Is There an Optimal Size for Magrid Casings?

[tombo]

My latest understanding is that with pBj the heat loading is about zero

EXCELLENT!
Yes, that was good news.

Eight inches is probably a good start

I just did the calcs with 0.100 meter radius coil casings which is 8 inches diameter.
(It really should not affect what I just did but it is good to know that I am in the ballpark with by assumptions.)

[tombo]

Work in Progress with some actual progress to show.

Size of space modeled in meters:
X=-0.50 to +0.50
Y=-0.70 to +0.70
Z=-0.50 to +0.50
Origin: at the polyhedron’s vertex.
Coil parts modeled are Kiteman’s X-Cusp laid out on a plane i.e. not yet bent around the sphere.
This is using Kiteman’s spreadsheet modified to export the B field at each point in the modeled volume to an AutoCAD script file that then draws simplistic vectors (and conductor casings) in AutoCAD.
Magrid Minor Radius (half thickness) is 0.100 m ~=4” (i.e. coil thickness 8”)
Points modeled: every 0.050 m in each dimension.
Length of cone: diagonal length of unit volume (i.e. square root of ((0.05^2)*3=0.087 m)
Direction of cone: B field direction
Apex of each cone is the tip of the vector is N (per Biot-Savart I assume North) & the base of the cone is the back of the vector is S.
Diameter of cone base: B field strength in Teslas
1. It is reduced by an adjustable scaling factor to fill the unit volumes where ever the field exceeds 1 T. This can be easily adjusted.
2. If the plasma heads tell me a value for a field strength that contains the plasma at the velocities it has in this region, I will show one at a scale factor that shows the space looking visually plugged wherever the field strength exceeds that number. (Yes, I know it is more complicated than that. It always is.)
Coil current: 5e5 amp turns (I reduced this to open up the space visually so we can see inside the model. This overrides the above scaling factor.)

There are ~12,000 vectors plotted.
This file is 31 meg and slow to move around in.

If we can post the file somewhere, anyone can go to Autodesk and download their free drawing viewer.
Then you all can turn the model every-which-way & zoom to your heart's content.
That will make it much easier to follow what is going on, but it is still confusing.
It should even allow you to use clipping planes, measure parts (to get the actual field numbers at a point from the model) and to print. (It even claims to allow mark-ups, but the one person that I know has used it said no.)

Top:

Front:

Left:

NW Isometric:

Looking at Wire End:

Central detail:

The vectors seem to follow and illuminate the field lines some times. This is when they go through the same relative position in adjacent unit volumes. So, it gives a good general picture of the field lines, but if following a single field line is your thing, caveat.

Notice the vectors buried inside the conductor. Those should not be there. I plan to eliminate those sometime.
Much of the fields are clear when you step back. But, details are hard to see because resolution is coarse (50mm~=2 inches) and because there are so many vectors.
I would really like to see 1mm resolution and be able to see them all clearly. This is an ergonomic/graphics design problem.
And I need to work on finding clipping planes that uncover regions of interest.


Next Tasks:
Model a smaller volume (i.e. just the volume inside of the rectangular opening.)
Finer Grid
More automation of the process
Chase down a few bugs that bother me.
Ergonomics & Graphics design ideas to make showing this density of data more intuitive (I could really use some Help here. If someone can point to some examples of well done presentations of this data density I would really like to see them.)
Different coil configurations
3D coils
Full 6 coil arrangement
Check out the Autodesk free viewer. (if no one else reports in on it first)
Explore the fields.

[Admin may wish to edit some images to be just links after a few days.
But I did so much work on this that I wanted it to show for a while at least.]

[MSimon]

Admin likes things the way they are.

[tombo]

Modeling just the hole (with at .01 by .03 resolution) I see the vectors behaving reasonably well near the long crossovers.
Those long, close-together crossovers dominate the fields in the area even more thoroughly than I had thought they would.
But, near the short crossovers they dive nearly straight into the metal and out again.
This looks bad, lots of field lines intersecting metal.
This will make the can shape “interesting”.

On the other hand I can not see where any field nulls or reversals could be hiding.
I need to look closer. There should be 2 of them. They could be inside the can. That would be interesting and potentially very nice.
To look inside the can I have to satisfy myself on the issue of the field strength corrections for locations less than the minor radius away from the wire.
OTOOH I can’t see any field nulls on Kiteman’s excel chart of field intensity of the X-Cusp either.










--Edited to increase image sharpness ( *.PNG)
Still not a good as Betruger's astronaut though.

You can now see the vectors diving into and emerging from the metal cans.

[Betruger]

Is the problem with the hosting website, or the rendering program?

