasma can over power the MaGrid field and just blow itself out the wiffle ball. Electrostatics play a role in that too though, and I just don't know how the system will be have. The experimental data is critical to understand this.

The way I see it is:
The field lines are closed so any electron orbiting a field line will eventually follow it back into the center of the device. (barring collisional diffusion, walls etc.)

i.e. If it follows a field line out through a coil it will come back in through an adjacent cusp.
If you look at it in the plane of the closed field line it is following this motion also sort-of orbits in the attractive E field of the magrid.
So both effects force the electrons into these orbits.

Question:
It appears that the field lines through a coil or cusp have a much "blunter" funnel on the inside and a "thinner" funnel on the outside.
i.e. a gentle ramp from the outside and a steep ramp from the inside.
Does this make it easier for the electrons to transit from out to in than from in to out?
Would this work like a check valve?
Or does conservation of energy say that the "hill" is the same height from either side so the flow each way is the same?

Of course this only applies to electrons that have enough energy to get past the maximum field at the center of the coil.

So if the hole through the coil requires a lower energy (say) to get through and the gap at the cusp between the coils requires a higher energy to get through does that leave a population of electrons (between those 2 energies) stranded outside?
No, I think they reflect off of the high field (from the outside) and follow the line back in through the same coil they came out.

Is this reflection called "whistler mode"?

drmike,

That got me to thinking. I wonder if a suitably spaced set of coils outside the reactor coils and at ground potential with a suitable magnet direction might not enhance electron recirc in a smaller volume than required to "keep the field lines away from the walls".

Of course getting all that stuff in a vacuum chamber plus deceleration grids would be a real trick.

OTOH it may be that such coils could work outside the reactor vessel.

Simon

Helpful ilustration, courtesy Tom:

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

Am I crazy, or is the field convex (or at worst, flat) to the electrons the whole way around? Art keeps talking about "concave regions" but I don't see any.

TallDave wrote:Helpful ilustration, courtesy Tom:

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

Am I crazy, or is the field convex (or at worst, flat) to the electrons the whole way around? Art keeps talking about "concave regions" but I don't see any.

I think Indrek's simulations of field lines shows the convex nature better.