Lectures on Superconductivity: Applications
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Current Leads
More Information
Current leads are used to carry electric current to a device or component operating at cryogenic temperatures. These should have high electrical conductivity but low thermal conductivity to minimise heating from the room temperature end of the current lead: this combination of properties is difficult to find except in superconducting materials. To optimise a current lead, other factors including geometry and cooling must also be considered. This film introduces the optimisation of current lead design, taking CERN as an example.
Lecturers and Contributions
Lecturers in this Film
- Amalia Ballarino (CERN, Geneva, Switzerland)
- Anna Carrillo (ICMAB, University of Barcelona, Spain)
Articles, Books and Lecture Notes
- Notes on Current Lead Design from the US Particle Accelerator School, 2004
Questions and Answers
The following questions were kindly contributed by Amalia Ballarino, CERN
| T (K) | K (W m-1 K-1) | ρ (µΩ cm) |
|---|---|---|
| 300 | 400 | 1.7 |
| 250 | 406 | 1.1 |
| 200 | 410 | 1 |
| 150 | 416 | 0.72 |
| 100 | 454 | 0.36 |
| 80 | 527 | 0.22 |
| 70 | 610 | 0.158 |
| 50 | 1046 | 0.063 |
| 30 | 2290 | 0.0196 |
| 25 | 2627 | 0.016 |
| 20 | 2766 | 0.014 |
| 16 | 2598 | 0.0133 |
| 12 | 2148 | 0.013 |
| 10 | 1840 | 0.0129 |
| 4 | 457 | 0.0129 |
- The minimum heat load (Qmin) into the helium bath of a conduction-cooled current lead designed for transferring in DC mode a given current (I) and operating between room temperature (TH) and the liquid helium temperature (Tc=4.2K) can be derived from the solution of the mono-dimensional heat balance equation applied to a conductor with given thermal conductivity (k(T)) and electrical resistivity (ρ(T)). Qmin is calculated by imposing a zero slope of the temperature profile at the room temperature end (QH=0).
- Starting from the steady state mono-dimensional heat balance equation, show that:
[1]
- Apply the Wiedemann-Franz law to eq. [1] and show that Qmin does not depend on the material properties.
- Starting from the steady state mono-dimensional heat balance equation, show that:
- A conduction-cooled copper lead is optimized for transferring 1000 A from room temperature to the liquid helium temperature.
- Calculate the heat conducted into the helium bath when the lead is transferring the current for which it is optimized, and the corresponding mass flow (g/s) of helium vaporized.
- Calculate the heat conducted by the lead into the bath at zero current. For the properties of the copper, use the values provided in the table.
- Estimate the heat that the lead of question 2 would conduct into the helium bath at nominal current if it would be optimized for self-cooling operation. Which change in geometry do you expect with respect to the conduction-cooled case?
Estimate the heat that the lead of question 2 would conduct into the bath at nominal current if it would use HTS material in replacement of the normal conductor in the lower part of the lead. - A magnet operating in DC mode at 4.2 K is powered via a pair of conduction-cooled binary leads operating in the vacuum insulation of the cryostat. These leads, optimized for operating at 100 A, consist of a copper resistive part between room temperature and 60 K, and an HTS part between 60 K and 4.2 K. The 60 K temperature is provided by a cryo-cooler, which acts as heat-sink for the upper resistive part of the leads.
- Calculate the heat that the cryo-cooler has to adsorb at 60 K when the two leads are powered at 100 A.
- Calculate the heat conducted by the two leads at 4.2 K, assuming that the HTS part of each lead consists of a bulk Bi-2212 rod of 5 mm diameter and 150 mm length. The integral of thermal conductivity of the Bi-2212 between 60 K and 4.2 K is 100 W/m.