Calculation of the properties of a superconducting coil
The coil
This test of BiotSavart uses data for a Nb3Al superconducting wire coil built and measured at Hitachi Cable, Ltd. This coil is capable of producing a field of 21.68 Telsa! The publication is:
Genzo Iwaki, Kunihiro Fukuda, Hidezumi Moriai, Takao Takeuchi, Yasuo Iijima, Tsukasa Kiyoshi, Kikuo Itoh, Kiyoshi Inoue, and Hitoshi Wada, "High-Field Coil Using Nb3Al Superconducting Wire Manufactured by Rapid-Quenching and Transforming Process" (link).
The specifications of the coil from the article are
| Coil inner diameter | 20 mm |
| Coil out diameter | 46 mm |
| Coil length | 50 mm |
| Number of turns | 1331 |
| Inductance | 22.2 mH (calculated) 22.6 mH (measured) |
| Coil constant | 27.9 mT/A (calculated) 27.7 mT/A (measured) |
Simulation with BiotSavart
 | BiotSavart file: iwaki.biot |
We start with a new configuration, saving it under the file name "Iwaki". Then we make the coil. Select menu command Config > Make conductor > Solenoid. We give the new solenoid the name "coil":
Then, on the Specs tab we enter inner and outer radius:
and on the Wnd tab, we enter the number of windings. Set the specify option to "Winding" and enter the number of windings 1331 as shown. We do not care about the wire diameter at the moment.
On the Calc tab, we enter the desired simulation resolution:
Now the coil is approximated by the following bundle of coil elements like this:
To see the bundle of elements, we unchecked the Surface checkbox on the Looks tab, and checked the Elements checkbox. We also changed the # of phi steps to 32 to get a smoother picture.
To calculate the self-inductance of the coil we turn to the Calc tab and press the Self-inductance button:
Compared to the article, the calculated inductance of 21.76 mH is 2% lower. Changing the simulation resolution from 2mm to 1mm makes very little difference. The discrepancy lies in the approximations that BiotSavart uses for the magnetic vector potential inside the coil elements.
Evaluation of coil constant
The coil constant is the ratio of the central magnetic flux density B to the current I. BiotSavart can tell you the field at a point if you make a Linear probe and sample one of the plotted points.
Make a linear probe by selecting menu command Config > Make probe > Linear. Evaluate the probe using the Field > Recompute menu item. By default the linear probe starts at the origin and extends 1 m in the +z direction, so we change that to a 10 mm range We are interested here in the field at z=0, so click on the leftmost point on the curve on the graph. The value of the field is displayed below the graph:
The field at the center of the coil is 27.9 mT. The default current is 1 A, so the coil constant is 27.9 mT, as in the article.
To summarize, here is the table comparing the article's calculated and measured values and the BiotSavart results:
| Calculated | Measured | BiotSavart | |
|---|---|---|---|
| Inductance | 22.2 mH | 22.6 mH | 21.76 mH |
| Coil constant | 27.9 mT/A | 27.7 mT/A | 27.9 mT/A |
