Abstract
The present paper studies the problem of stable normal zones in a superconducting coil. It is shown that there are five solutions, namely; T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> (X), T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> (X), T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> (X), T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> (X), and T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</inf> (X), of the heat equatuon that describes a locally uncooled superconducting wire within certain ranges of currents and magnetic fields. Of the five solutions T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> (X), T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> (X), and T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</inf> (X) are stable, and T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> (X) and T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> (X) are unstable. Stable stationary solution T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> (X) describes the short normal zones mainly located in the nucleate boiling range of the coolant. T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> (X) is the superconducting state, and T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</inf> (X) having a longer region above the critical temperature than T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> (X) generally is the quench state. Unstable stationary solution T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> (X) describes the minimum propagating zones. Normal zones will develop if the temperature profile in the conductor is above T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> (X); it will contract if the temperature profile is below T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> (X). Stable normal zones in superconducting cooled by HeII are also discussed. It is easier to get conditions under which stable normal zones exist in HeII than in HeI. Using the theoretical model, a detailed numerical analysis is made that determines a range within which stable normal zones occur. Some experimental results are presented and compared with theoretical calculations.
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