magrid configuration brainstorming

[Roger]

What I interpreted from Bussard's papers (so I could be way off base) was that the wiffle-ball effect pushed the grid field up against the coils and closed off the cusps. In effect, it adds to the field of the grid and decreases the loss cone angle. So how could you do that?

Back the NASA forums, when I was considering making the IEC Fusion for Dummies video, I think Tom Ligon was saying that the electrons in the center pushed at the fields, while the fields pushed back at the electrons. Based on Toms comments, I made the video show this squeeze of the cusps. IIRC the Squeeze makes the cusps just slightly larger than the electron gyro radii.

I'd guess this is all linked to recirculation as well as annealing, and who know what else.

And that video continues to get hits, even though I haven't dropped a link for it in nearly 2 months. 7300 views.

http://www.youtube.com/watch?v=jmp1cg3-WDY

[TallDave]

Ditto what Roger said. Video is great too.

Picture the magetic fields as a bunch of rubber balloons enclosing air pressure in a space between them. The increase in pressure flattens out the sides facing the center and pushes them against each other, shrinking the spaces through which air can escape.

[drmike]

Nice job Roger! That's a great introduction to anyone with no background in magnetics (which is most people!)

[Roger]

Ditto what Roger said. Video is great too.

Picture the magetic fields as a bunch of rubber balloons enclosing air pressure in a space between them. The increase in pressure flattens out the sides facing the center and pushes them against each other, shrinking the spaces through which air can escape.

Thanks. Dave thats a great picture you just described, the balloons...

no background in magnetics (which is most people!)

Thats me, but with Tom's help I got the basics together.

[drmike]

I put up my notes on triangle coils in a pdf format for easier reading. I will try to get some code to create the fields and some pictures this week. Hopefully we can find better ways to get the data into a visual format.

[hanelyp]

As for electron motion, it may be helpful to consider an electron moving radially from the center and encountering the magnetic field. This electron will be turned anti-parallel to the current in the coil, reinforcing the magnetic field between it and the coil, canceling the field in the center. In effect pushing against the magnetic field.

Regarding mirror vs. cusp losses: Mirror losses are related to the ratio between max and min field. With a near zero interior magnetic field, mirror losses may be expected to become negligible. At this point cusp loss mechanisms become important.

[jmc]

Tombo:

The key thing about a cusp is that it is a region of very low field surrounded by high fields and is created where the fields of two or more magnets cancel each other out and the difference between cusp and mirror confinement is that the gyro-radius of the ions in a cusp confined regime are similar to the scalelength of the gradients and the size of the device, hence when they bounce from on side to another, they forget their adiabatic moments, mu. In mirror confinement they don't.

The result of this is that in mirror confiinement there is an effective loss cone in velocity space, while in cusp confinement the cusp present a loss area in actual space. You can visualize anything bouncing off the cusp confined region as getting lost.

The best way (simpler than trying to imagine all the induced currents in the plasma) to visuallize a wiffleball is to consider what would happen if you place a ballon coated with a superconductor in the centre of the cusp region and then inflated it, it would push back the field. A hot plasma has an exceedingly low restance (hundreds of times ) lower that copper so it acts remarkably similarly to an inflatable super conductor (although if the gas is ionized inside a field there is no phase transistion where the field is expelled unlike in a superconducter) increasing the pressure of the plasma is akin to inflating the balloon, in the region where the field is expelled the ratio of the fiel inside to the field outside is increased because the diamagnetic effects of the plasma reduce the field inside, this the mirror ratio is steadily increased, increasing confinement until you get cusp confinement.

With regards to your designs you should be aware that as you increase the number of faces you will also increase the area the cusps present to the electrons, if they are recirculated this will not result in electron loss except for those that are upscattered in velocity.

There is a complication however, since charge flowing along the fieldline meets virtually no restistance the fieldlines themselves can be regarded as perfect conductors. Since there is no flow of current along the fieldlines everywhere in the fieldline is at the same potential, this means that the ions are not perfectly electrostatically confined inside the Polywell and there will be "potential holes" at the cusps which it will be possible for them to escape from, this could represent a significant (overwhelming?) power loss and so the area of the cusps and their number should be limited.

The only reason to make the polywell spherical is to obtain convergence, this amplifies the fusion power by four times the convergence ratio, without increasing cusp losses for a given machine. There is reason to believe it will be very challenging to get convergence (though since the truncated cube has been investigated at the expense of neglecting other geometries it cannot be ruled out). If convergence cannot be achieved then there is no point in increasing the number of cusps to make the machine more spherical.

Annealing is another advanced physics idea that will not be obtainanble without good convergence. There is some controversy as to whether it can be made to work in practice, maybe its simply a matter of refining the experiment and conducting it with razor precision on a higher budget.

In anycase in theory if you can give birth to a bunch of ions all at the same potential in a perfectly spherical well, then they will speed up as they reach the core and when they collide with ions of the opposite velocity in the core, while any full head-on collission will massively perturb their velocity because they are moving so fast the cross-section for collission there is far lower then at the edge as a result most collissions are only glancing perturbations. After every pass through the core they get back to the edge. Because the relative velocity between the ions at the edge is lower they collide more frequently they also spend more time in the edge (cough,cough at low densities and large debye lengths) so the number of collission they make in the edge at each pass is larger. This causes their velocities to smooth out and allows them to retain their mono-energetic qualities when they return to the core.

Lets say at the edge of a 100keV Polywell all the ions are born at the same potential, with an energy spread of 10eV then a collision in the core displaces an ions energy by 30eV on one pass, when it reaches the edge again it will now be moving 30eV faster then all the other ions in the edge and will get slowed down by them back to 10eV, so its velocity is “reset” by the collisions in the edge to be beamlike again on its next approach into the core.

