Electron interactions with the magnetic field

[D Tibbets]

Since things have been slow I'll take this opportunity to ask for feedback, expansion on my understanding of charged particle- magnetic field interactions. Much of my understanding of the effects are represented by this You-tube video of a declassified nuclear test. Most of the pertinent information is between 3-10 minutes into the video.
http://www.youtube.com/watch?v=YZu7et1dZlA

I've made various arguments in several threads about the electrons recirculating through the edge cusps/line cusps. I've received little feedback, perhaps because the audience was to busy laughing, I've commented that the electrons are most likely to slow and reverse (bounce) at the areas where the magnetic field lines are curving most (true in a bar magnet where the field lines curve more And become more dense) This is probably misleading. Actually, I believe it would be better to say they are more likely to bounce where the magnetic field strength in increasing- more dense 'field lines'. In the Polywell, with the ring magnets, field strength seems to be greatest in the region between the magnets where the opposing fields are compressed. Also, compression of the fields due to the 'Wiffle Ball ' effect would be greatest on the inside of the magnets, as opposed to the outside.
If an electron has enough kinetic energy/speed to pass this area of greatest field strength I've assumed that the it would speed up until such time as they approached a similar field strength. Is this true? If this is the case, I would not expect the electron that had enough speed to avoid bouncing at this greatest field strength area to bounce back towards the same area, but instead continue in an effective orbit till it had reentered the magrid interior through another 'weaker cusp', such as the center/ point cusps (weaker in the since that the magnetic field lines are not compressed together as much). Assuming the electron does not interact with other particles or the vacuum vessel wall. I could see an electron recirculating back through the edge cusp if it drifts- outward path is near where magnets are closest together with most compressed magnetic fields and inward through the corners where the magnets are furthest apart with less compressed magnetic fields. But, again , if the electron didn't bounce on its way out I don't see were it could bounce anywhere else, unless it lost energy due to interaction with other particles.

If the internal electrons are a little short on speed so that they bounce before reaching the critical area between the closest approach of adjacent magnets, could they drift (move sideways) until they are closer to the corners between magnets where there is more space and therefore weaker fields (less dense field lines) where they are less likely to bounce and manage to escape confinement. Is this the reasoning behind the efficiency gains of having more magnets- so that this area ratio between magnet corners verses edges is less. Is this why I have seen some proposals to use magnets with a square shape as opposed to round (still round in cross section)?


Second argument about electron behavior in the Polywell- Again, using the video as my starting point. As the electrons travel from the center towards the magrids they penetrate the magnetic fields until their outward motion is translated into lateral motion. They would then travel on the same field line, bouncing back and forth indefinitely, unless they were initially aimed precisely at a cusp or they had enough speed to avoid bouncing. In an isolated system I assume the electrons would therefore collect into a shell inside of the magrid, but away from the center. Any subsequent departure from this shell would only occur through up scattering or down scattering. Is this picture reasonable? Or is the interaction of the electrons more like billiards- the electrons are stoped and diverted sideways by the magnetic field, but when they bounce, at least some are slung back towards the center in a nearly opposite direction from the original. Or, is the positive potential on the magrid ( which in WB6 at least, was near the electron gun injection energy (?)) enough to pull the electrons deeper into the magnetic field so that they rebound back towards the center as described above? I'm struggling to define my thoughts, so let me state it another way. As the electron travels into the strengthening magnetic field it's forward motion is converted into lateral motion. Without the positive potential the electron would then bounce back and forth on the same field line. But, with the pos potential drawing the electron deeper into the field, the electron would build up more potential energy, so that when it bounced it would have a greater speed and escape the field line and travel back towards the center. Of course as the electron is leaving it is also pulling away from the positive grid. Would the effects cancel out or would the electron still travel back towards the center at a reduced speed or angle?
If this sounds confusing, then you appreciate my level of understanding of the system. And, my brain hurts to much to start to consider what the positive ions, virtual anode, etc do to the interactions. The lack of a good understanding of the vocabulary and religious avoidance of mathematical formulas do not help either.


Dan Tibbets

[drmike]

Howdy Dan,

Think of the electrons in the magnetic field as balls on a string. As you swing a ball around in a circle and change the length of the rope, the ball will move slower or faster. The magnetic field is the string to the electron being the ball. The number of field lines inside the electrons radius has to stay constant for a single electron - so its energy is constant. as the field lines compress (you get close to the magnet) the electron radius shrinks. It spins faster - so more energy goes into lateral motion. At some point it has no more energy to go forward and it bounces back.

But it has to have the same number of field lines in it's circle at all times. So as it moves towards the center of the polywell, it will have to go towards the magnet as part of it's orbit. So a single electron will follow the field lines.

Life gets way more complicated when the density of particles gets higher because things are no longer constant due to collisions. Electrons get bounced off of their circular orbits around field lines and the nice simple picture doesn't work anymore.

The math is non-linear, so no words can describe it as simply as the math. But computing the math is really hard - not too many people have access to the kind of compute power it takes to really understand this kind of problem. Don't worry too much about not quite understanding it. Nobody else does either!!!

[TallDave]

Also, compression of the fields due to the 'Wiffle Ball ' effect would be greatest on the inside of the magnets, as opposed to the outside.

Much greater inside. Bussard was looking at a 1000:1 or better ratio of electron density inside versus out.

this the reasoning behind the efficiency gains of having more magnets- so that this area ratio between magnet corners verses edges is less. Is this why I have seen some proposals to use magnets with a square shape as opposed to round (still round in cross section)?

