magrid configuration brainstorming

[KitemanSA]

Looking at it, the square design does keep the physical coils symmetrically opposed to each other.
That leaves the triangles vs inverted triangle question of the other example.

I'm not sure I get the other question. In the square plan form system, the virtual out magnets are much better formed than the WB6 resulting in shorter (negligable?) line cuspage and better virtual point cusps, no?. Dr. B. seemed to think that such a configuration was worth investigating in physical hardware.

[D Tibbets]

It is not the virtual magnets that worry me, it is the real ones. The square arrangement (actually seams ok. The other design with square and triangular real magnets are of concern. The opposing triangles are inverted from the one on the opposite side of the magrid. The magnetic fields that conform to the physical triangles are not symmetrical - triangle base on one is down, while it is on top on the other, so the fields would not push against each other the same over the extent of these magnets.

Dan Tibbets

[happyjack27]

what if you started with a baseball seam curve and did some kind of geometric recursion on it (e.g. an affine transform)? then you've got a single-coil system with no funny cusps or inflection points.

[happyjack27]

possibly by adding terms to the equations shown here:

http://www.darenscotwilson.com/spec/bbseam/bbseam.html

or put 3 baseball seem curved coils inside each, rotated so that their line cusps are orthogonal to each other.

it would certainly be interesting to see what these magnetic fields look line.

also i found a link talking about plasma physics in a non-iterated (or embedded) baseball-curve coil: (link)

also a paper on packing a closed line on the surface of a sphere: http://people.math.gatech.edu/~alben/Al ... ne.PRE.pdf
with regard to that, i'm talking about something like a/b in figure 4.

[KitemanSA]

It is not the virtual magnets that worry me, it is the real ones. The square arrangement (actually seams ok. The other design with square and triangular real magnets are of concern. The opposing triangles are inverted from the opne on the opposite side of the magrid. The magnetic fields that conform to the physical triangles are not symetrical - triangle base on one is down, while it is on top on the other, so the fields would not push against each other the same over the extent of these magnets.

Dan Tibbets

But the orientation of the magnets between the square plan form and the round plan form DOES NOT CHANGE, and if you are ok with WB6, why do you suppose an issue with Dr.B's WB7? I'm just not getting it.

[happyjack27]

problem w/the embedded baseball seam design is that the implied polyhedral geometry is that of a cubed, which has an odd number of faces at each vertex.

starting w/ the octohedron configuration, w/out (or in) facing magnets removed (i.e. 4 real coils), connecting adjacent pairs of coils so you have 2 baseball seams (ovals pinched at the center) might work (or at least be interesting), and you'd have much smaller line cusps.

[D Tibbets]

It is not the virtual magnets that worry me, it is the real ones. The square arrangement (actually seams ok. The other design with square and triangular real magnets are of concern. The opposing triangles are inverted from the opne on the opposite side of the magrid. The magnetic fields that conform to the physical triangles are not symetrical - triangle base on one is down, while it is on top on the other, so the fields would not push against each other the same over the extent of these magnets.

Dan Tibbets

But the orientation of the magnets between the square plan form and the round plan form DOES NOT CHANGE, and if you are ok with WB6, why do you suppose an issue with Dr.B's WB7? I'm just not getting it.

It is not the cusps that concern me, it is the shape of the magnetic fields facing the center . With the opposing inverted triangles the fields will be deformed where one section of the magnet surface is not equally opposed by the absent magnet in that local area. The base of one triangle produces a column of magnetic surface , but the opposite triangular magnet in that area is a corner with effectively a spherical crossection at that point . The columnar sections of the first triangle would not have a symmetrically placed opposing magnetic field, so the field would bulge more towards the center making for a more lumpy Wiffleball surface. Worse, the resultant portions of the B field may be concave towards the center. A drawing would help, but I'm not sure how to orientate it to show what I'm anticipating.

Dan Tibbets

[KitemanSA]

It is not the virtual magnets that worry me, it is the real ones. The square arrangement (actually seams ok. The other design with square and triangular real magnets are of concern. The opposing triangles are inverted from the opne on the opposite side of the magrid. The magnetic fields that conform to the physical triangles are not symetrical - triangle base on one is down, while it is on top on the other, so the fields would not push against each other the same over the extent of these magnets.

Dan Tibbets

But the orientation of the magnets between the square plan form and the round plan form DOES NOT CHANGE, and if you are ok with WB6, why do you suppose an issue with Dr.B's WB7? I'm just not getting it.

It is not the cusps that concern me, it is the shape of the magnetic fields facing the center . With the opposing inverted triangles the fields will be deformed where one section of the magnet surface is not equally opposed by the absent magnet in that local area. The base of one triangle produces a column of magnetic surface , but the opposite triangular magnet in that area is a corner with effectively a spherical crossection at that point . The columnar sections of the first triangle would not have a symmetrically placed opposing magnetic field, so the field would bulge more towards the center making for a more lumpy Wiffleball surface. Worse, the resultant portions of the B field may be concave towards the center. A drawing would help, but I'm not sure how to orientate it to show what I'm anticipating.