That’s the theory anyhow, I’m not sure whether or not it works in practice.

[tonybarry]

Hello jmc,
Thank you for this most enlightening discussion. Much appreciated.

Regards,
Tony Barry

[Solo]

Yes indeed, that's very helpful! Thank you. Now I realize I didn't understand what a cusp was. (I'm still not quite understanding it either!)

The result of this is that in mirror confiinement there is an effective loss cone in velocity space, while in cusp confinement the cusp present a loss area in actual space.

Ahh, now I understand Dr. Bussard's talk of a marble inside a wiffle-ball!

the mirror ratio is steadily increased, increasing confinement until you get cusp confinement.

I assume you mean what hanleyp said, that the mirror loss becomes negligible next to the cusp loss, and not that the mirrors become cusps due to the diamagnetic field produced by the plasma.

[drmike]

The difference between "mirror" and "cusp" is kind of minimal to me. But I guess one way to think of it is the difference between self inductance (mirror) and mutual inductance (cusp). As particles orbit around flux lines they may group one magnet coil (as in a face of a wiffle ball) or they might group several (as in a corner). Collisions in a corner will definitely cause more interesting orbits.

[jmc]

Well imagine a bubble of zero field surounded by magnetic fieldlines which for the most part lie along the surface of the bubble but just at the cusps point directly away from it, if a random electron comes to the edge of the zero field bubble into the field region, then in the absence of collision, with the exception of the cusp region the fielines laid along the edges of the zero field bubble will cause the electron to turn have a gyroradius and thus reflecting it back into the bubble.

If the electrons hit the edge of the zero field bubble in a region where the fieldlines point directly away from the bubble then it will get caught in the field and engage in a spiraling trajectory away from the bubble along the cusps. If you now think of electrons as hula hoops of one gyroradius which if they catch a cusp line get lost but otherwise get reflected, then you can see from this overly simplistic picture why the cusp loss area is intimitely linked to the electron gyroradius.

In the case of the mirror regime the electrons spiral around in regions of weak field bouncing between regions of strong field forever in the absence of collissions. In a cusp machine they will be lost even in the absence of collissions, as every bounce against the field counts as a collision even though it is with the field rather than other particles. This is because in the cusp regime particles forget all their adiabatic constants.

[tombo]

6. This requirement has two main consequences: (a) All
coil containers/casings must be of a shape conformal to the
B fields produced by their internal current conductors,

This means the corners of the triangles could be tricky.
The solution for the B field may not yield a circular curve at the corner.
That would be considerably harder to fabricate.

[tombo]

Thank you drmike
I can’t do those numbers.
I dug out my old Krall & Trivelpiece and worked on it for a few days.
I’m getting more now but it was painfully slow, line by line equation by equation.
Their math is still as intimidating as ever.
It is interesting to see how short a distance we’ve come since the 70’s.
That lack of funding and misguided large projects is part of why I bailed out way back then.
This size & type of system is what I imagined when I signed up for the program.
In fact that very picture of the cusp machine led me to propose something very close to the 6 sided polywell.
But my prof said “it looks like you are trying to build a magnetic monopole” and dismissed it and that was that. I went on with my life.
I’m sure others on this site had the same experience.
I am overjoyed that someone with more resources (both between the ears and in the wallet) took it up and followed it.

[tombo]

Hanylep,
Wouldn’t the currents induced in the plasma buck the currents in the coil?
I got this both from lenz’s law and from right hand rule.
A clockwise coil (positive) current looking into the device would produce a counterclockwise gyration in each positive ion and a clockwise gyration in each electron which would point against the original field.

If you look at a plane (say the size of the coil) of electrons gyrating the same way, all the inner currents cancel out and only the outer current counts but it is in the same direction as each of the electron gyrations so it still works out.

The induced currents would push the arches out by weakening the B field near the plasma.
There would still have to be the same flux between the plasma and the coil but it would be compressed closer to the coil making a higher field gradient and a sharper transition to the zero field in the plasma.

I could easily have my wires crossed.

[tombo]

Thank you jmc
Very enlightening.

But sometimes an answer only brings up more questions.

This is making more sense now.
I’m getting it about the changing gyro radius keeping the electron away from the hole.

Yes I’ve been seeing the balloon analogy.
But, I’m not sure how closely it models reality.

I can see how the induced plasma currents push back and flatten the field radially at the arches (nearest the coil body).
But, I can’t see the mechanism that pushes the field tangentially and closes the holes.
I see the balloon pushing the hole open (wedging it open.)
At low plasma density the balloon would follow a contour line of constant energy with protrusions at the holes.
Indrek has a good picture of this (somewhere).
As it is inflated the protrusions at the holes would grow too.

I can only see it happening:
1. If there is some strong surface-tension-like energy at the surface of the plasma.
And
2. If the field does not actually increase in the vicinity of the holes but the edge of the hole is sharpened by the removal of the field away from the hole.
This does kind of make sense as the field will be reduced more where it is closer to the plasma and less where it is further away (at the hole).
Almost like sharpening a scissor blade.

The loss is in “actual space” because the field lines are straight (not converging) in the area near the coil centerline?
(The tapered field lines along with the parallel and perpendicular velocities are part and parcel of the mirror effect.)

Pardon my ignorance but, what is convergence in this context?
What is converging?

I don’t get it about the adiabatic moment.
But I don’t mean to grill you.

so the number of collisions they make in the edge at each pass is larger. This causes their velocities to smooth out and allows them to retain their mono-energetic qualities when they return to the core.

But wouldn’t lots of collisions make them go all Boltzman on us?