Transport measurements of critical current density, J ct , in monocore powder-in-tube MgB 2 strands have been carried out at temperatures, T, of from 4.2 K to 40 K, and in transverse fields, B, of up to 14 T. Processing methods used were conventional continuous-tube-forming-filling (CTFF) and internal-magnesium-diffusion (IMD).Strands with several powder compositions were measured, including binary (undoped) MgB 2 , 2% carbon doped MgB 2 , and 3% carbon doped MgB 2 . Magnetization loops (M-B) were also measured, and magnetic critical current density, J cm , values extracted from them. The transport, J ct (B) and magnetic, J cm (B), critical current densities were compared.Also studied was the influence of doping on the resistively measured irreversibility field, B irr and upper critical field B c2 . Critical current densities, J ct , and n-values were extracted from transport measurements and were found to be universally related (for all B and T) according to n∝ J ct m in which m = 0.52 ± 0.11. Likewise n was found to be related to B according to n ∝ B -p with a T-dependent p in the range of about 0.08~0.21. Further analysis of the field (B) and temperature (T) dependencies of n-value resulted in an expression that enabled n(B,T), for all B and T, to be estimated for a given strand based on the results of transport J ct (B) measurements made at one arbitrarily chosen temperature.
Symbols
B Magnetic field strength B irrResistively determined irreversibility field B irr,trans Apparent irreversibility field for magnetically induced current paths which must always include a portion transverse to the strand axis B c2Upper critical field B 0 (t)Temperature-dependent field-normalization quotient in the exponential form of J c (B,t) -see below B 00 Zero-temperature value of B 0 (t) CTFF Continuous tube forming/filling (process for strand fabrication) d 0 Inner diameter of the Nb chemical barrier (both CTFF and IMD strands) d i Inner diameter of the annular MgB 2 reaction layer (IMD strands) ∆M Full height of the magnetization loop normalized to the actual SC volume F p Bulk pinning force density F p,max Maximum value of F p vs B or B/B irr IMD Internal magnesium diffusion (process for strand fabrication) J c Abbreviation for the words "critical current density" J ct Transport-measured critical current density J cm Magnetically measured critical current density J cte Transport critical current density found by normalized I ct to the whole area inside the Nb chemical barrier J c2Critical current density transverse to the strand axis (magnetically induced) J c (B,t) Field-and temperature dependent J c J ct (B,t) Transport-measured value of field-and temperature dependent J c J c0 (t)Fitted zero-field temperature-dependent J c J ct0 (t)Fitted zero-field temperature-dependent J c based on transport measured field and temperature dependent J c equation J c00Fitted value of J c at zero field and zero temperature