[tombo]

It is a gradual degradation over several steps: the CAD rendered bmp is fuzzier than the drawing, then the picture in photobucket is fuzzier than viewing it directly locally. Talk-polywell is about the same resolution as photobucket and jpg is about the same as bmp. I should take some time to understand and fine tune the rendering process more but I’ve done a fair amount of that already. And I’m more psyched to look at the fields now that I can finally see them.
--------

OK here it is.
The field null is about 25mm inside the 100mm radius casing.
I marked it with a red circle.
It seems to run along the casing (can, Magrid) parallel to the current flow in the short cross connect. (but the picture is not clear enough to present it.)
The can would need to have a weird concave/convex X cross section to be parallel to the B vectors.
I think the can has to be small enough to fit inside the null in order to maintain a convex cross section.
That puts the null very close to the can.
That is worrisome to me because the can is not protected by a strong field in the very spot where the leakage is highest.
I think it could be moved away from the can by making the aspect ratio of the opening more square.
But, now I remember. You are depending on the field strength up out of the XY plane to maintain confinement.

This is a section through the center of the short cross connect.
--Edited to change image format. It is now sharper, a .png

[krenshala]

It is a gradual degradation over several steps: the CAD rendered bmp is fuzzier than the drawing, then the picture in photobucket is fuzzier than viewing it directly locally. Talk-polywell is about the same resolution as photobucket and jpg is about the same as bmp. I should take some time to understand and fine tune the rendering process more but I’ve done a fair amount of that already.

Check to see what compression level you are using when you convert them to JPEG format. BMP is uncompressed (thus the obnoxiously large size for images bigger than icons). JPEG has variable compression meant to cut down on the data required to display large areas of the same or similar color. Since the vectors are in colors that only vary slightly I can easily see the JPEG compression "blurring" that so it is harder to read.

Personally, I'd recommend converting the BMP to PNG (with medium to high compression if you don't like the default filesize) over JPEG since PNG gives you the same or better compression with little (if any) loss in picture quality.

[tombo]

Here is the top view of the crescent shaped filed null that we predicted.
Notice that it is inside the magrid casing.
I'm not sure whether this is a problem or an opportunity.



^^^---many layers of vectors shown 10mm? resolution 18k vectors
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.
.

^^^---3 layers of vectors shown 4mm? resolution 12k vectors
look in the upper and lower left corners to orient yourself to the vectors
.
.
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^^^---one layer of vectors shown 2mm resolution 12739 vectors shown

use control-+ in Firefox about 6-8 times to zoom in on the pictures.
You can see various sized circles which are the tops and bottoms of conical vectors. (there are some smaller circles that are where the cone is cut off by the clipping plane which is more or less on the plane of the conductors.)
Their diameters are proportional to the field strength at their location.
They are pointing down on the left of the null crescent and up on the right of it in the center image. In the bottom image they are pointing up on the left and down on the right. (sorry)
The scallops on the far right are an aliasing that comes from the beat pattern between the curvature of the conductor and the rows of the grid and amplified by being so close to the singularity of the conductor. Please ignore the little scallops behind the curtain. i.e. they are the bases of the vectors that fall so close to the conductor that the field strength is very high. Likewise the top & bottom left corners of the last image.

---Edited to improve the last image. And to correct & clarify wording.---

[tombo]

^^^---Cross section through the crescent cusp on the center plane.---^^^

The cusp is at the lower end of the red curve. It is a minimum.
The center line of the rectangular opening far from the opening is at the top end of the red curve. It is a minimum.
The red curve represents a valley.
The lower left end of the red line is the center of the opening. It is a maximum.
The top end of the red curve is eyeballed into a high field region. It is a maximum. (It is actually some kind of spiraling curve.)
The red line represents a ridge.
SO:
The crossing of the two red lines is the saddle point.
The red vector is the closest (at this resolution) to the saddle point.
(determined by measuring all the vector diameters near the crossing.)
I can read the field in Tesla of this point given the desired magnet current by measuring the diameter of the vector. I can then find it in the Excel matrix to verify.

The saddle point is the maximum field on the minimum energy path from the inside of the polywell to the Magrid casing in this (vulnerable) vicinity.
The electrons need to mirror at or before that point.

Tell me what the minimum field should be and I can tell you what current you need.

[KitemanSA]

Interesting. I wish I understood this whole subject a bit better. I'm still trying to absorb what this is telling me.

[tombo]

Me too.
I feel a bit like Van Leeuwenhoek looking through his first microscope.

(Kiteman on 3/29/09 this thread) So you see that whatever the field nulls at the magnet's midplane are, the electrons will never get to them except in the very short slot in the center. And at that point there is NO METAL.
So we have a VERY short consrained bit of line-cusp that looks for all practical purposes like a funny cusp (or a point cusp) (its about the same size) that I call an X-cusp and will limit the electrons basically as well as a point cusp and will have NO path to the metal.

