Spherical and hierarchic grids

[blaisepascal]

Consider the analogous 2D case: six equally-spaced magnets, 3 pointing in, 3 pointing out, alternating around the center. If you plot the field lines, there is still no field in the center, and the lines go to the adjacent magnets, not to the opposite side.

True. But draw the little magnetic field circles around the each coil cross-section in your proposed 2D case: the fields cancel in the spaces between the magnets.

That's immaterial to the whole same/opposite direction of opposite coil issue. You get the same null field between adjacent coils in the 4-coil of alternating polarity case, yet opposing coils are both pointing in or out.

What I think happens in the 2D, alternating coil case is that the mag fields are normal to a radial passing between the coils, and tangent to a radial passing through the coils. In 3D, with 4 coils arranged in that pattern (since you can't really talk about EM fields properly in 2 dimensions) you get something similar to a mirror trap (two identical poles facing each other), but open on the top and bottom rather than having a line cusp.

[ankovacs]

Here is a cross-over between my original proposal of 3 spherical rings and hanelyp's 'spherical WB-6'.

It is composed out of 'equatorial arc segments'. There are 6 square-like faces and 8 hexagon-like faces. The last image shows enclosure of whole arrangement in tornado-trap.

Red lines: input currents
Black lines: output currents
Blue lines: polywell grid lines at high potential

When I have time, I will simulate the magnetic fields. I anticipate that this configuration has a good mix of electric and magnetic field properties.

[hanelyp]

Ankovacs, looks like you've taken the the basic octahedron grid, problematic because of field nulls through the intersection points, and split the 4 way intersections into sets of 4 3 way intersections with the grid avoiding the field null points. But in the process I think the field cusps in the new square faces are made into line cusps far leakier than anything in the WB-6 configuration on account of weak magnetic field over those faces.

[KitemanSA]

Hey Folks,

Please remember to check your "messages" box.

[blaisepascal]

Ankovaks,

What do you see the purpose of this octahedral grid design is? Is it to be a replacement for the coils used in the current WB-6/7 design? Is it intended to surround the existing WB-6/7 coils? Go inside?

You've been very clear that part of what you are doing is ensuring that the currents around the 8 faces is oriented into 8 loops, so the magnetic fields are properly oriented. That would suggest that it is a replacement for the coils, not a separate grid structure within the reactor.

As such, I have some questions, based on the original design you gave.

1) The WB-6/7 devices had a coil ID of 201mm, and a working magnetic field strength along the center of the coils of 0.3T (I believe). Assuming your octahedral grid was made to the same scale (internal diameter of 201mm), what is the current needed to get a magnetic field of 0.3T.

1a) If you don't feel that your design would require a field strength of 0.3T to create a whiffleball, what field strength do you think is necessary, what current is needed, and why do you feel 0.3T is not necessary.

2) One edge of each of the eight faces has twice the current of the other two in your design. How does that distort the symmetry of the generated magnetic field?

[ankovacs]

Now I have done magnetic field simulations of the arrangement I have shown in my previous post.

Taking Art Carlson's definition of cusps being places from which field lines go to regions of zero magnetic field strength, here are the lines through cusps:



There are 8 cusps, and they look point cusps to me. (as opposed to hanelyp's prediction of line cusps) In fact there is very little difference in the shape of these field lines in comparison with the case of rings meeting in a point junction.
Here you have some images of magnetic field strength in central planes of various orientations:



Altogether, the fields without plasma effect are pretty much whirling around the horizontal ring of double current strength:

To summarize once again what is the benefit of all this:
- more spherical symmetry of surfaces at high voltage should result in more spherical symmetry of electron plasma and ions -> cusp holes smaller -> plasma density can be increased
- strongly recirculating magnetic fields mean that energetic electrons cannot leave to exterior regions -> plasma density can be increased
- strongly recirculating magnetic fields mean that exterior magnetic trap(s) can be applied around the polywell -> plasma density can be increased

Since increasing plasma density is one key to beating Bremsstrahlung losses, it seems to me that proposed configuration has rather good advantages over WB-6 / WB-7.
I will probably elaborate this further into a journal article.

[Art Carlson]

Since increasing plasma density is one key to beating Bremsstrahlung losses, it seems to me that proposed configuration has rather good advantages over WB-6 / WB-7.

