I’ve updated this post with help from Msimon.
Here is the spec sheet for the YBCO I ordered, specifically 13 meters of SCS4050i.
Icvalues range from 80 –110 Amps at 77 K in 4 mm width
Engineering Current Density (Je) = 21 –29 kA/cm2
Now I’m going to walk through some calculations(full code here) based on a dodecahedral bussard reactor core about the size of a basketball (outside diameter of core is ~200 mm). Dimensions:
outside_radius: 99.9393315967242 mm
torus_midplane_radius: 79.4172368111867 mm
torus_radius: 34.62 mm
torus_circumference: 217.524 mm
For now I’m ignoring the effects of the critical magnetic field. In these ruby code samples, the “>>” indicates converting physical units.
We have 13 meter of 4mm YBCO. This allows for 4 turns for each of the 12 coils:
turns = ((ybco_length >> Unit("mm"))/torus_circumference/12).floor # 4 turns for each coil
The superconducting tape supports a critical current of ~100 amps. So with 4 turns, we have 400 Ampere-turns per coil. Plug this into Ampère’s force law and you get 0.021912 N or force, or 2.235 grams.
Prometheus Fusion Perfection 
I’m not sure if you should use the x-sectional area of the torus. To get a more reasonable answer I think that you should use the x-section of the conductor, ((80 / 21000) = 3.8095×10^-3 cm^2
4 turns/ coil * 100 Amps current = 400 Amp turns. at 34.62 mm radius for the coils I get 72 gauss. You need about 14X as many turns per coil as you have planned for to get to 1000 gauss (.1T).
Magnetic field calculator – circular loops
MSimon, where did you get 100 Amps? I’m calculating 182,720 Amps per loop, if you can reach the SC’s critical current.
Icvalues range from 80 –110 Amps at 77 K in 4 mm width
Engineering Current Density (Je) = 21 –29 kA/cm2
Ic is what your piece of wire will actually support. Je is what you could get with 1 sq cm of wire X meters long. Which says your wire is about .005 sq cm effective area. Put your mike to it and see if that isn’t about right.
MSimon, are you saying that my cable will support 80 –110 Amps regardless of length?
MSimon, are you saying that my cable will support 80 –110 Amps regardless of length?
Yes. Like any other conductor (of sufficient length) it is the area of the wire that matters.
I know how to do formatting. I just screwed up:
MSimon, are you saying that my cable will support 80 –110 Amps regardless of length?
Yes. Like any other conductor (of sufficient length) it is the area of the wire that matters.
Famulus,
How did you figure the correct corner spacing of the coils? According to Bussard & Nebel it’s a critical parameter for getting a good Beta and for keeping losses to coils at a minimum.
It should be between 6-9 electron gyro radius (Rge)at this point but how did you figure that without knowing the estimated field strength at that location?
tom,
I’m aware of the spacing consideration, but I have not yet incorporated them into my design. I don’t know how to calculated the electron gyro radius. I also don’t know how the dodecahedral shape plays into spacing.
Can you help me with those calculations?
Well I suck at algebra, but:
http://en.wikipedia.org/wiki/Electron_gyro_radius
is the radius of the circular motion of an electron in the plane perpendicular to the magnetic field:
Rge=V-Te / w-ce. We’re talking about a V-Te of whatever your electron injection temperature is. w-ce is 1.76×10^7rad/s *B, where B is the strength of your magnetic field (perpendicular component for your application) at that point, and whatever unit conversions you have to do to come back out with mm.
“That point” for your application should be the “center” of the coil corner, and for the electron heading straight out of corner from the center of the device, the perpendicular component B would be the actual magnetic field strength. I suck at algebra so I’d use ephi or another Biot-Savart calculator to figure it out. Try searching talk-polywell for a Biot-Savart calculator.
Ok the minimum physcial coil spacing for a dodec (based on truncated icosahedron) has to be at least [(SQRT(3)*SQRT(2) )/4]*R, (about 0.61R) where R= coil radius + coil container thickness. If your coil is 34.62 mm thick with 5.21mm of thickness around it, R= 25 mm.
At 25 mm from your 72 Gauss coil I get approx 4.74 Gauss. Assuming Te of 2.5 KeV, I come up with a V-Te of 1.88E5 mm/s and W-ce of 8.35E8 rad/s, which results in a gyro radius of .001mm…hmm…told you I sucked at Algebra. I’m pretty sure V-Te should be much higher.
tom,
Awesome. I’ll incorporate these calculations into the design.
[…] Did an iteration of the chassis incorporating the gyro-radii calculations tom provided. Also made the channel for the superconducting cable thicker to make it easier to work with, and […]