What we are seeing is that path to the field null and its choke point (saddle).
It also happens to hit metal before it gets to the null.
I really REALLY don't like the way the field lines intersect the casing.
What can we do about it?

BTW The field strength at the saddle point is 0.72 times the field at the center of the rectangular opening, which itself is much higher IIRC than the field at the center of the main coil which is expected to be 1-10 T

Also

(3/20/09) If you limit your view to the mid-plane, (and ONLY the mid-plane) that may be the case, but before the electrons reach the mid-plane they must pass thru a region that looks like mine. This will reflect all but a small number of the electrons which will continue on and see the very short line cusp.
Please note that the conductors in each corner have current flowing in the same direction. Thus at a distance it looks to be one conductor half way between them. Given the sizes of these things, the wiffleball face (inside the MaGrid) should have enough standoff from the centerline of the MaGrid to make the two "incoming" conductors in each corner of the right-hand sketch above look like a single one, resulting by superposition in a field effectively identical to what would be produced by the straight conductors of the left-hand sketch above.

It appears that the distance off the plane where the field reverts to the topology that it would have without the cross ties (if somewhat distorted) is less than the magrid minor radius. (This is good.)

Kiteman,
How did you generate the numbers for the loop paths in columns A, B & C?
Did you do it by hand? Did you have a separate spreadsheet calculate it from the parametric equations? Did you ???
I want to generate some other coils to model and if you found an easy way then I would just a soon use it. My mind is only coming up with awkward solutions. Ideally I want to make AutoCAD generate them.

Are there any slices through the model or details of it that you would like to see?

[tombo]

One of the things I'm seeing is that the crescent shaped null connects two 3-sided vertexes making them in a sense 4 sided vertexes which agrees with the requirement for all vertexes to have an even number of faces.
The null is not actually a current however it is a separation between domains of opposite field direction.

It also bears a superficial resemblance to the classic cusp machine's field generated by 2 opposing coils having field curvature type stability but containing large leak in velocity space.

[KitemanSA]

The cusp is at the lower end of the red curve. It is a minimum.

We must have different understandings of the word "cusp". My understanding has the cusp at the TOP end of the red curve, not the bottom. At the bottom is the field null that is the analog to the field null that is in or near the cross sectional center of most coils. A cusp is a null TANGENTIAL field, not a null field. Cusps can have very strong RADIAL fields.

The center line of the rectangular opening far from the opening is at the top end of the red curve. It is a minimum.

THAT is the cusp. Beyond here is terra incognito to me.

The red curve represents a valley.
The lower left end of the red line is the center of the opening. It is a maximum.
The top end of the red curve is eyeballed into a high field region. It is a maximum. (It is actually some kind of spiraling curve.)
The red line represents a ridge.
SO:
The crossing of the two red lines is the saddle point.
The red vector is the closest (at this resolution) to the saddle point.
(determined by measuring all the vector diameters near the crossing.)
I can read the field in Tesla of this point given the desired magnet current by measuring the diameter of the vector. I can then find it in the Excel matrix to verify.

The saddle point is the maximum field on the minimum energy path from the inside of the polywell to the Magrid casing in this (vulnerable) vicinity.
The electrons need to mirror at or before that point.

Tell me what the minimum field should be and I can tell you what current you need.

I have no idea.

[KitemanSA]

Kiteman,
How did you generate the numbers for the loop paths in columns A, B & C?
Did you do it by hand? Did you have a separate spreadsheet calculate it from the parametric equations? Did you ???
I want to generate some other coils to model and if you found an easy way then I would just a soon use it. My mind is only coming up with awkward solutions. Ideally I want to make AutoCAD generate them.

I did my first crude one by hand. I then discretized more finely with a combination of hand and simple circular values. The straight segments were a simple 3.5 to 2.5 slope. At the point where the two coils diverged, I calculated the radius (hypotenus) of the two curves and just found the sine and cosine (opposite/adjacent) values every X degrees.

Are there any slices through the model or details of it that you would like to see?

Could you generate a slice thru the other side of the coil, the long side?

[KitemanSA]

What we are seeing is that path to the field null and its choke point (saddle).
It also happens to hit metal before it gets to the null.
I really REALLY don't like the way the field lines intersect the casing.
What can we do about it?

As I have opined before (not with any real data to support my opinion of course) I don't yet see any issue with the field lines intersecting the casing. Such intersection only matters if the electrons are following that field line, and I am not convinced they will.

Indrek seemed to have a method of calculating the path of electrons in a complex field. Maybe we can persuade him to trace some thru this field.

If worse comes to worst, we can always split the coils into D shaped segments rather than pull aside the layers. That would pull the casing perhaps 40% closer to the center. But that would make winding and cooling the system much more difficult, so I would like some indication of a problem before changing the layup process.