# Transition and Recovery of a Cryogenically Stable Superconductor

• O. Christianson
• R. W. Boom
Chapter
Part of the Advances in Cryogenic Engineering book series (ACRE, volume 29)

## Abstract

The transition and recovery of cryogeninially stable superconductors has been theoretically studied.1,2 The two coupled equations which describe the redistribution of current and the temperature distribution are the current diffusion equation (in one dimension)
$${\partial ^{2}}\left( {\rho \left( {T\left( x \right)} \right)j\left( x \right)} \right)/\partial {x^{2}} = - \mu {\kern 1pt} \partial {\kern 1pt} j{\kern 1pt} \left( x \right)/\partial {\kern 1pt} t$$
(1)
and the heat conduction equation
$$\partial \left( {k\left( {T\left( x \right)} \right)\partial {\kern 1pt} T\left( x \right)} \right)/\partial x{\kern 1pt} {\kern 1pt} + \rho \left( {T\left( x \right)} \right){j^{2}}\left( x \right) = C\left( {T\left( x \right)} \right){\kern 1pt} \partial {\kern 1pt} T/\partial {\kern 1pt} t$$
(2)
where T is temperature, ρ is resistivity, j is current density, and C is specific heat. Following the model of Ref. 1, and simultaneously solving the coupled equations using a finite difference routine including temperature dependent physical parameters yields an estimate of the current and temperature distributions, and the generated power, see Fig. 1. After the superconductor is turned normal, the current quickly exits the superconductor and flows in a small area of the copper adjacent to the superconductor, generating power, and perhaps causing a large temperature excursion. Thermal recovery tends to occur at large times after current diffusion reduces the power generated to less than the perimeter cooling.

### Keywords

Migration Boulder Line Source

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### References

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