Time dependence of magnetic flux penetration in Nb and Nb<inf>3</inf>Sn

Abstract

We have investigated a single crystal sample of Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn at low frequencies, 100 Hz to 13 kHz, and found a value of B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c1</inf> = (45.6 ± 2.7)mT for the lower critical field extrapolated to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T \simeq 0</tex> K at 497 HZ. The critical field, as we have defined here, was observed to increase by 32 ± 5% in going from 0.5 to 13 kHz. Hysteretic energy loss was used to determine the critical fields and was observed to decrease rapidly with frequency, dropping a factor of ten between 0.5 and 13 kHz. Samples of Nb wire were pulsed with field rise times of 2 μsec and found to have a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T \simeq 0</tex> K value of B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c1</inf> = 158 ± 8 mT, unchanged from lower frequency values. The Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn sample had undetectable signal levels under similar pulse conditions (up to 150 mT maximum field). Temperature dependence of the critical fields is consistent with 1 - (T/T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> behavior from 2 K to T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> (18.0±0.1 K for the Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn sample).