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The paper is devoted to the investigation of critical state stability against flux jumps in hard superconductors accounting the critical current density dependence on the temperature and magnetic field. A flat sample with finite thickness is considered. The stability criteria were found for the Kim-Anderson critical state model as well as for the region close to the upper critical field Ha,. It was shown that the stability diminishes near Ha,. The stability conditions were found for the total range of external fields below Ho,. It was found that under certain conditions the magnetic instabilities may develop in two isolated regions of the external fields.

Abstract. The stability of electric currents in multifilamentary superconducting composites against flux jumps is discussed in detail. The normal procedure for such a quantitative stability investigation is carried out. In some particular cases the stability criteria are found and analysed.

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