Why do you say this? Both fusion power density and bremsstrahlung power density are proportional to n^2.

[ankovacs]

The Yoshikawa paper claims that inertial confinement fusion rate can be n^3, citing reference [11]. See figure 6:
http://wwwsoc.nii.ac.jp/aesj/division/f ... hikawa.pdf

Of course this is still speculative until that claim is more thoroughly verified.

[Art Carlson]

The Yoshikawa paper claims that inertial confinement fusion rate can be n^3, citing reference [11]. See figure 6:
http://wwwsoc.nii.ac.jp/aesj/division/f ... hikawa.pdf

Of course this is still speculative until that claim is more thoroughly verified.

No it doesn't. It claims (quoting Ohnishi) a fusion rate proportional to the third power of the ion current. Ohnishi clearly attributes this dependency to the spatial and temporal structure of the potential, not simply to density. Neither Yoshikawa nor Ohnishi specifically mentions bremsstrahlung.

[blaisepascal]

Now I have done magnetic field simulations of the arrangement I have shown in my previous post.

There are 8 cusps, and they look point cusps to me. (as opposed to hanelyp's prediction of line cusps) In fact there is very little difference in the shape of these field lines in comparison with the case of rings meeting in a point junction.

From the geometry of the system, I would expect those 8 cusps to be along the vectors (1-epsilon, 1, 1), (1-epsilon, -1, 1), (1-epsilon, 1, -1), (1-epsilon, -1, -1), (-(1-epsilon), 1, 1), etc. I would expect epsilon to be positive but non-zero, because of the doubled currents along the Y-Z plane.

1) What is the approximate magnitude of epsilon?

The "whiffleball" of a polywell device is within the coils producing the magnetic field. The simulations you generated show (some) of the magnetic field lines outside of the octahedral cage.

2) What do the magnetic fields look like within the core of the octahedral cage?

The simulations show the magnetic field lines, but don't show their direction. By the design of the cage, 4 of the cusps should be directed into the core, and 4 should be directed out of the core, with adjacent cusps oriented in opposite directions. As such, of the four loops shown in the simulations, two opposing loops should be coming out of the core in the +X direction and going into the core from the -X direction, while the other two opposing loops should be coming out in the -X direction and going in from the +x direction. The XY and XZ planes are exactly between the sets of loops. By symmetry, again, the magnetic field along those planes should be 0.

3) What do your simulations show the magnetic field in the XY and XZ planes to be?

4) Similarly, what do your simulations and analysis show the magnetic field looks like along the X axis?

Kirchoff's current law says your cage cannot work without the input and output current feeds, which carry the same current as the equatorial conductors of your cage (the ones in the YZ plane of the simulation).

5) How does the magnetic field from these input and output conductors distort the magnetic field produced by the cage?

And unanswered question from last time...

6) What is the current needed in a 205mm-diameter cage to generate 0.3T magnetic fields?

[ankovacs]

Art:
OK, I realize I was looking the wrong way at the issue of beating Bremsstrahlung. For a given mix of ions, according to Bussard calculations, the higher the potential, the better the fusion/brems energy ratio.
The challenge of WB-6/7 design is that plasma density must be decreased as grid potential is raised in order to avoid Paschen arcing. The reason is that energetic electrons lost through cusps - i.e. the ones failing to recirculate - create arcing capability. That is why my proposed design applies an exterior magnetic trap, so that grid potential can be substantially raised without arcing.

IF there is some focusing of ions in the center (does not have to be perfect), the assertion of Onishi is that higher ion current results in fusion rates at density exponent between 2 and 3. The Onishi paper is found here:
http://mr-fusion.hellblazer.com/pdfs/co ... in-iec.pdf
What I have overlooked is that electrons of course will be focused at same rate in the center, meaning that brems losses will have the same exponent. So this issue of exponent determines scaling of power output from reactor if brems losses are outweighed, and it is neutral from gain/loss balancing point of view. Do others agree with this statement?