Dan Tibbets

But the exact same arguments can be applied to the WB6+ series, and if it wasn't a problem there...

[hanelyp]

It is not the cusps that concern me, it is the shape of the magnetic fields facing the center . With the opposing inverted triangles the fields will be deformed where one section of the magnet surface is not equally opposed by the absent magnet in that local area. The base of one triangle produces a column of magnetic surface , but the opposite triangular magnet in that area is a corner with effectively a spherical crossection at that point . The columnar sections of the first triangle would not have a symmetrically placed opposing magnetic field, so the field would bulge more towards the center making for a more lumpy Wiffleball surface. Worse, the resultant portions of the B field may be concave towards the center. A drawing would help, but I'm not sure how to orientate it to show what I'm anticipating.

Dan Tibbets

If I understand you correctly...

A magnetic field line in a polywell doesn't pass in one side, through the center, and out the other. It passes in one side and out an adjacent side. Even absent the plasma and wiffleball effect the magnetic field nulls in the center. So what is adjacent to a face matters a lot, what is opposite a face doesn't matter to that face.

A single element need not be balanced by a single counterpart. A set of symmetric elements may do as well. This applies to the sides of a triangular face or the faces of a rectified tetrahedron.

[D Tibbets]

Actually, I am arguing the opposite. The opposing magnetic fields approach the center, but does not reach it due to repulsion from the exactly symmetrical field on the opposite side. The Wiffleball does two things. It pushes this surface outward, increasing the field free symmetrical zone. And, while doing so it tends to flatten the field lines that are closest to the center, effectively making the original highly elliptical field lines almost flat towards the center (almost spherical) except where the cusps are.
Without the opposing exactly symmetrical (or close enough) magnetic fields (generated from symmetrically matching magrids) the elliptical field lines facing the center may be uneven- there may be some waffling or unsymmetrical bulges inward or outward. With the Wiffleball formation these distortions would be magnified. If not symmetrical an outward bulge on one side could be matched by an inward bulge on the other. If these bulges have a portion of their surface concave towards the center instabilities could form that compromises the magnetic confinement (a major problem in Tokamaks). Also, at Beta= 1, the Wiffleball is pushing out as much as it can without blowing out the cusps. If there is asymmetry in these cusps, the Wiffleball pressure could only build till the most vulnerable cusp blew. So the effective pressure gradient would be less than an ideal symmetrical system. The question (in my mind) is the asymmetry of the triangular magnets ( the base of one faces the apex of the other- a columnar magnetic field faces a ~ spherical magnetic field). Do they exceed the limits mentioned above. This asymmetry cannot help, and may hurt a small to a catastrophic amount.

Dan Tibbets

[KitemanSA]

But an octahedral Polywell is one of the basic designs in Dr.B's patent and they don't have exactly opposing magnets. Indeed, the magnet opposite an in magnet is an out magnet, but the octahedral polywell is anticipated to work just fine.

I think your recent train of thought needs re-thinking. There is no reason to believe that identical opposing magnets are needed. In my understanding, what is needed is the vector summation tozero, and that can be had with many different configurations.

[happyjack27]

i've been kicking this idea around in my head for a while, i suppose i might as well make it explicit:

why don't you just plug up the cusps with another magnetic field?

e.g. just put another coil outside the cusp, tangent to the 2nd normal of the escaping field line(s).

it might not plug it up exactly but it could make it harder for electrons to escape; it could pack them in better, thus deepening the well.

[hanelyp]

...In my understanding, what is needed is the vector summation tozero...

Good way of looking at it. Do the vector magnetic fields from the face magnets add to zero in the center on the system? Not a sufficient condition for a good polywell, but the major global condition.

The other major condition I see for magnetic field shape is as much surface of the sphere as practical having magnetic field parallel to the surface of the sphere. Those points failing this condition are leaky cusps, to be kept as small as practical. This rule applies locally across the sphere.

[D Tibbets]

i've been kicking this idea around in my head for a while, i suppose i might as well make it explicit:

why don't you just plug up the cusps with another magnetic field?

e.g. just put another coil outside the cusp, tangent to the 2nd normal of the escaping field line(s).

it might not plug it up exactly but it could make it harder for electrons to escape; it could pack them in better, thus deepening the well.

Electrostatic or magnetic plugging of the cusps was tried in various machines, including WB5. In short, they do not work. Anything that tends to confine the electrons better, tends to create large leaks for the ions. This frustrating result apparently helped Bussard to realize that recirculation was absolutly essential to any of these cusp designs, thus the realization that no closed box machine (magnets outside the vacuum vessel) could work, and thus the design of WB6.

Dan Tibbets

[happyjack27]

Single-coil octahedron magrid (wireframe):



notice north-in and north-out fields are perfectly symmetrical.