Is There an Optimal Size for Magrid Casings?

tombo · Post by **tombo** » Tue Jun 23, 2009 8:16 am

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

slice thru centers of long sides on xz plane:

same with current turned down to make vectors more clear.

Resolution has deteriorated again. I don't know why and I'm too tired to fix it right now.

MSimon · Post by **MSimon** » Tue Jun 23, 2009 2:14 pm

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.

Nothing wrong with it if you can accept the increased losses. In any case field lines will intersect the casings. The question is: is the field conformal to the casings for maximum shielding (you know - the purpose of the magnets).

KitemanSA · Post by **KitemanSA** » Wed Jun 24, 2009 11:25 am

Tom,
I hate to suggest it, but is it possible to change the format of your plot a bit so that the magnitude of the field is shown by color, not size, and the arrows are all the same small size? It may back it easier to view the results.

If it is not feasible, well thanks for what you have accomplished.

tombo · Post by **tombo** » Wed Jun 24, 2009 8:10 pm

I suppose it's theoretically possible. But, I don't know how to do it.
It would have a time consuming learning curve and I have other things I want to do.
Also the only approaches I can think of would increase processing time incredibly. My gut tells me the the 20 minute excel macro could stretch out to days. Inside each loop it would have to compare the value to a table of values. Then, when the overall field changes that whole mapping would have to be redone by hand to normalize it.

One advantage the way it is now is that I can say "I wonder how strong the field is here?", pick an arrow and measure its base diameter to get the field strength.
Yes it would be easier to see past the nearer arrows.
But it does give a visual feel for where the field is strong, & better to my eye than some kind of color coding mapping scheme.
Also I would bet that autocad's use of color during rendering would change the colors from the starting ones essentially terminally messing with our data.
Now making different colors above vs below an adjustable cutoff field strength should not be too hard. Say red to show where the field is too low.

tombo · Post by **tombo** » Wed Jun 24, 2009 8:48 pm

Now that I have the model working here is some data analysis:

Slice thru the middles of the 2 short sides
Showing field nulls and weakening field as it gets further from (above) the nulls.
http://i299.photobucket.com/albums/mm31 ... 000_-6.png

Same with different rendering parameters

Slice in the plane of the coils looking from the top. (i.e. from the outside looking toward the center of the Polywell.)
Showing crescent shaped field nulls.

Slice 1 cm above the plane of the coils.
Showing crescent shaped field nulls smaller.

Slice 2 cm above the plane of the coils.
Showing crescent shaped field nulls smaller still.

Slice 3 cm above the plane of the coils. Showing crescent shaped field nulls pretty much gone.
http://i299.photobucket.com/albums/mm31 ... 000_-2.png

Slice 5 cm above the plane of the coils.
Showing the crescent shaped field nulls gone.
http://i299.photobucket.com/albums/mm31 ... 000_-1.png

Slice 20 cm above the plane of the coils.
Showing weakening fields as we get further from the coils.
http://i299.photobucket.com/albums/mm31 ... 00_Top.png

oooooooooooooooooooooooooooooooooooooooooooo

The coils really have a 3D geometry and the shorter legs will be further from the poly well center point.
This difference can be controlled by adjusting the relative coil curve radii.
I hypothesized a few weeks ago that the field nulls may be reduced or eliminated by offsetting one set of crossovers. So…

Slice thru the middles of the 2 short sides with:
Coils offset by 10 cm
Showing weakened crescent field nulls at +1 cm and new field null at -4 cm
The new null is where the field enters from 2 opposite directions and leaves in the 2 orthogonal directions which is the same geometry as the crescent ones.
Notice also how the field above this interesting region is much stronger than when the coils were aligned.
This should provide a barrier between the reactor core and the weakened fields.

Same with different rendering parameters
http://i299.photobucket.com/albums/mm31 ... 10_Rig.png

Slice +1 cm above the plane of the coils looking from the top. (i.e. from the outside looking toward the center of the polywell.)

Showing the field nulls no longer crescent shaped and with arms reaching out toward the new null.

Slice -4 cm above (i.e. below) the plane of the coils.
Showing the new field null from the top.

oooooooooooooooooooooooooooooooooooooooooooo

Slice thru the middles of the 2 short sides
Coils offset by 15 cm
Showing weakened field nulls at +1 cm and new field null at -4 cm
Notice also how the field above this interesting region is even stronger than when the coils were offset by 10 cm.