I could be wrong, but my understanding was Bussard's "3-5 times better" performance with a truncated dodec vs. truncube was based on reducing the "funny" corner cusp losses by making the angle the magnets' corners meet at less acute, yielding a magnetic field geometry less friendly to escaping electrons.

The only small scale machine work remaining, which can
yet give further improvements in performance, is test of one
or two WB-6-scale devices but with “square“ or polygonal
coils aligned approximately (but slightly offset on the main
faces) along the edges of the vertices of the polyhedron. If
this is built around a truncated dodecahedron, near-optimum
performance is expected; about 3-5 times better than WB-6.

And also

This will also
incorporate another feature found useful, that is to go to a
higher order polyhedron, in order to retain good Child-
Langmuir extraction by the machine itself (which is more
straightforward than relying on stand-alone e-guns for the
cusp-axis, very-high-B-field environment), while not giving
excessive electrostatic droop in the well edges. These small
scale tests are discussed further, below.

[D Tibbets]

Thanks for the replies. A video that shows well what I was trying to describe is at :
http://www.youtube.com/watch?v=hHrKLlvk ... re=related
It shows a single electron in a Polywell. I guess this would represent the simplist situation, befor multiple electrons and ions start mixing up the picture.
What I haven't seen is an argument (that I might be able to follow) why orbiting/ recirculation through another cusp isn't possible- such as that shown in the video link below (assuming it is acurate).
http://www.youtube.com/watch?v=jmp1cg3- ... re=related

Dan Tibbets

[Art Carlson]

What I haven't seen is an argument (that I might be able to follow) why orbiting/ recirculation through another cusp isn't possible- such as that shown in the video link below (assuming it is accurate).

Then listen carefully. You can do this.

Fields lines passing closer to one coil than another will loop around the closer coil. Fields lines passing closer to the other coil will loop around that coil. The field line that passes directly between two coils goes directly to the wall.

Field lines passing close to a coil make a small loop. Field lines passing nearly but not quite exactly between two coils make a big loop. The field lines passing closest to the line between two coils will make loops so big that they intersect the wall.

Particles lost through a cusp are expected to be on loops that are so big that they will intersect the wall before returning to another cusp. This is good. You do not want to solve this problem by letting electrons also escape on field lines that make small loops. The hole is big enough already.

[Mike Holmes]

So, the larger the chamber, the higher the proportion of lines that are short enough to come back without hitting the wall. Yes?

Mike

[Art Carlson]

So, the larger the chamber, the higher the proportion of lines that are short enough to come back without hitting the wall. Yes?Mike

Correct. But the fact that you ask this question makes me fear that you did not read the last paragraph.

Particles lost through a cusp are expected to be on loops that are so big that they will intersect the wall before returning to another cusp. This is good. You do not want to solve this problem by letting electrons also escape on field lines that make small loops. The hole is big enough already.

I'm not sure what our best numbers are, but simply making the chamber bigger is not a practical way to solve the problem.

[Mike Holmes]

I read it, I just don't understand the implication. Are the cusps so tight right now that the chamber would have to be kilometers across or something to achieve some significant higher rate of return? If we don't know the numbers, then isn't it possible that a slight increase in size may have substantial benefits?

My apollogies if my misunderstanding is because I'm wading into waters that are over my head. Feel free to tell me so, if that's the case. I'm really just hoping that somebody else who understands better than I will pick up on something here.

Mike

[MSimon]

Mike,

You are only considering the magnetic field. There is an electrostatic field as well.

The electron losses are less than pure magnetic confinement because the electrons that have less than the energy that would be imparted from the wall to the grid voltage will oscillate.

I have never liked the term recirculate for the BFR because it gets people thinking the wrong way about how I think the machine operates.

[Torulf2]

The WB7 looks tight compared to the box. It may have this problem.

[alexjrgreen]

My apollogies if my misunderstanding is because I'm wading into waters that are over my head. Feel free to tell me so, if that's the case. I'm really just hoping that somebody else who understands better than I will pick up on something here.

When I was at college, we used vacuum tubes with patches of phosphor paint to make the electron paths visible...

Surely someone with a lab can cross wire six Helmholtz coils round a vacuum tube and set up a basic electron well?

There won't be any recirculation, but it has to be better than everyone saying they don't know...

[Solo]

MSimon: is there any way we could make a sticky at the top of the "theory" forum to house links to relevant documents, or possibly citations of documents that are not available electronically?

DW: that's what you woul think. Apparently, nobody actually tried Bussard's exact idea, and we don't know enough to bridge the gap from what they did try in order to understand this.

See what you all can make out of this:

http://mr-fusion.hellblazer.com/pdfs/ma ... nement.pdf

[MSimon]

My apollogies if my misunderstanding is because I'm wading into waters that are over my head. Feel free to tell me so, if that's the case. I'm really just hoping that somebody else who understands better than I will pick up on something here.

When I was at college, we used vacuum tubes with patches of phosphor paint to make the electron paths visible...

Surely someone with a lab can cross wire six Helmholtz coils round a vacuum tube and set up a basic electron well?

There won't be any recirculation, but it has to be better than everyone saying they don't know...

I was playing with one of those in high school in '62. Neat stuff. In the case of a six coil job you would have to make the vacuum tube movable.

We can do just as good a job these days with magnetic field measuring eqpt. Or for that matter in a static situation with field simulators.

Once you get a lot of plasma and electron guns etc. things get complicated.

[Mike Holmes]

One of the undergrads at the University of Wisconsin IEC fusion program should pick up on this as an experiment to run. http://iec.neep.wisc.edu/

Makes me want to go back to school and try stuff like this myself.

Mike