The critical state instability in Nb 3 Al: Experiment and simulation Victor Chabanenko a, * , Adam Nabiałek b , Alexander Dyachenko a , Sergiy Vasiliev a , Ganna Svinchuk a , Andrzej Szewczyk b , Maria Gutowska b , Henryk Szymczak b , Stanisław Piechota b a O. Galkin Institute of Physics and Engineering, National Academy of Sciences, R. Luxemburg 72, 83114 Donetsk, Ukraine b Institute of Physics, Polish Academy of Sciences, Al. Lotniko ´ w 32/46, O2-668 Warsaw, Poland Available online 27 March 2007 Abstract We report our study of the critical state instability and thermomagnetic avalanches in Nb 3 Al superconducting alloy. Flux jumping was investigated in this material both theoretically and experimentally. Remagnetization loops of the Nb 3 Al plate were calculated using the experimental dependencies of the heat capacity and of the critical current density as functions of temperature and magnetic field. Magnetic field–temperature diagrams, showing the ranges where the flux jumps occur, were built. Ó 2007 Published by Elsevier B.V. PACS: 74.60.Ec; 74.60.Ge; 74.70.Ad Keywords: Thermomagnetic instability; H–T diagram; Magnetization and magnetostriction 1. Introduction Recently new fabrication technique for Nb 3 Al wires, strands and tapes, with superior characteristic, was devel- oped [1]. In this letter, we report our study of the critical state instability and of the thermomagnetic avalanches (called flux jumps) in superconducting Nb 3 Al alloy. Flux jumping was investigated in this material both theoretically and experimentally. 2. Experiment and simulations We have measured the magnetization (Fig. 1a) and the magnetostriction (Fig. 1c) of the Nb 3 Al superconductor in magnetic fields up to 12 T using the vibrating sample magnetometer and the strain gauge technique. In trans- verse magnetostriction experiment (Fig. 1c) we studied large (11 · 7 · 2 mm 3 ) polycrystalline slab. The changes of the sample dimensions in the external magnetic field H were measured along the longest edge of the sample. Magnetization M(H)(Fig. 1b) and magnetostriction DL(H)/L 0 (Fig. 1d) hysteresis loops for the Nb 3 Al plate were calculated using the criterion of the thermomagnetic instability, according to formulas and algorithm given in Refs. [2,3]. In our calculations we took into account the experimental dependencies of the heat capacity C(T,B) and of the critical current density J c (T,H) as functions of temperature (T) and magnetic field (H). Experimental data were fitted by the following analytical formulas: J c ðT Þ¼ J 0 ðBÞð1  T =T x ðBÞÞ; J c ðT ; H Þ¼ J 0 ðT ÞH 0 ðT Þ=ðH 0 ðT ÞþjH jÞ; CðT ; BÞ¼ cðBÞT þ aðBÞexp DðBÞ=T þ aT 3 ; where J c0 , H 0 , T x , c, a and a are fitting parameters. The magnitude of each flux jump was determined by the rela- tion J c (T * )/J c (T 0 ), where T * and T 0 are temperatures of the sample before and after the jump, respectively. 3. H–T diagram of instability The magnetization and magnetostriction hysteresis loops were constructed for different temperatures in a wide 0921-4534/$ - see front matter Ó 2007 Published by Elsevier B.V. doi:10.1016/j.physc.2007.03.117 * Corresponding author. Fax: +380 622 52 1074. E-mail address: chaban@host.dipt.donetsk.ua (V. Chabanenko). www.elsevier.com/locate/physc Physica C 460–462 (2007) 768–769