Same with different rendering parameters
http://i299.photobucket.com/albums/mm31 ... 15_Rig.png

Slice +1 cm above the plane of the coils looking from the top. (i.e. from the outside looking toward the center of the polywell.)
Showing the field nulls no longer crescent shaped and with arms reaching out further toward the new null.
http://i299.photobucket.com/albums/mm31 ... 015_-1.png

Slice -4 cm above (i.e. below) the plane of the coils.
Showing the new field null in the center looking from the top.
http://i299.photobucket.com/albums/mm31 ... 15_Top.png

oooooooooooooooooooooooooooooooooooooooooooo

Slice thru the middles of the 2 short sides
Coils offset by 20 cm
Showing crescent field nulls merged into one field null at +5.6 cm and strong even fields above about 10 cm.
In fact the fields are strongest just above the null shielding it from electrons.

Same with different rendering parameters
http://i299.photobucket.com/albums/mm31 ... 20_Rig.png

Slice +5.6 cm above the plane of the coils looking from the top. (i.e. from the outside looking toward the center of the polywell.)
Showing the merged field null in the center looking from the top.
http://i299.photobucket.com/albums/mm31 ... 020_-1.png

Slice +20 cm above the plane of the coils.
Showing even strong fields between the reactor core and the region of weakened fields.
http://i299.photobucket.com/albums/mm31 ... 20_Top.png

Offsetting the closer pair of cross connects toward the reactor core will shield the field null from the escaping electron flux (& ion flux too of course). The more offset the better for this effect. Less offset helps other parameters of course.

The changes with coil offsets are so big that we really have to do this over (heavy sigh) with the real 3D positions of the coils.
This flat approximation really is not good enough to show some major field features because the positions change much more than the offsets that I just modeled.
I predict an enhanced strong field region just inside (toward the reactor core) the region we are exploring here. (This would be a good thing.)
If you send me the list of the x,y,z point positions for the 3D coil locations, I will work on it some more. (It needn’t be the same length list as before.)

The AutoCAD drawing, showing all these configurations as different layers, is available on request but beware it is 147 Megabytes big.
My little old computer complains about its size but can barely handle it.
If you can view it you can glean much more information about the details of the field vector behavior.
I could make the rest of the tools available if you want but they are not set up for others to use.

--Edited for multiple errors and insights---
(Sorry, but sometimes I have to actually see the final product and think about it for a while, then I see more stuff. Somehow it is easier to see errors after I let it go.)

KitemanSA · Post by **KitemanSA** » Fri Jun 26, 2009 12:36 am

Ok, if color is out, can you plot the same as the top plot in your 8:48PM yesterday post but plotting ONLY the tangential component? I mean only the horizontal in this particular model. That, I think, would reveal the cusp without confusion.

tombo · Post by **tombo** » Fri Jun 26, 2009 6:42 am

Do you mean a Scalar representation of the tangential (x & y) field strengths?
Perhaps a ball with a diameter proportional to the sqrt(Bx^2+By^2) at each point.
Or do you mean a vector arrow constrained to being parallel to the xy plane?

Also, I can easily turn down the current to make all the arrows smaller and easier to see past.
Some of those plots are very crowded because I plotted them all to the same B field scale.

I have some paid work coming up, so it might be a while.

KitemanSA · Post by **KitemanSA** » Fri Jun 26, 2009 12:41 pm

Either way, I think.

Have fun in you work, be productive in your play!

tombo · Post by **tombo** » Thu Jul 09, 2009 7:26 pm

plotting ONLY the tangential component?

I think your excel charts actually show the tangential field data better than I could do with my tools.
Especially when we have the file available to rotate the plot to see it from different vantages.

tombo · Post by **tombo** » Thu Jul 09, 2009 7:34 pm

Work in progress:
Here is the whole truncube at coarse (170 mm) resolution.

EDIT:
Better image below.
Better render lighting and conversion to *.png in Gimp.

Zooming in with "control +" repeatedly you can see the vectors going in through the square coils and out through the triangular corners and curling around the coils again.

This was generated by:
The coil path shape in acad is generated by a formula in excell via an acad script.
The acad path part is then marked every 100 mm (easily changeable).
The x,y,z coordinates of all marked points are then pulled into excell.
Where they are:
First used to generate a script to draw the Magrid along that path (for checking and showing full cross section.)
Second run through Kiteman's integration routine to generate the B fields then the script file to draw the B field vectors in acad.

This routine can be used to draw the B fields around any (reasonable) shape of coil that I can draw in autocad.

The fields can be drawn zoomed into any region to show greater detail .
I can also ask it for the B field vector info at any point in 3 space.

Finer resolution takes longer to crunch the numbers but viewing the field through the clutter is really the limit.

Now, if I can only get the images to come across more clearly.