(Note: While the overall setup that Onishi investigates is not polywell, his calculations on the potential created by focused ions in a proton-electron plasma apply in our case too. He is not talking about a temporary effect of a very special potential design: he is doing time-averaging of fusion rate in a potential field created by ion focusing.
He finds that overall fusion rate is inversely proportional to the focusing radius. For a given focusing radius, he finds that fusion rate depends on ion current through an exponent between 2 and 3 - the more mono-energetic the ions are, the closer is the exponent to 3. And yes, in our wiffle-ball trapping case this ion current is directly related to plasma density.
Unfortunately there is no investigation of how this exponent depends on the focusing radius.
The question is whether there is any ion focusing in the wiffle-ball trapping case. As some arguments pointed out, the focusing is poor, because of the un-even wiffle-ball surface. That I believe is true, but it is also true of the setup that Yoshikawa measured, when each time that the ion passes through the grid, it also gets some lateral kick from the static potential field; ions pass e.g. 20 times before hitting the grid in that setup. Despite this non-perfect focusing, Yoshikawa did measure a double-dip potential, which was predicted in the Onishi paper.
An interesting experiment would be to measure whether a double-dip potential appears in wiffle-ball trapping; if it does, then there is strong reason to believe that fusion rate depends on plasma density at an exponent larger than 2.)

blaisepascal:
It is interesting question what happen e.g. along the x axis. Because of symmetry, the magnetic field at exactly the axis is zero. What one shall look at is the fields near the axis. Here is how they look like:
http://www.broadbit.net/download/polywe ... X-axis.png
The field lines transfer from one direction into a 90 degree rotated orientation around x axis. I do not think there is any cusp here.
About your other questions:
- epsilon is practically zero. The higher current of y-z plane determines which way the field lines will curve.
- I did not compare the magnetic field of quasi-polygon centers to WB-6/7 case. The field should be larger for given current levels than for WB-6/7, because for WB-6/7 nearby rings attenuate the field generated by each other.

[KitemanSA]

Art:
The challenge of WB-6/7 design is that plasma density must be decreased as grid potential is raised in order to avoid Paschen arcing. The reason is that energetic electrons lost through cusps - i.e. the ones failing to recirculate - create arcing capability. That is why my proposed design applies an exterior magnetic trap, so that grid potential can be substantially raised without arcing.

How does an electron that is leaving the MaGrid with more energy than the MaGrid voltage induct arching? What archs to what? Excess neutrals, sure, excess ions too, but electrons?

[ankovacs]

KitemanSA: I understand the arcing problem to be created by those electrons, which have less energy than MaGrid voltage, but are outside the wiffle-ball trap.

There are excess electrons in the system, so I am not sure what you men by excess ions. In any case, if an ion gets outside the magrid, it is pushed by electrostatics all the way to the wall.

Design goal is to have very few neutrals in the system.

[KitemanSA]

KitemanSA: I understand the arcing problem to be created by those electrons, which have less energy than MaGrid voltage, but are outside the wiffle-ball trap.
There are excess electrons in the system, so I am not sure what you men by excess ions. In any case, if an ion gets outside the magrid, it is pushed by electrostatics all the way to the wall.

Hmm. The electrons that have LESS than the MaGrid voltage get stopped and returned by the MaGrid. That is the purpose of the voltage on the MaGrid. It accelerates low energy electrons into the sphere which form the virtual cathode...

I thought the problem was that at a high voltage, electrons from the chamber walls arch across the gap (which SHOULD be in a vacuum) aided by neutrals in the system which lower the breakdown (?) voltage. The electrons effectively step across the neutrals from the wall to the MaGrid (actually starts the other way withthe MaGrid sucking electrons off the neutrals outside. How electrons can step across fleeing electrons is beyond me. Is my understanding THAT far off?

Sorry, I was using my shorthand. In this case "excess" means those particles that have gotten outside the MaGrid.

Design goal is to have very few neutrals in the system.

Hence the contract to build the ion gun rather than rely on the gas puffer!

[hanelyp]

ankovacs, your field plots don't appear match the symmetry of the coil configuration. What about field cusps on the square faces? If I'm reading the current path correctly (in at 2 opposite corners, out through the other corners) you'll have very bad crossed line cusps on those faces. Note that a cusp in a polywell isn't always a field null, but may be a a point or line where the magnetic field isn't aligned to prevent charged particle flow.