Empirical scaling formulas for critical current and critical field for commercial NbTi

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Abstract
Short sample 4.2 K experimental facilities are plentiful, but equipment for measurements of current as functions of temperature and field is scarce. An analysis has been made of published data comprising at least six manufacturers and spanning a range of critical current density at 4.2 K, 8 T of 50 to 108 kA/cm2, and linear equations have been found to fit the data over a wide range of field B and temperature T. For a constant temperature of 4.2 K, the following expression holds for B in the range of 3 to 10 T: jc(B, T = 4.2 K) = jo[1 - 0.096B], where [Bc2(4.2 K)]-1= 0.096 with a standard deviation of 3% for ten samples. The constant jocan be determined for any sample from a single point measurement at a convenient field. For a constant field of 8 T, the following expression holds for T in the range of 2 to 5.5 K: jc(B = 8 T, T) = j'o[1 - 0.177T], where [Tc(8 T)]-1= 0.177 with a standard deviation of less than 1%. Linear equations have also been obtained for higher fields and lower temperatures. The critical field vs temperature is Bc2(T) = Bc2(0) [1 - (T/Tc(0))n], where Bc2(0) = 14.5 T, Tc(0) = 9.2 K, and n = 1.7 (not 2, which is used in theoretical derivations). For more accurate critical temperature calculations above 10 T, this equation can be used with the modification Bc2(0) = 14.8 T. No one simple power law for the upper critical field holds over the whole temperature range.