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Wiffleball Equipotential Surface Approximations
Posted: Mon Feb 21, 2011 6:40 am
by DeltaV
Posted: Mon Feb 21, 2011 1:08 pm
by KitemanSA
Can you do one with an image magnet representing the plasma? This looks similat to KCDodd's bagshot.
Posted: Mon Feb 21, 2011 3:49 pm
by ladajo
To be fair, I think my now 7 year old son gets credit.
These look good, but what about the cusp in the center of the field? There would seem to be a way to mix two polyhedrals to get the effect.
Good find.
Posted: Mon Feb 21, 2011 8:32 pm
by DeltaV
KitemanSA wrote:Can you do one with an image magnet representing the plasma?
These are just exact expressions for surfaces which superficially resemble what one might expect for Polywell surfaces of equal <
insert relevant physical parameter here>, not anything based on field solutions. With jiggled constants to approximate (soon to appear?) experimental data they might have some minor utility for rough estimates of <???>.
Posted: Mon Feb 21, 2011 8:34 pm
by KitemanSA
DeltaV wrote:These are just exact expressions for surfaces which superficially resemble what one might expect for Polywell surfaces of equal <insert relevant physical parameter here>, not anything based on field solutions.
Aw dang!
Posted: Mon Feb 21, 2011 8:42 pm
by DeltaV
ladajo wrote:but what about the cusp in the center of the field? There would seem to be a way to mix two polyhedrals to get the effect.
I'm not sure what you mean. The rhombic dodecahedral star seems to capture all 14 point cusps of the 6-coil cube magrid. Do you mean center of the magrid "sphere"?
Posted: Mon Feb 21, 2011 8:43 pm
by DeltaV
duplicate post - deleted
Posted: Mon Feb 21, 2011 8:58 pm
by ladajo
Yes it does. But how would you account for coil spacing verses field strength? I was thinking that if you combined two shapes as a merged one, maybe you could do it.
Posted: Tue Feb 22, 2011 5:11 am
by DeltaV
ladajo wrote:Yes it does. But how would you account for coil spacing verses field strength?
Not including the leading "1" term, I count 9 coefficients* in the rhombic dodecahedral star equation. I think those can be tweaked to approximate what you're referring to. In other words, shaping the parts of the surface that are rotationally symmetric about the coil/cusp axes.
If I had time during the next few weeks, I'd code up a Mathematica demo with 9 sliders for the coefficients.
* Or, 14 unique integers making up the rational numbers which make up the 9 coefficients.