Superconductors and Current capacity

[D Tibbets]

I have seen magnetic field limits on superconductors, especially high temperature superconductors, but had not appreciated the corresponding current limits (B field =amp turns)

This link shows a new design that may be a step in the right direction.

http://www.technologyreview.com/energy/32424/?p1=A5

In WB 6 (ignoring cooling concerns) this new superconducter cable (~ 8 mm wide with a capacity of ~ 3000 Amps) could fit ~ 30 windings into the ~ 5 cm minor diameter of the WB6 magrid.
This would yield ~ 3000 A * 30 windings = ~ 90,000 amp-turns. This compares to perhaps ~ 400,000 amp-turns in WB6. So this high temperature superconductor could provide a maximum of ~ 200G, or ~ 50 G if you assume a 40% packing fraction.

A large Polywell with a major diameter of 3 meters and a fat diameter of 1 meter would allow for ~ 14,000 windings maximum, or ~ 6,000 windings if you assume a 40% packing fraction.
Number of windings in large machine =14,000 / 30 windings in WB6 size machine = ~ 450 X gain. For a 40% packing fraction that would be ~ 180 X gain.

Multiply 200 G by these gains gives maximum performance of ~ 90,000 G or ~ 9 Tesla maximum, and a more realistic 3.6 T for a 40% packing fraction.

This high temperature superconductor is not quite there, but it is getting close.
I assume the current/ B field limits per cable is proportional to the limits on a bundle of these cables.

Dan Tibbets

[imaginatium]

The way I read it, it's 7.5mm=2800 A. The minor diameter is 50mm so that is a ratio of ~6.66 to 1. So according to this table there are ~33 windings. However, 6.5mm =1200 A. With a 50mm minor radius, the ratio is ~7.69 to 1, resulting in ~46 windings

2800 *33 =92,000 Amp-turns
1200 * 46 = 55,000 Amp-Turns

Therefore, we can see that if we made a wider cable, with fewer turns, we would get significantly greater amp-turns. So why not make it 1 turn of a 50mm cable?

[D Tibbets]

My short term memory wasn't so good. At least I was in the ball park. Your more acurate number would result in in a ~ 10% improvement., so perhaps 4 T could be obtained with a 40% packing fraction. Also, since this would be at liquid nitrogen temperatures instead of liquid helium temperatures, a layer less of insulation/cooling may serve. This would increase the packing fraction and resulting B field strength to perhaps 5 or even 6 T.

Increasing the diameter might allow for more capacity , but based on the two cables presented, the improvement is perhaps peaked at the 7.5 cm. There may be some balance between the copper core, the insulation thickness and the superconductor wrappings. Or perhaps not, no information was given.

The important point is that this design matches the performance of a older high temperature superconductor design that could carry 3,000 amps, but at a cable diameter of 7 cm. Also important is the radius of curvature of the cable. If too great, it could not be used in a Polywell. This would be especially true if you were using non round magnets- like square shapes. You could not bend the superconductor around the corners.

What I do not know is how this compares to low temperature superconductors. Using MRI machines as an example, they seem able to achieve at least 3+ T in ~ 1 meter diameters, so each cable can carry more current, and can be bent to reasonable radii of curvature.

Dan Tibbets