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The magnetothermal instability (MTI) is an issue in the high-Jc Nb3Sn superconducting strands for accelerator magnets. The first kind of MTI is magnetization instability, which may be significantly reduced by using small filaments and with a high copper residual resistivity ratio (RRR) ≥ 100. However, theoretical and experimental evidence suggests that there is a second kind of MTI, which is self-field instability, which seems to be highly sensitive to external perturbations and less sensitive to RRRs. Recently at the European Organization for Nuclear Research (CERN), for studying this effect, a new measurement setup based on a Q-switched laser has been developed. By using the setup, it is possible to provide a local and controlled perturbation in nanosecond timescale from 0.5 to 26 μJ , which is absorbed by the strand at cryogenic temperature. In this paper, we report the results obtained by testing high-Jc Nb3Sn strands with different RRRs. It is shown that the self-field instability is sensitive to the trigger energy in moderately high magnetic fields. Therefore, the stability is highly dependent on the perturbation spectrum, i.e., the conventional stability measurements might not be fully representative of the strand stability in magnets wound with high-Jc Nb3Sn strands.