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High critical current density (Jc) Nb3Sn conductor is the best candidate for next generation high field (>10 T) accelerator magnets. Although very promising, state of the art high-Jc Nb3Sn strands suffer magneto-thermal instabilities that can severely limit the strand performance. Recently it has been shown that at 1.9 K the self field instability is the dominating mechanism that limits the performance of strands with a low (<10) residual resistivity ratio (RRR) of the stabilizing copper. In this paper the self-field instability is investigated in high-Jc Nb3Sn strands with high RRR. At CERN several state of the art rod re-stack process (RRP) and powder in tube (PIT) Nb3Sn strands have been tested at 4.2 K and 1.9 K to study the effects on strand stability of: RRR, strand diameter and, strand impregnation with stycast. The experimental results are reported and discussed. A new 2-D finite element model for simulating magneto-thermal instabilities and its preliminary results are also presented. The model, which describes the whole development of the flux jump in the strand cross section taking into account the heat and current diffusion in the stabilizing copper, is in good agreement with the experimental data.