D Tibbets · Post by **D Tibbets** » Thu Jul 09, 2009 9:43 pm

I don't know what conversions you are going through to get a final published image, but if it looks better at some stage a simple screen capture may be the way to go.

Dan Tibbets

tombo · Post by **tombo** » Sun Jul 12, 2009 5:00 am

Actually the bottleneck now seems to be autocad's render function.
I need to learn to use it better.
There must be something I can do with lighting etc. as I am already generating a 4000+ x 3000+ pixel image which is its maximum size.

tombo · Post by **tombo** » Tue Jul 14, 2009 7:33 pm

Using the same model to show B field at various points of interest on a truncube with square coils.
I adjusted current to 3.47e6 amp turns to make B at center of the square coil = 1 Tesla
truncube radius 1.5m
magrid conductor 0.05 m radius
magrid casing 0.10 m radius
bends at corners = 0.5 m radius on centerline
all from the autocad model just above.

Code: Select all

B field at locations					x			y			z			Bx		By		Bz			|B|		|Btan|
center of square						0.0000	0.0000	1.5000	-0.0057	-0.0142	-1.0000	1.0001	0.0153
center of lone square of current	0.0000	0.0000	1.5000	0.0000	0.0000	-1.8575	1.8575	0.0000
center of triangle					 1.0000	1.0000	1.0000	1.3461	1.3378	1.3681	2.3395	
center of sphere						0.0000	0.0000	0.0000	-0.0279	-0.0140	0.0000	0.0312	
between bends							0.0000	1.3964	1.3964	0.0042	5.1234	5.1438	7.2600	
surface of casing square				0.6793	0.6793	1.5000	0.2874	0.2745	-6.9149	6.9263	
surface of conductor square			0.7146	0.7146	1.5000	0.3149	0.3014	-16.7625	16.7682	
surface of casing triangle			0.7908	0.7908	1.4184	4.4309	4.4193	4.2657	7.5736	
surface of conductor triangle		0.7704	0.7704	1.4592	10.1313	10.1185	9.9397	17.4306	
surface of casing inside bend		0.0000	1.1929	1.5000	0.0018	0.5824	-7.9080	7.9294	
surface of conductor inside bend	0.0000	1.2429	1.5000	0.0023	0.7607	-12.8761	12.8986	
surface of casing outside bend		0.0000	1.3929	1.5000	0.0037	1.6954	6.1386	6.3684	
surface of conductor outside bend	0.0000	1.3429	1.5000	0.0033	1.3231	9.8009	9.8898	
surface of casing between bends		0.0000	1.3636	1.4293	0.0038	5.8934	5.6048	8.1330	
surface of conductor between bends	0.0000	1.3282	1.4646	0.0088	8.2544	7.6108	11.2276

There are some anomalies, some values that should be zero are not quite zero.
This gives some idea of the error bars on the model.
I hope these descriptions make sense to others. I have been looking at the model so long that it is too obvious to me.
Square and triangle refer to which side of the magrid the point is located.
Between bends means halfway between coils at the point of closest approach.
Surface of casing values might be useful as boundary condition for plasma models.
Surface of conductor impacts the design of the superconductor.
Model agrees with analytical solution for 1 square turn to better than 1%.

(This table is about as straight as I can make it with this tool, sorry.)

KitemanSA · Post by **KitemanSA** » Tue Aug 04, 2009 5:55 pm

Greetings All,

I finally got around to calculating a different slice thru the cusps. After a bit of repeat effort, I also finally got my charts from Excel to not crash my powerpoint, so I was able to provide the following graphic.

The graphics show the magnitude of the tangential portion of the field viewing the YZ plane. The radial direction is up/down. The tangentials are thus obviously the side to side and in/out directions.

The top panel shows the field for the REAL Funny cusp, not the Line-like cusp that the toroids make. The bottom it the X-cusp. The blue circles/ellipses are the location of the coils. I didn't show the field for the Line-like cusp in because the graphic is almost solid blue, i.e. no tangential field to speak of anywhere on the graphed plane. No metal except the nub, but quite a large tangential null.

As you can see, the Funny cusp produces a smaller null in the tangential field (smaller hole) than the X-cusp, but the null leads directly to the coil. Any electrons or ions excaping thru said null will impact the coil casing, 100% loss. The X-cusp produces a broader null in the tangential field but has no metal in the way of the null. The charged particles will zip out the hole and the electrons, in theory, will be recirculated back into the machine. The Line-like cusp produces a MUCH bigger tangential null than the X-cusp.

Aero · Post by **Aero** » Tue Aug 04, 2009 8:58 pm

Does that look like Mickey and Minnie Mouse on their first date to anyone else?